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b(of)f(the)h(refraction.)39 b(The)27 b(complemen)m(tary)f (routines)g(sla)p Fq(_)p FA(A)m(OP)427 577 y(\(or)39 b(sla)p Fq(_)p FA(A)m(OPQK\))f(and)g(sla)p Fq(_)p FA(O)m(AP)g(\(or)h (sla)p Fq(_)p FA(O)m(APQK\))f(are)h(self-consisten)m(t)g(to)g(b)s (etter)g(than)427 690 y(1)31 b(microarcsecond)f(all)g(o)m(v)m(er)h(the) g(celestial)f(sphere.)311 836 y(3.)46 b(It)c(is)e(advisable)h(to)h(tak) m(e)h(great)g(care)f(with)e(units,)j(as)f(ev)m(en)g(unlik)m(ely)d(v)-5 b(alues)41 b(of)h(the)f(input)427 948 y(parameters)31 b(are)g(accepted)g(and)f(pro)s(cessed)g(in)f(accordance)j(with)d(the)i (mo)s(dels)e(used.)311 1094 y(4.)46 b Fn(App)-5 b(ar)g(ent)35 b FA([)15 b Fi(\013;)g(\016)20 b FA(])25 b(means)e(the)i(geo)s(cen)m (tric)g(apparen)m(t)f(righ)m(t)g(ascension)f(and)h(declination,)g(whic) m(h)427 1207 y(is)44 b(obtained)g(from)g(a)h(catalogue)h(mean)f(place)f (b)m(y)h(allo)m(wing)e(for)h(space)h(motion,)j(parallax,)427 1320 y(precession,)34 b(n)m(utation,)g(ann)m(ual)f(ab)s(erration,)g 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Fi(\013;)g(\016)21 b FA(])33 b(b)m(y)g(al-)427 2143 y(lo)m(wing)25 b(for)g(Earth)h(orien)m (tation)g(and)f(diurnal)d(ab)s(erration,)k(rotating)g(from)g(equator)g (to)g(horizon)427 2256 y(co)s(ordinates,)f(and)d(then)h(adjusting)f (for)h(refraction.)38 b(The)23 b([)15 b Fi(h;)g(\016)20 b FA(])j(is)g(obtained)f(b)m(y)h(rotating)h(bac)m(k)427 2369 y(in)m(to)38 b(equatorial)f(co)s(ordinates,)i(using)d(the)h(geo)s (detic)h(latitude)f(corrected)h(for)f(p)s(olar)f(motion,)427 2481 y(and)27 b(is)f(the)i(p)s(osition)d(that)j(w)m(ould)e(b)s(e)g (seen)i(b)m(y)f(a)g(p)s(erfect)g(equatorial)g(lo)s(cated)h(at)g(the)f (observ)m(er)427 2594 y(and)c(with)f(its)h(p)s(olar)f(axis)h(aligned)f (to)i(the)g(Earth's)f(axis)g(of)h(rotation)f(\()p Fn(n.b.)h FA(not)f(to)h(the)g(refracted)427 2707 y(p)s(ole\).)40 b(Finally)-8 b(,)29 b(the)i Fi(\013)g FA(is)e(obtained)h(b)m(y)g (subtracting)g(the)g Fn(h)38 b FA(from)30 b(the)h(lo)s(cal)e(apparen)m (t)i(ST.)311 2853 y(6.)46 b(T)-8 b(o)37 b(predict)e(the)h(required)e (setting)i(of)g(a)g(real)g(telescop)s(e,)i(the)e(observ)m(ed)g(place)g (pro)s(duced)f(b)m(y)427 2966 y(this)28 b(routine)f(w)m(ould)g(ha)m(v)m (e)j(to)f(b)s(e)e(adjusted)h(for)g(the)h(tilt)e(of)i(the)f(azim)m(uth)g (or)h(p)s(olar)e(axis)h(of)g(the)427 3079 y(moun)m(ting)e(\(with)f (appropriate)g(corrections)i(for)f(moun)m(t)g(\015exures\),)h(for)f (non-p)s(erp)s(endicularit)m(y)427 3191 y(b)s(et)m(w)m(een)j(the)g (moun)m(ting)e(axes,)j(for)e(the)g(p)s(osition)e(of)j(the)f(rotator)i (axis)d(and)h(the)h(p)s(oin)m(ting)d(axis)427 3304 y(relativ)m(e)38 b(to)g(it,)g(for)f(tub)s(e)g(\015exure,)h(for)f(gear)i(and)d(enco)s (der)h(errors,)i(and)e(\014nally)e(for)i(enco)s(der)427 3417 y(zero)c(p)s(oin)m(ts.)45 b(Some)32 b(telescop)s(es)g(w)m(ould,)g (of)g(course,)h(exhibit)d(other)i(prop)s(erties)f(whic)m(h)g(w)m(ould) 427 3530 y(need)f(to)i(b)s(e)d(accoun)m(ted)j(for)e(at)h(the)g (appropriate)e(p)s(oin)m(t)h(in)f(the)h(sequence.)311 3676 y(7.)46 b(This)36 b(routine)g(tak)m(es)i(time)f(to)h(execute,)i (due)d(mainly)e(to)j(the)f(rigorous)f(in)m(tegration)h(used)g(to)427 3789 y(ev)-5 b(aluate)33 b(the)f(refraction.)44 b(F)-8 b(or)33 b(pro)s(cessing)d(m)m(ultiple)f(stars)j(for)g(one)g(lo)s (cation)f(and)g(time,)h(call)427 3902 y(sla)p Fq(_)p FA(A)m(OPP)-8 b(A)41 b(once)h(follo)m(w)m(ed)f(b)m(y)g(one)g(call)g(p)s (er)f(star)h(to)h(sla)p Fq(_)p FA(A)m(OPQK.)e(Where)h(a)h(range)f(of) 427 4014 y(times)31 b(within)d(a)j(limited)e(p)s(erio)s(d)f(of)j(a)h (few)e(hours)g(is)g(in)m(v)m(olv)m(ed,)h(and)f(the)h(highest)f (precision)f(is)427 4127 y(not)g(required,)e(call)g(sla)p Fq(_)p FA(A)m(OPP)-8 b(A)28 b(once,)i(follo)m(w)m(ed)e(b)m(y)g(a)g (call)g(to)h(sla)p Fq(_)p FA(A)m(OPP)-8 b(A)g(T)28 b(eac)m(h)h(time)f (the)427 4240 y(time)i(c)m(hanges,)i(follo)m(w)m(ed)e(b)m(y)g(one)h (call)f(p)s(er)f(star)h(to)i(sla)p Fq(_)p FA(A)m(OPQK.)311 4386 y(8.)46 b(The)26 b(D)m(A)-8 b(TE)27 b(argumen)m(t)g(is)e(UTC)h (expressed)g(as)g(an)g(MJD.)h(This)e(is,)h(strictly)f(sp)s(eaking,)i (wrong,)427 4499 y(b)s(ecause)33 b(of)g(leap)g(seconds.)48 b(Ho)m(w)m(ev)m(er,)35 b(as)e(long)g(as)g(the)g(\001UT)f(and)h(the)g (UTC)f(are)h(consisten)m(t)427 4612 y(there)j(are)h(no)f (di\016culties,)f(except)i(during)d(a)i(leap)g(second.)57 b(In)36 b(this)f(case,)j(the)f(start)f(of)g(the)427 4725 y(61st)i(second)f(of)g(the)g(\014nal)f(min)m(ute)g(should)f(b)s(egin)g (a)j(new)e(MJD)h(da)m(y)h(and)e(the)h(old)f(pre-leap)427 4837 y(\001UT)i(should)e(con)m(tin)m(ue)i(to)h(b)s(e)e(used.)63 b(As)38 b(the)g(61st)h(second)f(completes,)j(the)d(MJD)g(should)427 4950 y(rev)m(ert)31 b(to)h(the)e(start)h(of)g(the)f(da)m(y)h(as,)g(sim) m(ultaneously)-8 b(,)29 b(the)h(\001UT)g(c)m(hanges)h(b)m(y)g(one)f (second)h(to)427 5063 y(its)f(p)s(ost-leap)g(new)g(v)-5 b(alue.)311 5209 y(9.)46 b(The)27 b(\001UT)h(\(UT1)p Fl(\000)p FA(UTC\))g(is)e(tabulated)i(in)e(IERS)h(circulars)f(and)h (elsewhere.)39 b(It)28 b(increases)g(b)m(y)427 5322 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b(p)s(olar)f(co)s(ordinates)h(XP)-8 b(,YP)38 b(can)f(b)s(e)g(obtained)f(from)h(IERS)f(circulars)f(and)i (equiv)-5 b(alen)m(t)427 828 y(publications.)36 b(The)24 b(maxim)m(um)f(amplitude)g(is)g(ab)s(out)h(0)2373 791 y Fh(0)m(0)2377 828 y Fi(:)p FA(3.)40 b(If)24 b(XP)-8 b(,YP)25 b(v)-5 b(alues)24 b(are)h(una)m(v)-5 b(ailable,)427 941 y(use)31 b(XP=YP=0D0.)43 b(See)32 b(page)g(B60)g(of)f(the)g(1988)i Fn(Astr)-5 b(onomic)g(al)36 b(A)n(lmanac)h FA(for)30 b(a)i(de\014nition)427 1054 y(of)f(the)f(t)m(w)m(o)i(angles.)266 1191 y(12.)46 b(The)35 b(heigh)m(t)g(ab)s(o)m(v)m(e)h(sea)f(lev)m(el)g (of)g(the)g(observing)f(station,)i(HM,)g(can)f(b)s(e)g(obtained)f(from) g(the)427 1304 y Fn(Astr)-5 b(onomic)g(al)39 b(A)n(lmanac)h FA(\(Section)35 b(J)f(in)f(the)i(1988)h(edition\),)f(or)f(via)g(the)h (routine)e(sla)p Fq(_)p FA(OBS.)427 1417 y(If)h(P)-8 b(,)34 b(the)g(pressure)e(in)h(mB,)h(is)f(a)m(v)-5 b(ailable,)34 b(an)f(adequate)i(estimate)g(of)f(HM)g(can)g(b)s(e)f(obtained)427 1530 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b(should)d(b)s(e)h(b)s(etter)i(than)427 4285 y(1)21 b(arcmin)m(ute;)j(useful)19 b(results)g(are)i(a)m(v)-5 b(ailable)20 b(for)g(a)h(further)f(3)2512 4252 y Fm(\016)2551 4285 y FA(,)j(b)s(ey)m(ond)d(whic)m(h)f(the)i(sla)p Fq(_)p FA(REFR)m(O)427 4398 y(routine)26 b(returns)f(a)i(\014xed)f(v)-5 b(alue)27 b(of)f(the)h(refraction.)39 b(The)27 b(complemen)m(tary)f (routines)g(sla)p Fq(_)p FA(A)m(OP)427 4511 y(\(or)39 b(sla)p Fq(_)p FA(A)m(OPQK\))f(and)g(sla)p Fq(_)p FA(O)m(AP)g(\(or)h (sla)p Fq(_)p FA(O)m(APQK\))f(are)h(self-consisten)m(t)g(to)g(b)s (etter)g(than)427 4624 y(1)31 b(microarcsecond)f(all)g(o)m(v)m(er)h (the)g(celestial)f(sphere.)311 4763 y(3.)46 b(It)c(is)e(advisable)h(to) h(tak)m(e)h(great)g(care)f(with)e(units,)j(as)f(ev)m(en)g(unlik)m(ely)d (v)-5 b(alues)41 b(of)h(the)f(input)427 4876 y(parameters)31 b(are)g(accepted)g(and)f(pro)s(cessed)g(in)f(accordance)j(with)d(the)i (mo)s(dels)e(used.)311 5016 y(4.)46 b Fn(App)-5 b(ar)g(ent)35 b FA([)15 b Fi(\013;)g(\016)20 b FA(])25 b(means)e(the)i(geo)s(cen)m (tric)g(apparen)m(t)f(righ)m(t)g(ascension)f(and)h(declination,)g(whic) m(h)427 5128 y(is)44 b(obtained)g(from)g(a)h(catalogue)h(mean)f(place)f (b)m(y)h(allo)m(wing)e(for)h(space)h(motion,)j(parallax,)427 5241 y(precession,)34 b(n)m(utation,)g(ann)m(ual)f(ab)s(erration,)g (and)g(the)h(Sun's)e(gra)m(vitational)i(lens)e(e\013ect.)52 b(F)-8 b(or)427 5354 y(star)32 b(p)s(ositions)d(in)h(the)i(FK5)g (system)g(\()p Fn(i.e.)f FA(J2000\),)j(these)e(e\013ects)g(can)g(b)s(e) f(applied)e(b)m(y)j(means)427 5467 y(of)38 b(the)g(sla)p Fq(_)p FA(MAP)f Fn(etc.)g FA(routines.)61 b(Starting)37 b(from)g(other)h(mean)f(place)h(systems,)i(additional)427 5580 y(transformations)22 b(will)e(b)s(e)i(needed;)j(for)d(example,)i (FK4)f(\()p Fn(i.e.)g FA(B1950\))i(mean)d(places)h(w)m(ould)e(\014rst) 427 5693 y(ha)m(v)m(e)32 b(to)f(b)s(e)f(con)m(v)m(erted)i(to)f(FK5,)g (whic)m(h)e(can)i(b)s(e)e(done)h(with)g(the)g(sla)p Fq(_)p FA(FK425)h Fn(etc.)f FA(routines.)p eop %%Page: 18 20 18 19 bop 0 52 a FA(18)311 351 y(5.)46 b Fn(Observe)-5 b(d)49 b FA([)15 b Fi(Az)t(;)g(E)5 b(l)42 b FA(])d(means)g(the)g(p)s (osition)d(that)k(w)m(ould)d(b)s(e)i(seen)f(b)m(y)h(a)g(p)s(erfect)g (theo)s(dolite)427 464 y(lo)s(cated)33 b(at)h(the)f(observ)m(er.)49 b(This)31 b(is)h(obtained)g(from)g(the)h(geo)s(cen)m(tric)h(apparen)m (t)f([)15 b Fi(\013;)g(\016)21 b FA(])33 b(b)m(y)g(al-)427 577 y(lo)m(wing)25 b(for)g(Earth)h(orien)m(tation)g(and)f(diurnal)d(ab) s(erration,)k(rotating)g(from)g(equator)g(to)g(horizon)427 690 y(co)s(ordinates,)f(and)d(then)h(adjusting)f(for)h(refraction.)38 b(The)23 b([)15 b Fi(h;)g(\016)20 b FA(])j(is)g(obtained)f(b)m(y)h (rotating)h(bac)m(k)427 803 y(in)m(to)38 b(equatorial)f(co)s (ordinates,)i(using)d(the)h(geo)s(detic)h(latitude)f(corrected)h(for)f (p)s(olar)f(motion,)427 916 y(and)27 b(is)f(the)i(p)s(osition)d(that)j (w)m(ould)e(b)s(e)g(seen)i(b)m(y)f(a)g(p)s(erfect)g(equatorial)g(lo)s (cated)h(at)g(the)f(observ)m(er)427 1029 y(and)c(with)f(its)h(p)s(olar) f(axis)h(aligned)f(to)i(the)g(Earth's)f(axis)g(of)h(rotation)f(\()p Fn(n.b.)h FA(not)f(to)h(the)g(refracted)427 1142 y(p)s(ole\).)40 b(Finally)-8 b(,)29 b(the)i Fi(\013)g FA(is)e(obtained)h(b)m(y)g (subtracting)g(the)g Fn(h)38 b FA(from)30 b(the)h(lo)s(cal)e(apparen)m (t)i(ST.)311 1314 y(6.)46 b(T)-8 b(o)37 b(predict)e(the)h(required)e (setting)i(of)g(a)g(real)g(telescop)s(e,)i(the)e(observ)m(ed)g(place)g (pro)s(duced)f(b)m(y)427 1426 y(this)28 b(routine)f(w)m(ould)g(ha)m(v)m (e)j(to)f(b)s(e)e(adjusted)h(for)g(the)h(tilt)e(of)i(the)f(azim)m(uth)g (or)h(p)s(olar)e(axis)h(of)g(the)427 1539 y(moun)m(ting)e(\(with)f (appropriate)g(corrections)i(for)f(moun)m(t)g(\015exures\),)h(for)f (non-p)s(erp)s(endicularit)m(y)427 1652 y(b)s(et)m(w)m(een)j(the)g (moun)m(ting)e(axes,)j(for)e(the)g(p)s(osition)e(of)j(the)f(rotator)i (axis)d(and)h(the)h(p)s(oin)m(ting)d(axis)427 1765 y(relativ)m(e)38 b(to)g(it,)g(for)f(tub)s(e)g(\015exure,)h(for)f(gear)i(and)d(enco)s (der)h(errors,)i(and)e(\014nally)e(for)i(enco)s(der)427 1878 y(zero)c(p)s(oin)m(ts.)45 b(Some)32 b(telescop)s(es)g(w)m(ould,)g (of)g(course,)h(exhibit)d(other)i(prop)s(erties)f(whic)m(h)g(w)m(ould) 427 1991 y(need)f(to)i(b)s(e)d(accoun)m(ted)j(for)e(at)h(the)g (appropriate)e(p)s(oin)m(t)h(in)f(the)h(sequence.)311 2163 y(7.)46 b(The)40 b(star-indep)s(enden)m(t)f(apparen)m(t-to-observ) m(ed-place)k(parameters)e(in)e(A)m(OPRMS)i(ma)m(y)g(b)s(e)427 2276 y(computed)31 b(b)m(y)f(means)g(of)h(the)g(sla)p Fq(_)p FA(A)m(OPP)-8 b(A)30 b(routine.)40 b(If)30 b(nothing)g(has)g(c)m (hanged)h(signi\014can)m(tly)427 2389 y(except)45 b(the)g(time,)i(the)d (sla)p Fq(_)p FA(A)m(OPP)-8 b(A)g(T)45 b(routine)e(ma)m(y)h(b)s(e)g (used)f(to)i(p)s(erform)e(the)h(requisite)427 2502 y(partial)29 b(recomputation)i(of)f(A)m(OPRMS.)311 2673 y(8.)46 b(The)24 b(\\sidereal)g(\001UT")g(whic)m(h)g(forms)f(part)i(of)f(A)m (OPRMS\(13\))i(is)e(UT1)p Fl(\000)p FA(UTC)g(con)m(v)m(erted)i(from)427 2786 y(solar)k(to)h(sidereal)e(seconds)i(and)e(expressed)h(in)f (radians.)311 2958 y(9.)46 b(A)m(t)32 b(zenith)e(distances)h(b)s(ey)m (ond)f(ab)s(out)h(76)1890 2925 y Fm(\016)1930 2958 y FA(,)g(the)g(need)g(for)f(sp)s(ecial)g(care)i(with)d(the)i(corrections) 427 3071 y(for)j(refraction)f(causes)h(a)g(mark)m(ed)g(increase)f(in)f (execution)i(time.)50 b(Moreo)m(v)m(er,)37 b(the)c(e\013ect)i(gets)427 3184 y(w)m(orse)k(with)d(increasing)h(zenith)g(distance.)64 b(Adroit)37 b(programming)g(in)g(the)h(calling)e(applica-)427 3297 y(tion)d(ma)m(y)h(allo)m(w)e(the)i(problem)d(to)j(b)s(e)e (reduced.)49 b(Prepare)33 b(an)g(alternativ)m(e)g(A)m(OPRMS)g(arra)m(y) -8 b(,)427 3410 y(computed)32 b(for)f(zero)h(air-pressure;)f(this)f (will)f(disable)h(the)i(refraction)f(corrections)h(and)f(cause)427 3523 y(rapid)25 b(execution.)40 b(Using)25 b(this)h(A)m(OPRMS)g(arra)m (y)-8 b(,)29 b(a)e(preliminary)c(call)j(to)h(the)g(presen)m(t)f (routine)427 3636 y(will,)e(dep)s(ending)f(on)j(the)g(application,)f 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Ft(SUN/67.45)3252 b FA(25)0 351 y Fy(GIVEN)45 b FA(:)277 523 y Fn(IY,IM,ID)356 b Fy(I)605 b FA(y)m(ear,)32 b(mon)m(th,)e(da)m(y)h(in)e(Gregorian)h(calendar)0 858 y Fy(RETURNED)46 b FA(:)277 1004 y Fn(DJM)537 b Fy(D)565 b FA(mo)s(di\014ed)28 b(Julian)g(Date)k(\(JD)p Fl(\000)p FA(2400000.5\))j(for)30 b(0)3385 971 y Fr(h)277 1117 y Fn(J)688 b Fy(I)605 b FA(status:)1825 1230 y(0)31 b(=)f(OK)1825 1343 y(1)h(=)f(bad)f(y)m(ear)1825 1456 y(2)i(=)f(bad)f(mon)m(th)1825 1569 y(3)i(=)f(bad)f(da)m(y)0 1896 y Fy(NOTES)44 b FA(:)311 2080 y(1.)i(When)d(an)g(in)m(v)-5 b(alid)40 b(y)m(ear)k(or)f(mon)m(th)g (is)f(supplied)e(\(status)k(J)e(=)h(1)g(or)g(2\))h(the)f(MJD)g(is)g Fy(not)427 2193 y FA(computed.)e(When)30 b(an)g(in)m(v)-5 b(alid)28 b(da)m(y)j(is)e(supplied)e(\(status)k(J)f(=)g(3\))i(the)e (MJD)h Fy(is)g FA(computed.)311 2335 y(2.)46 b(The)30 b(y)m(ear)h(m)m(ust)g(b)s(e)e Fl(\000)p FA(4699)j(\()p Fn(i.e.)e FA(4700BC\))j(or)d(later.)41 b(F)-8 b(or)31 b(y)m(ear)g Fi(n)p FA(BC)f(use)g(IY)h(=)f 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y(\014rst)f(time,)h(the)g(caller)f(m)m(ust)h(set)g(the)g(\014rst)f (elemen)m(t)h(of)f(the)h(LIST)f(arra)m(y)h(to)g(zero)h(\(an)m(y)f(v)-5 b(alue)427 5394 y(less)30 b(than)g(1)h(will)d(do\))i(to)h(cause)g (initialization.)311 5544 y(3.)46 b(The)30 b(\014rst)g(com)m(bination)f (to)j(b)s(e)d(generated)j(is:)597 5693 y(LIST\(1\)=1,)f(LIST\(2\)=2,)g (.)15 b(.)g(.)h(,)30 b(LIST\(NSEL\)=NSEL)p eop %%Page: 27 29 27 28 bop 0 52 a Ft(SUN/67.45)3252 b FA(27)427 351 y(This)33 b(is)h(also)h(the)g(com)m(bination)f(returned)g(for)h(the)g (\\\014nished")e(\(J=1\))i(case.)55 b(The)35 b(\014nal)e(p)s(er-)427 464 y(m)m(utation)e(to)g(b)s(e)f(generated)h(is:)597 617 y(LIST\(1\)=NCAND,)g(LIST\(2\)=NCAND)p Fl(\000)p FA(1,)g(.)16 b(.)f(.)g(,)1537 730 y(LIST\(NSEL\)=NCAND)p Fl(\000)p FA(NSEL+1)311 883 y(4.)46 b(If)20 b(the)h(\\\014nished")e (\(J=1\))i(status)g(is)f(ignored,)i(the)f(routine)e(con)m(tin)m(ues)i (to)h(deliv)m(er)d(com)m(binations,)427 996 y(the)31 b(pattern)f(rep)s(eating)g(ev)m(ery)h(NCAND!/\(NSEL!\(NCAND)p Fl(\000)p FA(NSEL\)!\))i(calls.)311 1149 y(5.)46 b(The)30 b(algorithm)g(is)f(b)m(y)h(R.)16 b(F.)f(W)-8 b(arren-Smith)30 b(\(priv)-5 b(ate)30 b(comm)m(unication\).)p 0 1301 3780 8 v 0 1414 a Fu(SLA)p Fk(_)p Fu(CR2AF)331 b Fj(Radians)38 b(to)g(Deg,Arcmin,Arcsec)329 b Fu(SLA)p Fk(_)p Fu(CR2AF)0 1764 y Fy(A)m(CTION)44 b FA(:)c(Con)m(v)m(ert)32 b(an)e(angle)g(in)f (radians)g(to)i(degrees,)h(arcmin)m(utes,)e(arcseconds)h(\(single)e (precision\).)0 1952 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_CR2AF)g(\(NDP,)g(ANGLE,)g(SIGN,)g(IDMSF\))0 2323 y Fy(GIVEN)f FA(:)277 2469 y Fn(NDP)537 b Fy(I)605 b FA(n)m(um)m(b)s(er)29 b(of)i(decimal)e(places)h(of)h(arcseconds)277 2582 y Fn(ANGLE)411 b Fy(R)567 b FA(angle)31 b(in)e(radians)0 2970 y Fy(RETURNED)46 b FA(:)277 3116 y Fn(SIGN)512 b Fy(C)569 b FA(`+')31 b(or)f(`)p Fl(\000)p FA(')277 3229 y Fn(IDMSF)440 b Fy(I\(4\))471 b FA(degrees,)31 b(arcmin)m(utes,)f (arcseconds,)h(fraction)0 3618 y 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b(spherical)f(co)s(ordinates)h(are)h([)15 b Fi(\013;)g(\016)20 b FA(],)31 b([)p Fi(\025;)15 b(\036)p FA(])31 b Fn(etc.)p FA(,)f(in)f(radians.)311 1660 y(2.)46 b(The)33 b(result)f(is)h(the)h(b)s(earing)e(\(p)s(osition)f(angle\),)k (in)d(radians,)h(of)h(p)s(oin)m(t)e([A2,B2])k(as)d(seen)h(from)427 1773 y(p)s(oin)m(t)j([A1,B1].)65 b(It)38 b(is)f(in)g(the)h(range)g Fl(\006)p Fi(\031)s FA(.)63 b(The)37 b(sense)h(is)f(suc)m(h)h(that)g (if)f([A2,B2])j(is)d(a)h(small)427 1885 y(distance)f(due)f(east)i(of)g ([A1,B1])h(the)e(result)f(is)g(ab)s(out)h(+)p Fi(\031)s(=)p FA(2.)61 b(Zero)37 b(is)f(returned)g(if)g(the)h(t)m(w)m(o)427 1998 y(p)s(oin)m(ts)30 b(are)g(coinciden)m(t.)311 2134 y(3.)46 b(If)32 b(either)g(B-co)s(ordinate)h(is)f(outside)f(the)i (range)g Fl(\006)p Fi(\031)s(=)p FA(2,)g(the)g(result)e(ma)m(y)i (corresp)s(ond)f(to)h(\\the)427 2247 y(long)d(w)m(a)m(y)i(round".)311 2382 y(4.)46 b(The)38 b(routine)g(sla)p Fq(_)p FA(DP)-8 b(A)e(V)39 b(p)s(erforms)e(an)h(equiv)-5 b(alen)m(t)38 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y(A)40 b(t)m(ypical)e(v)-5 b(alue)39 b(is)f(`ZXZ',)h(indicating)e (that)j(RMA)-8 b(T)40 b(is)e(to)i(b)s(ecome)f(the)h(direction)e(cosine) 427 3227 y(matrix)29 b(corresp)s(onding)f(to)j(rotations)f(of)g(the)g (reference)g(frame)g(through)f(PHI)g(radians)g(ab)s(out)427 3340 y(the)21 b(old)e Fn(z)p FA(-axis,)k(follo)m(w)m(ed)d(b)m(y)g(THET) -8 b(A)20 b(radians)f(ab)s(out)h(the)h(resulting)d Fn(x)p FA(-axis,)k(then)e(PSI)g(radians)427 3453 y(ab)s(out)30 b(the)h(resulting)d Fn(z)p FA(-axis.)311 3589 y(3.)46 b(The)34 b(axis)f(names)h(can)g(b)s(e)g(an)m(y)g(of)g(the)h(follo)m (wing,)e(in)g(an)m(y)h(order)g(or)g(com)m(bination:)47 b(X,)34 b(Y,)h(Z,)427 3702 y(upp)s(ercase)30 b(or)g(lo)m(w)m(ercase,)i (1,)f(2,)g(3.)42 b(Normal)30 b(axis)g(lab)s(elling/n)m(um)m(b)s(ering) 25 b(con)m(v)m(en)m(tions)32 b(apply;)427 3815 y(the)c Fn(xyz)f FA(\()p Fl(\021)f FA(123\))j(triad)d(is)g(righ)m(t-handed.)39 b(Th)m(us,)27 b(the)g(`ZXZ')g(example)g(giv)m(en)g(ab)s(o)m(v)m(e)i (could)d(b)s(e)427 3928 y(written)h(`zxz')j(or)e(`313')i(\(or)e(ev)m (en)h(`ZxZ')f(or)g(`3xZ'\).)h(ORDER)f(is)f(terminated)h(b)m(y)g(length) f(or)i(b)m(y)427 4041 y(the)g(\014rst)f(unrecognized)g(c)m(haracter.)42 b(F)-8 b(ew)m(er)29 b(than)g(three)f(rotations)h(are)g(acceptable,)h (in)e(whic)m(h)427 4153 y(case)k(the)e(later)h(angle)f(argumen)m(ts)h (are)f(ignored.)40 b(Zero)31 b(rotations)f(pro)s(duces)f(a)i(unit)e (RMA)-8 b(T.)p 0 4256 V 0 4369 a Fu(SLA)p Fk(_)p Fu(DFL)d(TIN)150 b Fj(Deco)s(de)39 b(a)f(Double)h(Precision)e(Num)m(b)s(er)150 b Fu(SLA)p Fk(_)p Fu(DFL)-11 b(TIN)0 4720 y Fy(A)m(CTION)44 b FA(:)c(Con)m(v)m(ert)32 b(free-format)f(input)d(in)m(to)j(double)e (precision)f(\015oating)i(p)s(oin)m(t.)0 4907 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_DFLTIN)f(\(STRING,)h(NSTRT,)g(DRESLT,)g (JFLAG\))0 5217 y Fy(GIVEN)f FA(:)277 5363 y Fn(STRING)381 b Fy(C)569 b FA(string)29 b(con)m(taining)h(n)m(um)m(b)s(er)f(to)j(b)s (e)d(deco)s(ded)277 5476 y Fn(NSTR)-7 b(T)428 b Fy(I)605 b FA(p)s(oin)m(ter)30 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1698 y(ma)m(y)31 b(ha)m(v)m(e)h(a)f(leading)e (min)m(us)f(sign)i(but)f(a)i(zero)g(degrees)g(\014eld.)311 1842 y(2.)46 b(A)32 b(T)-8 b(AB)32 b(is)f(in)m(terpreted)g(as)h(a)g (space,)h(and)e(lo)m(w)m(ercase)i(c)m(haracters)g(are)f(in)m(terpreted) f(as)h(upp)s(er-)427 1955 y(case.)42 b Fn(n.b.)30 b FA(The)g(test)h (for)f(T)-8 b(AB)31 b(is)f(ASCI)s(I-sp)s(eci\014c.)311 2098 y(3.)46 b(The)38 b(basic)f(format)h(is)f(the)h(sequence)h(of)f (\014elds)e Fl(\006)p Fi(n:nx)24 b Fl(\006)h Fi(n)p FA(,)40 b(where)d Fl(\006)h FA(is)f(a)h(sign)f(c)m(haracter)427 2211 y(`+')f(or)g(`)p Fl(\000)p FA(',)i Fi(n)e FA(means)f(a)i(string)e (of)h(decimal)f(digits,)h(`.')58 b(is)35 b(a)h(decimal)f(p)s(oin)m(t,)i (and)e Fi(x)p FA(,)j(whic)m(h)427 2324 y(indicates)30 b(an)h(exp)s(onen)m(t,)h(means)f(`D')h(or)f(`E'.)h(V)-8 b(arious)31 b(com)m(binations)f(of)h(these)h(\014elds)e(can)h(b)s(e)427 2437 y(omitted,)g(and)f(em)m(b)s(edded)f(blanks)g(are)i(p)s(ermissible) 26 b(in)j(certain)h(places.)311 2581 y(4.)46 b(Spaces:)506 2725 y Fl(\017)g FA(Leading)30 b(spaces)h(are)g(ignored.)506 2853 y Fl(\017)46 b FA(Em)m(b)s(edded)38 b(spaces)i(are)g(allo)m(w)m (ed)f(only)f(after)i(+,)i Fl(\000)p FA(,)g(D)d(or)h(E,)f(and)g(after)h (the)f(decimal)597 2966 y(p)s(oin)m(t)30 b(if)f(the)i(\014rst)e (sequence)i(of)f(digits)f(is)h(absen)m(t.)506 3095 y Fl(\017)46 b FA(T)-8 b(railing)38 b(spaces)i(are)h(ignored;)j(the)c (\014rst)f(signi\014es)f(end)h(of)h(deco)s(ding)f(and)g(subsequen)m(t) 597 3207 y(ones)31 b(are)g(skipp)s(ed.)311 3351 y(5.)46 b(Delimiters:)506 3495 y Fl(\017)g FA(An)m(y)32 b(c)m(haracter)h(other) f(than)f(+,)p Fl(\000)p FA(,0-9,.,D,E)j(or)e(space)g(ma)m(y)g(b)s(e)f (used)g(to)h(signal)e(the)i(end)597 3608 y(of)f(the)f(n)m(um)m(b)s(er)f (and)h(terminate)h(deco)s(ding.)506 3736 y Fl(\017)46 b FA(Comma)29 b(is)e(recognized)i(b)m(y)f(sla)p Fq(_)p FA(DFL)-8 b(TIN)28 b(as)h(a)g(sp)s(ecial)e(case;)j(it)e(is)g(skipp)s (ed,)e(lea)m(ving)i(the)597 3849 y(p)s(oin)m(ter)i(on)g(the)g(next)h(c) m(haracter.)42 b(See)31 b(13,)g(b)s(elo)m(w.)506 3978 y Fl(\017)46 b FA(Deco)s(ding)31 b(will)c(in)i(all)h(cases)h(terminate) f(if)g(end)f(of)i(string)e(is)h(reac)m(hed.)311 4122 y(6.)46 b(Both)31 b(signs)f(are)g(optional.)40 b(The)30 b(default)g(is)f(+.)311 4265 y(7.)46 b(The)30 b(man)m(tissa)g Fi(n:n)g FA(defaults)g(to)h(unit)m(y)-8 b(.)311 4409 y(8.)46 b(The)30 b(exp)s(onen)m(t)h Fi(x)5 b Fl(\006)g Fi(n)29 b FA(defaults)h(to)h(`D0'.)311 4553 y(9.)46 b(The)30 b(strings)f(of)i(decimal)e(digits)g(ma)m(y)i(b)s(e)f(of)g(an)m(y)h (length.)266 4697 y(10.)46 b(The)30 b(decimal)f(p)s(oin)m(t)h(is)f (optional)h(for)g(whole)g(n)m(um)m(b)s(ers.)266 4841 y(11.)46 b(A)28 b Fn(nul)5 b(l)30 b(r)-5 b(esult)37 b FA(o)s(ccurs)28 b(when)e(the)i(string)f(of)h(c)m(haracters)h(b)s(eing)d (deco)s(ded)h(do)s(es)h(not)g(b)s(egin)e(with)427 4954 y(+,)p Fl(\000)p FA(,0-9,.,D)44 b(or)d(E,)g(or)g(consists)g(en)m (tirely)f(of)h(spaces.)74 b(When)41 b(this)f(condition)g(is)g (detected,)427 5067 y(JFLA)m(G)31 b(is)f(set)h(to)g(1)g(and)e(DRESL)-8 b(T)30 b(is)g(left)g(un)m(touc)m(hed.)266 5210 y(12.)46 b(NSTR)-8 b(T)30 b(=)g(1)h(for)f(the)g(\014rst)g(c)m(haracter)i(in)d (the)i(string.)266 5354 y(13.)46 b(On)21 b(return)f(from)h(sla)p Fq(_)p FA(DFL)-8 b(TIN,)21 b(NSTR)-8 b(T)21 b(is)f(set)i(ready)f(for)g (the)g(next)h(deco)s(de)f({)h(follo)m(wing)d(trail-)427 5467 y(ing)31 b(blanks)g(and)g(an)m(y)h(comma.)47 b(If)31 b(a)i(delimiter)c(other)j(than)g(comma)h(is)e(b)s(eing)f(used,)i(NSTR) -8 b(T)427 5580 y(m)m(ust)36 b(b)s(e)f(incremen)m(ted)g(b)s(efore)g (the)h(next)g(call)f(to)h(sla)p Fq(_)p FA(DFL)-8 b(TIN,)36 b(otherwise)f(all)f(subsequen)m(t)427 5693 y(calls)c(will)e(return)h(a) i(n)m(ull)d(result.)p eop %%Page: 41 43 41 42 bop 0 52 a Ft(SUN/67.45)3252 b FA(41)266 351 y(14.)46 b(Errors)30 b(\(JFLA)m(G=2\))i(o)s(ccur)e(when:)506 491 y Fl(\017)46 b FA(a)31 b(+,)f Fl(\000)p FA(,)h(D)f(or)h(E)f(is)f(left)h (unsatis\014ed;)f(or)506 617 y Fl(\017)46 b FA(the)30 b(decimal)e(p)s(oin)m(t)h(is)f(presen)m(t)i(without)f(at)h(least)g(one) f(decimal)g(digit)f(b)s(efore)h(or)h(after)g(it;)597 730 y(or)506 856 y Fl(\017)46 b FA(an)31 b(exp)s(onen)m(t)f(more)g (than)h(100)g(has)f(b)s(een)g(presen)m(ted.)266 996 y(15.)46 b(When)31 b(an)f(error)h(has)f(b)s(een)g(detected,)j(NSTR)-8 b(T)30 b(is)g(left)g(p)s(oin)m(ting)f(to)j(the)f(c)m(haracter)h(follo)m (wing)427 1109 y(the)41 b(last)g(one)g(used)g(b)s(efore)f(the)h(error)g (came)h(to)f(ligh)m(t.)72 b(This)39 b(ma)m(y)j(b)s(e)e(after)i(the)f(p) s(oin)m(t)f(at)427 1222 y(whic)m(h)g(a)h(more)f(sophisticated)g (program)h(could)e(ha)m(v)m(e)j(detected)g(the)f(error.)71 b(F)-8 b(or)42 b(example,)427 1334 y(sla)p Fq(_)p FA(DFL)-8 b(TIN)28 b(do)s(es)f(not)h(detect)h(that)f(`1D999')i(is)d(unacceptable) g(\(on)h(a)g(computer)f(where)h(this)427 1447 y(is)i(so\))h(un)m(til)d (the)j(en)m(tire)f(n)m(um)m(b)s(er)f(has)h(b)s(een)g(deco)s(ded.)266 1587 y(16.)46 b(Certain)28 b(highly)f(unlik)m(ely)g(com)m(binations)h (of)h(man)m(tissa)g(and)f(exp)s(onen)m(t)h(can)h(cause)f(arithmetic)427 1700 y(faults)j(during)e(the)i(deco)s(de,)i(in)d(some)i(cases)g (despite)e(the)i(fact)g(that)g(they)g(together)h(could)d(b)s(e)427 1813 y(construed)f(as)h(a)g(v)-5 b(alid)28 b(n)m(um)m(b)s(er.)266 1952 y(17.)46 b(Deco)s(ding)31 b(is)e(left)h(to)h(righ)m(t,)f(one)h (pass.)266 2092 y(18.)46 b(See)31 b(also)f(sla)p Fq(_)p FA(FLOTIN)f(and)h(sla)p Fq(_)p FA(INTIN.)p 0 2196 3780 8 v 0 2309 a Fu(SLA)p Fk(_)p Fu(DH2E)885 b Fj(Az,El)38 b(to)g Fd(h;)20 b(\016)890 b Fu(SLA)p Fk(_)p Fu(DH2E)0 2659 y Fy(A)m(CTION)44 b FA(:)c(Horizon)31 b(to)g(equatorial)f(co)s (ordinates)g(\(double)f(precision\).)0 2847 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_DH2E)g(\(AZ,)h(EL,)f(PHI,)h(HA,)g(DEC\))0 3170 y Fy(GIVEN)e FA(:)277 3316 y Fn(AZ)612 b Fy(D)565 b FA(azim)m(uth)30 b(\(radians\))277 3429 y Fn(EL)617 b Fy(D)565 b FA(elev)-5 b(ation)30 b(\(radians\))277 3542 y Fn(PHI)571 b Fy(D)565 b FA(latitude)30 b(\(radians\))0 3849 y Fy(RETURNED)46 b FA(:)277 3995 y Fn(HA)600 b Fy(D)565 b FA(hour)30 b(angle)g(\(radians\))277 4108 y Fn(DEC)540 b Fy(D)565 b FA(declination)29 b(\(radians\))0 4416 y Fy(NOTES)44 b FA(:)311 4597 y(1.)i(The)30 b(sign)g(con)m(v)m(en)m(tion) h(for)f(azim)m(uth)g(is)g(north)f(zero,)j(east)f(+)p Fi(\031)s(=)p FA(2.)311 4736 y(2.)46 b(HA)31 b(is)e(returned)h(in)f (the)h(range)h Fl(\006)p Fi(\031)s FA(.)40 b(Declination)30 b(is)f(returned)h(in)f(the)h(range)h Fl(\006)p Fi(\031)s FA(.)311 4876 y(3.)46 b(The)33 b(latitude)g(is)f(\(in)h(principle\))d (geo)s(detic.)51 b(In)33 b(critical)f(applications,)h(corrections)g (for)h(p)s(olar)427 4989 y(motion)c(should)f(b)s(e)g(applied)g(\(see)i (sla)p Fq(_)p FA(POLMO\).)311 5128 y(4.)46 b(In)34 b(some)g (applications)e(it)i(will)d(b)s(e)j(imp)s(ortan)m(t)f(to)i(sp)s(ecify)e (the)h(correct)h(t)m(yp)s(e)f(of)h(elev)-5 b(ation)34 b(in)427 5241 y(order)42 b(to)h(pro)s(duce)f(the)g(required)f(t)m(yp)s (e)h(of)h([)15 b Fi(h;)g(\016)20 b FA(].)77 b(In)42 b(particular,)i(it) e(ma)m(y)h(b)s(e)e(imp)s(ortan)m(t)427 5354 y(to)f(distinguish)35 b(b)s(et)m(w)m(een)k(the)g(elev)-5 b(ation)39 b(as)g(a\013ected)h(b)m (y)f(refraction,)i(whic)m(h)c(will)f(yield)h(the)427 5467 y Fn(observe)-5 b(d)32 b FA([)15 b Fi(h;)g(\016)20 b FA(],)31 b(and)e(the)i(elev)-5 b(ation)30 b Fn(in)j(vacuo)p FA(,)e(whic)m(h)e(will)f(yield)g(the)j Fn(top)-5 b(o)g(c)g(entric)33 b FA([)15 b Fi(h;)g(\016)20 b FA(].)41 b(If)427 5580 y(the)28 b(e\013ects)h(of)f(diurnal)d(ab)s(erration)i(can)h(b)s(e)f (neglected,)i(the)f(top)s(o)s(cen)m(tric)g([)15 b Fi(h;)g(\016)20 b FA(])28 b(ma)m(y)g(b)s(e)f(used)427 5693 y(as)k(an)f(appro)m (ximation)f(to)j(the)e Fn(app)-5 b(ar)g(ent)33 b FA([)15 b Fi(h;)g(\016)21 b FA(].)p eop %%Page: 42 44 42 43 bop 0 52 a FA(42)311 351 y(5.)46 b(No)31 b(range)g(c)m(hec)m (king)g(of)g(argumen)m(ts)f(is)g(carried)f(out.)311 490 y(6.)46 b(In)28 b(applications)e(whic)m(h)i(in)m(v)m(olv)m(e)g(man)m(y) h(suc)m(h)f(calculations,)g(rather)g(than)g(calling)f(the)h(presen)m(t) 427 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Fy(a)427 3284 y FA(where)g Fy(a)f FA(and)g Fy(b)h FA(are)g(the)g(3-v)m(ectors)i(V)-10 b(A)30 b(and)f(VB)i(resp)s (ectiv)m(ely)-8 b(,)30 b(and)f Fy(M)h FA(is)f(the)h(3)19 b Fl(\002)g FA(3)30 b(matrix)427 3397 y(DM.)311 3536 y(2.)46 b(The)34 b(main)g(function)f(of)i(this)e(routine)h(is)f(apply)g (an)i(in)m(v)m(erse)f(rotation;)j(under)c(these)i(circum-)427 3649 y(stances,)d(M)e(is)g Fn(ortho)-5 b(gonal)p FA(,)34 b(with)29 b(its)g(in)m(v)m(erse)i(the)f(same)h(as)g(its)e(transp)s (ose.)311 3788 y(3.)46 b(T)-8 b(o)25 b(comply)f(with)g(the)h(ANSI)f(F) -8 b(ortran)26 b(77)f(standard,)g(V)-10 b(A)25 b(and)f(VB)i(m)m(ust)e Fy(not)h FA(b)s(e)f(the)h(same)g(ar-)427 3901 y(ra)m(y)-8 b(.)40 b(The)25 b(routine)f(is,)i(in)e(fact,)k(co)s(ded)d(so)g(as)h(to) g(w)m(ork)f(prop)s(erly)f(on)h(the)g(V)-10 b(AX)26 b(and)f(man)m(y)g (other)427 4014 y(systems)31 b(ev)m(en)g(if)e(this)g(rule)g(is)h (violated,)g(something)g(that)h(is)e Fy(not)p FA(,)i(ho)m(w)m(ev)m(er,) h(recommended.)p 0 4125 V 0 4238 a Fu(SLA)p Fk(_)p Fu(DJCAL)347 b Fj(MJD)40 b(to)e(Gregorian)e(for)i(Output)347 b Fu(SLA)p Fk(_)p Fu(DJCAL)0 4588 y Fy(A)m(CTION)44 b FA(:)39 b(Mo)s(di\014ed)27 b(Julian)f(Date)j(to)g(Gregorian)f(Calendar)f(Date,)k(expressed)c(in)g (a)i(form)e(con)m(v)m(enien)m(t)227 4701 y(for)22 b(formatting)g (messages)i(\(namely)e(rounded)e(to)j(a)g(sp)s(eci\014ed)d(precision,)j (and)e(with)g(the)i(\014elds)d(stored)227 4814 y(in)29 b(a)i(single)e(arra)m(y\).)0 5001 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_DJCAL)g(\(NDP,)g(DJM,)h(IYMDF,)f(J\))0 5322 y Fy(GIVEN)f FA(:)277 5468 y Fn(NDP)537 b Fy(I)605 b FA(n)m(um)m(b)s(er)29 b(of)i(decimal)e(places)h(of)h(da)m(ys)f(in)f (fraction)277 5581 y Fn(DJM)537 b Fy(D)565 b FA(mo)s(di\014ed)28 b(Julian)g(Date)k(\(JD)p Fl(\000)p FA(2400000.5\))p eop %%Page: 43 45 43 44 bop 0 52 a Ft(SUN/67.45)3252 b FA(43)0 351 y Fy(RETURNED)46 b FA(:)277 497 y Fn(IYMDF)423 b Fy(I\(4\))471 b FA(y)m(ear,)32 b(mon)m(th,)e(da)m(y)-8 b(,)32 b(fraction)e(in)f(Gregorian)h(calendar) 277 610 y Fn(J)688 b Fy(I)605 b FA(status:)41 b(nonzero)31 b(=)f(out)g(of)h(range)0 946 y Fy(NOTES)44 b FA(:)311 1131 y(1.)i(An)m(y)31 b(date)g(after)g(4701BC)h(Marc)m(h)f(1)g(is)e (accepted.)311 1274 y(2.)46 b(NDP)31 b(should)d(b)s(e)i(4)h(or)f(less)g (to)h(a)m(v)m(oid)g(o)m(v)m(er\015o)m(w)h(on)e(mac)m(hines)g(whic)m(h)f (use)h(32-bit)h(in)m(tegers.)0 1618 y Fy(REFERENCE)44 b FA(:)c(The)28 b(algorithm)f(is)h(deriv)m(ed)f(from)h(that)h(of)g (Hatc)m(her,)h Fn(Q.)15 b(Jl.)h(R.)f(astr.)i(So)-5 b(c.)29 b FA(\(1984\))i Fy(25)p FA(,)227 1731 y(53-55.)p 0 1838 3780 8 v 0 1951 a Fu(SLA)p Fk(_)p Fu(DJCL)456 b Fj(MJD)40 b(to)e(Y)-10 b(ear,Mon)m(th,Da)m(y)g(,F)g(rac)452 b Fu(SLA)p Fk(_)p Fu(DJCL)0 2302 y Fy(A)m(CTION)44 b FA(:)c(Mo)s(di\014ed)29 b(Julian)f(Date)k(to)f(Gregorian)g(y)m(ear,)g(mon)m(th,)g(da)m(y)-8 b(,)31 b(and)f(fraction)g(of)h(a)f(da)m(y)-8 b(.)0 2489 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_DJCL)g(\(DJM,)g(IY,)h(IM,)g (ID,)g(FD,)g(J\))0 2829 y Fy(GIVEN)e FA(:)277 3000 y Fn(DJM)537 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y(sion\).)0 5606 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_DM2AV)g(\(RMAT,)g(AXVEC\))p eop %%Page: 44 46 44 45 bop 0 52 a FA(44)0 351 y Fy(GIVEN)45 b FA(:)277 523 y Fn(RMA)-7 b(T)462 b Fy(D\(3,3\))350 b FA(rotation)31 b(matrix)0 976 y Fy(RETURNED)46 b FA(:)277 1148 y Fn(AXVEC)405 b Fy(D\(3\))431 b FA(axial)30 b(v)m(ector)i(\(radians\))0 1601 y Fy(NOTES)44 b FA(:)311 1826 y(1.)i(A)32 b(rotation)f(matrix)g (describ)s(es)e(a)i(rotation)h(ab)s(out)f(some)g(arbitrary)f(axis.)43 b(The)30 b(axis)h(is)f(called)427 1939 y(the)g Fn(Euler)i(axis)p FA(,)f(and)e(the)h(angle)g(through)f(whic)m(h)g(the)h(reference)g (frame)g(rotates)h(is)e(called)g(the)427 2051 y Fn(Euler)k(angle)p FA(.)42 b(The)30 b Fn(axial)k(ve)-5 b(ctor)41 b FA(returned)30 b(b)m(y)g(this)g(routine)g(has)g(the)h(same)g(direction)e(as)i(the)427 2164 y(Euler)e(axis,)h(and)g(its)g(magnitude)f(is)h(the)g(Euler)f (angle)i(in)e(radians.)311 2329 y(2.)46 b(The)35 b(magnitude)g(and)g 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Fy(D\(6\))431 b FA(Mo)s(on)41 b([)15 b Fi(x;)g(y)s(;)g(z)t(;)33 b FA(_)-43 b Fi(x)r(;)32 b FA(_)-42 b Fi(y)s(;)31 b FA(_)-41 b Fi(z)20 b FA(],)44 b(mean)d(equator)h(and)f(equino)m(x)1658 5519 y(of)31 b(date)g(\(A)m(U,)g(A)m(U)h(s)2389 5486 y Fm(\000)p Fr(1)2483 5519 y FA(\))p eop %%Page: 46 48 46 47 bop 0 52 a FA(46)0 351 y Fy(NOTES)44 b FA(:)311 531 y(1.)i(This)27 b(routine)g(is)g(a)i(full)d(implemen)m(tation)h(of)h (the)h(algorithm)e(published)d(b)m(y)29 b(Meeus)f(\(see)h(refer-)427 644 y(ence\).)311 781 y(2.)46 b(Meeus)e(quotes)g(accuracies)g(of)f(10) 1664 745 y Fh(0)m(0)1748 781 y FA(in)f(longitude,)j(3)2347 745 y Fh(0)m(0)2431 781 y FA(in)d(latitude)g(and)h(0)3131 745 y Fh(0)l(0)3135 781 y Fi(:)p FA(2)h(arcsec)h(in)c(HP)427 894 y(\(equiv)-5 b(alen)m(t)43 b(to)h(ab)s(out)f(20)h(km)f(in)f (distance\).)80 b(Comparison)41 b(with)h(JPL)h(DE200)i(o)m(v)m(er)f (the)427 1007 y(in)m(terv)-5 b(al)31 b(1960-2025)k(giv)m(es)c(RMS)g (errors)g(of)g(3)2041 970 y Fh(0)m(0)2045 1007 y Fi(:)p 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b(sla_DMXM)g(\(A,)h(B,)g(C\))0 3591 y Fy(GIVEN)e FA(:)277 3737 y Fn(A)668 b Fy(D\(3,3\))350 b FA(matrix)30 b Fy(A)277 3850 y Fn(B)672 b Fy(D\(3,3\))350 b FA(matrix)30 b Fy(B)0 4145 y(RETURNED)46 b FA(:)277 4317 y Fn(C)671 b Fy(D\(3,3\))350 b FA(matrix)30 b(result:)40 b Fy(A)p Fl(\002)p Fy(B)0 4621 y(NOTE)k FA(:)c(T)-8 b(o)30 b(comply)e(with)g(the)h(ANSI)g(F)-8 b(ortran)29 b(77)h(standard,)f(A,)h (B)f(and)f(C)h(m)m(ust)g(b)s(e)f(di\013eren)m(t)h(arra)m(ys.)227 4734 y(The)f(routine)g(is,)g(in)f(fact,)j(co)s(ded)e(so)g(as)h(to)g(w)m (ork)g(prop)s(erly)d(on)i(the)h(V)-10 b(AX)29 b(and)e(man)m(y)i(other)f (systems)227 4847 y(ev)m(en)j(if)f(this)f(rule)g(is)g(violated,)i (something)e(that)i(is)f Fy(not)p FA(,)g(ho)m(w)m(ev)m(er,)i (recommended.)p 0 4955 V 0 5068 a Fu(SLA)p Fk(_)p Fu(DMXV)641 b Fj(Apply)38 b(3D)h(Rotation)640 b Fu(SLA)p Fk(_)p Fu(DMXV)0 5418 y Fy(A)m(CTION)44 b FA(:)c(Multiply)28 b(a)j(3-v)m(ector)i(b)m(y)d (a)h(rotation)f(matrix)g(\(double)f(precision\).)0 5606 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_DMXV)g(\(DM,)h(VA,)f(VB\))p eop %%Page: 47 49 47 48 bop 0 52 a Ft(SUN/67.45)3252 b FA(47)0 351 y Fy(GIVEN)45 b FA(:)277 497 y Fn(DM)585 b Fy(D\(3,3\))350 b FA(rotation)31 b(matrix)277 610 y Fn(V)-9 b(A)609 b Fy(D\(3\))431 b FA(v)m(ector)32 b(to)f(b)s(e)f(rotated)0 967 y Fy(RETURNED)46 b FA(:)277 1138 y Fn(VB)604 b Fy(D\(3\))431 b FA(result)29 b(v)m(ector)0 1503 y Fy(NOTES)44 b FA(:)311 1692 y(1.)i(This)29 b(routine)g(p)s(erforms)g(the)i(op)s(eration:)597 1839 y Fy(b)g FA(=)f Fy(M)p Fl(\001)p Fy(a)427 1985 y FA(where)g Fy(a)f FA(and)g Fy(b)h FA(are)g(the)g(3-v)m(ectors)i(V)-10 b(A)30 b(and)f(VB)i(resp)s(ectiv)m(ely)-8 b(,)30 b(and)f Fy(M)h FA(is)f(the)h(3)19 b Fl(\002)g FA(3)30 b(matrix)427 2098 y(DM.)311 2245 y(2.)46 b(The)30 b(main)f(function)g(of)i(this)e (routine)g(is)h(apply)f(a)h(rotation;)h(under)e(these)i(circumstances,) f Fy(M)427 2358 y FA(is)g(a)g Fn(pr)-5 b(op)g(er)36 b(r)-5 b(e)g(al)34 b(ortho)-5 b(gonal)43 b FA(matrix.)311 2505 y(3.)j(T)-8 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b(RAZ1)h(and)e(RAZ2)i(v)-5 b(alues)29 b(returned)h(are)g(in)f(the)i (range)g(0)5 b Fl(\000)g FA(2)p Fi(\031)s FA(.)311 1886 y(2.)46 b(Cases)39 b(where)f(there)h(is)f(no)g(solution)f(can)i(only)f (arise)g(near)g(the)h(p)s(oles.)64 b(F)-8 b(or)40 b(example,)g(it)e(is) 427 1999 y(clearly)27 b(imp)s(ossible)d(for)j(a)h(star)f(at)h(the)g(p)s (ole)e(itself)g(to)j(ha)m(v)m(e)f(a)g(non-zero)g Fi(\030)j FA(v)-5 b(alue,)28 b(and)e(hence)i(it)427 2112 y(is)k(meaningless)g(to) h(ask)g(where)f(the)h(tangen)m(t)i(p)s(oin)m(t)c(w)m(ould)h(ha)m(v)m(e) i(to)f(b)s(e)g(to)g(bring)e(ab)s(out)i(this)427 2225 y(com)m(bination)d(of)g Fi(\030)35 b FA(and)30 b Fi(\016)s FA(.)311 2388 y(3.)46 b(Also)33 b(near)f(the)h(p)s(oles,)f(cases)i(can) f(arise)f(where)g(there)h(are)g(t)m(w)m(o)g(useful)e(solutions.)46 b(The)32 b(argu-)427 2501 y(men)m(t)j(N)g(indicates)e(whether)h(the)h (second)g(of)g(the)f(t)m(w)m(o)i(solutions)d(returned)h(is)f(useful.)52 b(N)15 b(=)g(1)427 2614 y(indicates)41 b(only)h(one)g(useful)e 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b(c)m(hange)i(from)e(the)h(classic)f(\\textb)s(o) s(ok")i(expression)d(\001)p Fi( )18 b(cos)d(\017)30 b FA(o)s(ccurred)f(with)f(IA)m(U)i(Res-)427 5252 y(olution)44 b(C7,)49 b(Recommendation)c(3)g(\(1994\).)87 b(The)44 b(new)h(form)m(ulation)f(tak)m(es)i(in)m(to)f(accoun)m(t)427 5365 y(cross-terms)d(b)s(et)m(w)m(een)h(the)f(v)-5 b(arious)41 b(precession)f(and)i(n)m(utation)f(quan)m(tities,)j(amoun)m(ting)e(to) 427 5478 y(ab)s(out)d(3)f(milliarcsec.)64 b(The)38 b(transition)f(from) h(the)h(old)e(to)j(the)e(new)g(mo)s(del)g(o\016cially)f(tak)m(es)427 5591 y(place)31 b(on)f(1997)i(F)-8 b(ebruary)30 b(27.)p eop %%Page: 68 70 68 69 bop 0 52 a FA(68)0 351 y Fy(REFERENCE)44 b FA(:)d(Capitaine,)29 b(N.)i(&)f(Gon)m(tier,)h(A.-M.)g(\(1993\),)j Fn(Astr)-5 b(on.)42 b(Astr)-5 b(ophys.)p FA(,)33 b Fy(275)p FA(,)f(645-650.)p 0 477 3780 8 v 0 590 a Fu(SLA)p Fk(_)p Fu(EQGAL)530 b Fj(J2000)38 b Fd(\013)q(;)20 b(\016)43 b Fj(to)38 b(Galactic)530 b Fu(SLA)p Fk(_)p Fu(EQGAL)0 941 y Fy(A)m(CTION)44 b FA(:)62 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y(ITYPE=6,)39 b(all)d(six)g(co)s(e\016cien)m(ts)i(are)g(indep)s (enden)m(t,)f(mo)s(delling)d(squash)i(and)h(shear)g(as)g(w)m(ell)427 2094 y(as)d(origin,)f(scale,)i(and)e(orien)m(tation.)50 b(Ho)m(w)m(ev)m(er,)37 b(ITYPE=4)c(selects)h(the)f Fn(solid)k(b)-5 b(o)g(dy)37 b(r)-5 b(otation)427 2207 y FA(option;)41 b(the)d(mo)s(del)e(COEFFS)h(still)e(consists)i(of)h(the)f(same)h(six)f (co)s(e\016cien)m(ts,)j(but)d(no)m(w)g(t)m(w)m(o)427 2320 y(of)32 b(them)f(are)g(used)f(t)m(wice)i(\(appropriately)e (signed\).)42 b(Origin,)29 b(scale)i(and)g(orien)m(tation)g(are)h (still)427 2433 y(mo)s(delled,)d(but)h(not)g(squash)g(or)g(shear)g({)h (the)f(units)f(of)i(X)f(and)g(Y)h(ha)m(v)m(e)g(to)g(b)s(e)f(the)h (same.)311 2584 y(2.)46 b(F)-8 b(or)31 b(NC=4,)g(NP)f(m)m(ust)h(b)s(e)e (at)i(least)g(2.)41 b(F)-8 b(or)31 b(NC=6,)g(NP)f(m)m(ust)g(b)s(e)g(at) h(least)g(3.)311 2736 y(3.)46 b(The)33 b(mo)s(del)e(is)h(returned)g(in) f(the)i(arra)m(y)g(COEFFS.)g(Naming)f(the)h(six)f(elemen)m(ts)h(of)g (COEFFS)427 2849 y Fi(a;)15 b(b;)g(c;)g(d;)g(e)43 b FA(&)d Fi(f)10 b FA(,)42 b(the)e(mo)s(del)f(transforms)g Fn(me)-5 b(asur)g(e)g(d)52 b FA(co)s(ordinates)40 b([)p Fi(x)2968 2863 y Fc(m)3035 2849 y Fi(;)15 b(y)3120 2863 y Fc(m)3201 2849 y FA(])41 b(in)m(to)f Fn(exp)-5 b(e)g(cte)g(d)427 2962 y FA(co)s(ordinates)30 b([)p Fi(x)987 2976 y Fc(e)1024 2962 y Fi(;)15 b(y)1109 2976 y Fc(e)1161 2962 y FA(])31 b(as)g(follo)m(ws:)597 3114 y Fi(x)649 3128 y Fc(e)711 3114 y FA(=)25 b Fi(a)c FA(+)e Fi(bx)1057 3128 y Fc(m)1144 3114 y FA(+)h Fi(cy)1319 3128 y Fc(m)597 3227 y Fi(y)642 3241 y Fc(e)704 3227 y FA(=)25 b Fi(d)20 b FA(+)g Fi(ex)1052 3241 y Fc(m)1139 3227 y FA(+)g Fi(f)10 b(y)1330 3241 y Fc(m)427 3378 y FA(F)-8 b(or)33 b(the)g Fn(solid)i(b)-5 b(o)g(dy)36 b(r)-5 b(otation)42 b FA(option)32 b(\(ITYPE=4\),)h(the)g (magnitudes)e(of)i Fi(b)f FA(and)g Fi(f)10 b FA(,)32 b(and)g(of)g Fi(c)427 3491 y FA(and)k Fi(e)p FA(,)i(are)e(equal.)57 b(The)35 b(signs)g(of)h(these)h(co)s(e\016cien)m(ts)f(dep)s(end)f(on)h (whether)f(there)h(is)f(a)h(sign)427 3604 y(rev)m(ersal)41 b(b)s(et)m(w)m(een)g([)p Fi(x)1210 3618 y Fc(e)1247 3604 y Fi(;)15 b(y)1332 3618 y Fc(e)1369 3604 y FA(])41 b(and)f([)p Fi(x)1699 3618 y Fc(m)1766 3604 y Fi(;)15 b(y)1851 3618 y Fc(m)1917 3604 y FA(];)47 b(\014ts)40 b(are)h(p)s(erformed)e(with)h (and)g(without)f(a)i(sign)427 3717 y(rev)m(ersal)31 b(and)e(the)i(b)s (est)f(one)h(c)m(hosen.)311 3869 y(4.)46 b(Error)27 b(status)h(v)-5 b(alues)27 b(J=)p Fl(\000)p FA(1)h(and)f Fl(\000)p FA(2)h(lea)m(v)m(e)h (COEFFS)e(unc)m(hanged;)i(if)d(J=)p Fl(\000)p FA(3)i(COEFFS)f(ma)m(y) 427 3982 y(ha)m(v)m(e)32 b(b)s(een)e(c)m(hanged.)311 4133 y(5.)46 b(See)31 b(also)f(sla)p Fq(_)p FA(PXY,)g(sla)p Fq(_)p FA(INVF,)h(sla)p Fq(_)p FA(XY2XY,)g(sla)p Fq(_)p FA(DCMPF.)p 0 4277 3780 8 v 0 4390 a Fu(SLA)p Fk(_)p Fu(FK425)862 b Fj(FK4)39 b(to)f(FK5)862 b Fu(SLA)p Fk(_)p Fu(FK425)0 4741 y Fy(A)m(CTION)44 b FA(:)c(Con)m(v)m(ert)31 b(B1950.0)h(FK4)f(star)e(data)i(to)f(J2000.0)i(FK5.)41 b(This)28 b(routine)h(con)m(v)m(erts)i(stars)f(from)227 4853 y(the)37 b(old,)g(Bessel-New)m(com)m(b,)j(FK4)d(system)f(to)h(the) g(new,)g(IA)m(U)g(1976,)j(FK5,)f(F)-8 b(ric)m(k)m(e)37 b(system.)59 b(The)227 4966 y(precepts)34 b(of)h(Smith)d Fn(et)37 b(al.)d FA(\(see)h(reference)g(1\))g(are)g(follo)m(w)m(ed,)g (using)e(the)h(implemen)m(tation)f(b)m(y)h(Y)-8 b(al-)227 5079 y(lop)34 b Fn(et)i(al.)f FA(\(reference)g(2\))h(of)e(a)h(matrix)f (metho)s(d)g(due)g(to)h(Standish.)51 b(Kinoshita's)32 b(dev)m(elopmen)m(t)j(of)227 5192 y(Ando)m(y)m(er's)40 b(p)s(ost-New)m(com)m(b)g(precession)e(is)g(used.)66 b(The)39 b(n)m(umerical)e(constan)m(ts)k(from)d(Seidelman-)227 5305 y(n)30 b Fn(et)j(al.)e FA(\(reference)g(3\))g(are)g(used)e (canonically)-8 b(.)0 5493 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_FK425)g(\(R1950,D1950,DR1950,DD1)o(950,)o(P19)o(50,V)o(1950)o(,) 1192 5606 y(R2000,D2000,DR2000,DD2)o(000,)o(P20)o(00,V)o(2000)o(\))p eop %%Page: 72 74 72 73 bop 0 52 a FA(72)0 351 y Fy(GIVEN)45 b FA(:)277 497 y Fn(R1950)486 b Fy(D)565 b FA(B1950.0)33 b Fi(\013)e FA(\(radians\))277 610 y Fn(D1950)483 b Fy(D)565 b FA(B1950.0)33 b Fi(\016)i FA(\(radians\))277 723 y Fn(DR1950)417 b Fy(D)565 b FA(B1950.0)39 b(prop)s(er)c(motion)h(in)f Fi(\013)i FA(\(radians)f(p)s(er)f(tropical)1658 836 y(y)m(ear\))277 949 y Fn(DD1950)414 b Fy(D)565 b FA(B1950.0)41 b(prop)s(er)c(motion)i (in)e Fi(\016)42 b FA(\(radians)37 b(p)s(er)h(tropical)1658 1062 y(y)m(ear\))277 1175 y Fn(P1950)490 b Fy(D)565 b FA(B1950.0)33 b(parallax)d(\(arcsec\))277 1288 y Fn(V1950)484 b Fy(D)565 b FA(B1950.0)48 b(radial)c(v)m(elo)s(cit)m(y)i(\(km)f(s)2884 1255 y Fm(\000)p Fr(1)2978 1288 y FA(,)50 b(+v)m(e)45 b(=)g(mo)m(ving)1658 1401 y(a)m(w)m(a)m(y\))0 1817 y Fy(RETURNED)h FA(:)277 1963 y Fn(R2000)486 b Fy(D)565 b FA(J2000.0)33 b Fi(\013)e FA(\(radians\))277 2075 y Fn(D2000)483 b Fy(D)565 b FA(J2000.0)33 b Fi(\016)h FA(\(radians\))277 2188 y Fn(DR2000)417 b Fy(D)565 b FA(J2000.0)50 b(prop)s(er)c(motion)h (in)f Fi(\013)i FA(\(radians)e(p)s(er)g(Julian)1658 2301 y(y)m(ear\))277 2414 y Fn(DD2000)414 b Fy(D)565 b FA(J2000.0)52 b(prop)s(er)c(motion)h(in)f Fi(\016)54 b FA(\(radians)48 b(p)s(er)g(Julian)1658 2527 y(y)m(ear\))277 2640 y Fn(P2000)490 b Fy(D)565 b FA(J2000.0)33 b(parallax)c(\(arcsec\))277 2753 y Fn(V2000)484 b Fy(D)565 b FA(J2000.0)50 b(radial)c(v)m(elo)s (cit)m(y)i(\(km)g(s)2876 2720 y Fm(\000)p Fr(1)2970 2753 y FA(,)53 b(+v)m(e)48 b(=)f(mo)m(ving)1658 2866 y(a)m(w)m(a)m(y\))0 3282 y Fy(NOTES)d FA(:)311 3494 y(1.)i(The)37 b Fi(\013)h FA(prop)s(er)e(motions)h(are)57 b(_)-45 b Fi(\013)38 b FA(rather)f(than)57 b(_)-44 b Fi(\013)15 b FA(cos)h Fi(\016)s FA(,)40 b(and)d(are)h(p)s(er)e(y)m(ear)i(rather)f(than)g(p)s (er)427 3607 y(cen)m(tury)-8 b(.)311 3766 y(2.)46 b(Con)m(v)m(ersion)31 b(from)f(Besselian)g(ep)s(o)s(c)m(h)h(1950.0)i(to)f(Julian)c(ep)s(o)s (c)m(h)j(2000.0)i(only)d(is)g(pro)m(vided)f(for.)427 3879 y(Con)m(v)m(ersions)42 b(in)m(v)m(olving)e(other)i(ep)s(o)s(c)m (hs)g(will)d(require)h(use)i(of)g(the)g(appropriate)f(precession,)427 3992 y(prop)s(er)29 b(motion,)i(and)e(E-terms)i(routines)e(b)s(efore)h (and/or)g(after)h(FK425)h(is)d(called.)311 4150 y(3.)46 b(In)41 b(the)h(FK4)g(catalogue)h(the)f(prop)s(er)e(motions)h(of)h (stars)f(within)e(10)2905 4117 y Fm(\016)2987 4150 y FA(of)j(the)f(p)s(oles)g(do)g(not)427 4263 y(include)29 b(the)j Fn(di\013er)-5 b(ential)34 b(E-terms)39 b FA(e\013ect)33 b(and)d(should,)g(strictly)g(sp)s(eaking,)g(b)s(e)h(handled)e(in)h(a) 427 4376 y(di\013eren)m(t)37 b(manner)f(from)g(stars)h(outside)f(these) h(regions.)60 b(Ho)m(w)m(ev)m(er,)40 b(giv)m(en)d(the)g(general)g(lac)m (k)427 4489 y(of)i(homogeneit)m(y)g(of)f(the)h(star)f(data)h(a)m(v)-5 b(ailable)38 b(for)g(routine)f(astrometry)-8 b(,)42 b(the)d (di\016culties)c(of)427 4602 y(handling)30 b(p)s(ositions)g(that)j(ma)m (y)g(ha)m(v)m(e)h(b)s(een)e(determined)f(from)h(astrometric)h(\014elds) d(spanning)427 4715 y(the)25 b(p)s(olar)e(and)h(non-p)s(olar)f (regions,)i(the)f(lik)m(eliho)s(o)s(d)d(that)k(the)g(di\013eren)m(tial) e(E-terms)h(e\013ect)i(w)m(as)427 4828 y(not)31 b(tak)m(en)h(in)m(to)f (accoun)m(t)h(when)d(allo)m(wing)h(for)g(prop)s(er)f(motion)i(in)e (past)i(astrometry)-8 b(,)32 b(and)e(the)427 4941 y(undesirabilit)m(y)c (of)j(a)h(discon)m(tin)m(uit)m(y)d(in)h(the)i(algorithm,)f(the)g (decision)f(has)h(b)s(een)f(made)i(in)e(this)427 5053 y(routine)c(to)h(include)d(the)j(e\013ect)h(of)f(di\013eren)m(tial)e (E-terms)h(on)h(the)f(prop)s(er)f(motions)h(for)h(all)e(stars,)427 5166 y(whether)h(p)s(olar)f(or)h(not.)39 b(A)m(t)25 b(ep)s(o)s(c)m(h)f (J2000,)j(and)d(measuring)f(on)h(the)h(sky)f(rather)g(than)g(in)f (terms)427 5279 y(of)34 b(\001)p Fi(\013)p FA(,)h(the)e(errors)g (resulting)f(from)h(this)f(simpli\014cation)e(are)k(less)f(than)g(1)h (milliarcsecond)d(in)427 5392 y(p)s(osition)e(and)h(1)g(milliarcsecond) e(p)s(er)h(cen)m(tury)i(in)e(prop)s(er)g(motion.)311 5551 y(4.)46 b(See)31 b(also)f(sla)p Fq(_)p FA(FK45Z,)h(sla)p Fq(_)p FA(FK524,)g(sla)p Fq(_)p FA(FK54Z.)p eop %%Page: 73 75 73 74 bop 0 52 a Ft(SUN/67.45)3252 b FA(73)0 351 y Fy(REFERENCES)44 b FA(:)311 527 y(1.)i(Smith,)29 b(C.A.)i Fn(et)h(al.)p FA(,)g(1989.)g Fn(Astr.J.)e Fy(97)p FA(,)h(265.)311 661 y(2.)46 b(Y)-8 b(allop,)30 b(B.D.)i Fn(et)h(al.)p FA(,)e(1989.)h Fn(Astr.J.)e Fy(97)p FA(,)h(274.)311 794 y(3.)46 b(Seidelmann,)27 b(P)-8 b(.K.)28 b(\(ed\),)i(1992.)41 b Fn(Explanatory)34 b(Supplement)e(to)f(the)g(Astr)-5 b(onomic)g(al)33 b(A)n(lmanac,)427 907 y FA(ISBN)d(0-935702-68-7.)p 0 986 3780 8 v 0 1099 a Fu(SLA)p Fk(_)p Fu(FK45Z)305 b Fj(FK4)39 b(to)f(FK5,)h(no)f(P)-10 b(.M.)39 b(or)f(P)m(arallax)302 b Fu(SLA)p Fk(_)p Fu(FK45Z)0 1449 y Fy(A)m(CTION)44 b FA(:)j(Con)m(v)m(ert)35 b(B1950.0)h(FK4)e (star)g(data)h(to)f(J2000.0)i(FK5)e(assuming)f(zero)h(prop)s(er)e (motion)i(in)227 1562 y(the)i(FK5)f(frame.)55 b(This)33 b(routine)h(con)m(v)m(erts)j(stars)e(from)g(the)g(old,)h(Bessel-New)m (com)m(b,)i(FK4)d(system)227 1675 y(to)e(the)f(new,)f(IA)m(U)h(1976,)i (FK5,)f(F)-8 b(ric)m(k)m(e)33 b(system,)f(in)f(suc)m(h)g(a)h(w)m(a)m(y) h(that)f(the)g(FK5)g(prop)s(er)e(motion)h(is)227 1788 y(zero.)54 b(Because)36 b(suc)m(h)e(a)h(star)g(has,)h(in)d(general,)j (a)f(non-zero)g(prop)s(er)e(motion)h(in)f(the)i(FK4)g(system,)227 1901 y(the)e(routine)f(requires)g(the)h(ep)s(o)s(c)m(h)f(at)i(whic)m(h) d(the)i(p)s(osition)e(in)h(the)h(FK4)g(system)g(w)m(as)h(determined.) 227 2014 y(The)c(metho)s(d)g(is)f(from)h(app)s(endix)e(2)j(of)f (reference)h(1,)g(but)f(using)f(the)h(constan)m(ts)i(of)e(reference)h (4.)0 2201 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_FK45Z)g (\(R1950,D1950,BEPOCH,R20)o(00,D)o(200)o(0\))0 2502 y Fy(GIVEN)f FA(:)277 2648 y Fn(R1950)486 b Fy(D)565 b FA(B1950.0)33 b(FK4)e Fi(\013)g FA(at)g(ep)s(o)s(c)m(h)f(BEPOCH)g (\(radians\))277 2761 y Fn(D1950)483 b Fy(D)565 b FA(B1950.0)33 b(FK4)e Fi(\016)j FA(at)d(ep)s(o)s(c)m(h)g(BEPOCH)f(\(radians\))277 2874 y Fn(BEPOCH)345 b Fy(D)565 b FA(Besselian)30 b(ep)s(o)s(c)m(h)g (\()p Fn(e.g.)g FA(1979.3D0\))0 3142 y Fy(RETURNED)46 b FA(:)277 3288 y Fn(R2000)486 b Fy(D)565 b FA(J2000.0)33 b(FK5)e Fi(\013)f FA(\(radians\))277 3401 y Fn(D2000)483 b Fy(D)565 b FA(J2000.0)33 b(FK5)e Fi(\016)j FA(\(radians\))0 3669 y Fy(NOTES)44 b FA(:)311 3844 y(1.)i(The)31 b(ep)s(o)s(c)m(h)f (BEPOCH)h(is)f(strictly)f(sp)s(eaking)h(Besselian,)h(but)f(if)g(a)h (Julian)d(ep)s(o)s(c)m(h)j(is)f(supplied)427 3957 y(the)h(result)e (will)f(b)s(e)i(a\013ected)h(only)f(to)h(a)g(negligible)d(exten)m(t.) 311 4091 y(2.)46 b(Con)m(v)m(ersion)31 b(from)f(Besselian)g(ep)s(o)s(c) m(h)h(1950.0)i(to)f(Julian)c(ep)s(o)s(c)m(h)j(2000.0)i(only)d(is)g(pro) m(vided)f(for.)427 4204 y(Con)m(v)m(ersions)42 b(in)m(v)m(olving)e (other)i(ep)s(o)s(c)m(hs)g(will)d(require)h(use)i(of)g(the)g (appropriate)f(precession,)427 4317 y(prop)s(er)29 b(motion,)i(and)e (E-terms)i(routines)e(b)s(efore)h(and/or)g(after)h(FK45Z)g(is)e (called.)311 4451 y(3.)46 b(In)41 b(the)h(FK4)g(catalogue)h(the)f(prop) s(er)e(motions)h(of)h(stars)f(within)e(10)2905 4418 y Fm(\016)2987 4451 y FA(of)j(the)f(p)s(oles)g(do)g(not)427 4564 y(include)29 b(the)j Fn(di\013er)-5 b(ential)34 b(E-terms)39 b FA(e\013ect)33 b(and)d(should,)g(strictly)g(sp)s (eaking,)g(b)s(e)h(handled)e(in)h(a)427 4677 y(di\013eren)m(t)37 b(manner)f(from)g(stars)h(outside)f(these)h(regions.)60 b(Ho)m(w)m(ev)m(er,)40 b(giv)m(en)d(the)g(general)g(lac)m(k)427 4790 y(of)i(homogeneit)m(y)g(of)f(the)h(star)f(data)h(a)m(v)-5 b(ailable)38 b(for)g(routine)f(astrometry)-8 b(,)42 b(the)d (di\016culties)c(of)427 4903 y(handling)30 b(p)s(ositions)g(that)j(ma)m (y)g(ha)m(v)m(e)h(b)s(een)e(determined)f(from)h(astrometric)h(\014elds) d(spanning)427 5016 y(the)25 b(p)s(olar)e(and)h(non-p)s(olar)f (regions,)i(the)f(lik)m(eliho)s(o)s(d)d(that)k(the)g(di\013eren)m(tial) e(E-terms)h(e\013ect)i(w)m(as)427 5128 y(not)31 b(tak)m(en)h(in)m(to)f (accoun)m(t)h(when)d(allo)m(wing)h(for)g(prop)s(er)f(motion)i(in)e (past)i(astrometry)-8 b(,)32 b(and)e(the)427 5241 y(undesirabilit)m(y)c (of)j(a)h(discon)m(tin)m(uit)m(y)d(in)h(the)i(algorithm,)f(the)g (decision)f(has)h(b)s(een)f(made)i(in)e(this)427 5354 y(routine)c(to)h(include)d(the)j(e\013ect)h(of)f(di\013eren)m(tial)e (E-terms)h(on)h(the)f(prop)s(er)f(motions)h(for)h(all)e(stars,)427 5467 y(whether)k(p)s(olar)f(or)i(not.)40 b(A)m(t)29 b(ep)s(o)s(c)m(h)e (2000,)j(and)d(measuring)f(on)i(the)f(sky)h(rather)f(than)g(in)g(terms) 427 5580 y(of)34 b(\001)p Fi(\013)p FA(,)h(the)e(errors)g(resulting)f (from)h(this)f(simpli\014cation)e(are)k(less)f(than)g(1)h (milliarcsecond)d(in)427 5693 y(p)s(osition)e(and)h(1)g(milliarcsecond) e(p)s(er)h(cen)m(tury)i(in)e(prop)s(er)g(motion.)p eop %%Page: 74 76 74 75 bop 0 52 a FA(74)311 351 y(4.)46 b(See)31 b(also)f(sla)p Fq(_)p FA(FK425,)h(sla)p Fq(_)p FA(FK524,)h(sla)p Fq(_)p FA(FK54Z.)0 707 y Fy(REFERENCES)44 b FA(:)311 894 y(1.)i(Aoki,)31 b(S.,)f Fn(et)j(al.)p FA(,)e(1983.)h Fn(Astr.Astr)-5 b(ophys.)p FA(,)33 b Fy(128)p FA(,)e(263.)311 1039 y(2.)46 b(Smith,)29 b(C.A.)i Fn(et)h(al.)p FA(,)g(1989.)g Fn(Astr.J.)e Fy(97)p FA(,)h(265.)311 1184 y(3.)46 b(Y)-8 b(allop,)30 b(B.D.)i Fn(et)h(al.)p FA(,)e(1989.)h Fn(Astr.J.)e Fy(97)p FA(,)h(274.)311 1329 y(4.)46 b(Seidelmann,)27 b(P)-8 b(.K.)28 b(\(ed\),)i(1992.)41 b Fn(Explanatory)34 b(Supplement)e(to)f (the)g(Astr)-5 b(onomic)g(al)33 b(A)n(lmanac,)427 1442 y FA(ISBN)d(0-935702-68-7.)p 0 1555 3780 8 v 0 1668 a Fu(SLA)p Fk(_)p Fu(FK524)862 b Fj(FK5)39 b(to)f(FK4)862 b Fu(SLA)p Fk(_)p Fu(FK524)0 2018 y Fy(A)m(CTION)44 b FA(:)c(Con)m(v)m(ert)31 b(J2000.0)h(FK5)e(star)g(data)g(to)h(B1950.0)h (FK4.)41 b(This)28 b(routine)h(con)m(v)m(erts)i(stars)f(from)227 2131 y(the)35 b(new,)h(IA)m(U)f(1976,)j(FK5,)e(F)-8 b(ric)m(k)m(e)36 b(system,)h(to)e(the)g(old,)g(Bessel-New)m(com)m(b,)j(FK4)d(system.)54 b(The)227 2244 y(precepts)22 b(of)h(Smith)d Fn(et)25 b(al.)d FA(\(reference)h(1\))g(are)f(follo)m(w)m(ed,)i(using)d(the)h (implemen)m(tation)f(b)m(y)h(Y)-8 b(allop)21 b Fn(et)k(al.)227 2357 y FA(\(reference)33 b(2\))g(of)f(a)h(matrix)e(metho)s(d)h(due)f (to)i(Standish.)44 b(Kinoshita's)30 b(dev)m(elopmen)m(t)j(of)f(Ando)m (y)m(er's)227 2470 y(p)s(ost-New)m(com)m(b)f(precession)e(is)f(used.)40 b(The)29 b(n)m(umerical)f(constan)m(ts)j(from)e(Seidelmann)e Fn(et)32 b(al.)e FA(\(refer-)227 2582 y(ence)h(3\))g(are)g(used)f (canonically)-8 b(.)0 2770 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_FK524)g(\(R2000,D2000,DR2000,DD2)o(000,)o(P20)o(00,V)o(2000)o(,) 1192 2883 y(R1950,D1950,DR1950,DD1)o(950,)o(P19)o(50,V)o(1950)o(\))0 3229 y Fy(GIVEN)f FA(:)277 3375 y Fn(R2000)486 b Fy(D)565 b FA(J2000.0)33 b Fi(\013)e FA(\(radians\))277 3488 y Fn(D2000)483 b Fy(D)565 b FA(J2000.0)33 b Fi(\016)h FA(\(radians\))277 3601 y Fn(DR2000)417 b Fy(D)565 b FA(J2000.0)50 b(prop)s(er)c(motion)h (in)f Fi(\013)i FA(\(radians)e(p)s(er)g(Julian)1658 3714 y(y)m(ear\))277 3827 y Fn(DD2000)414 b Fy(D)565 b FA(J2000.0)52 b(prop)s(er)c(motion)h(in)f Fi(\016)54 b FA(\(radians)48 b(p)s(er)g(Julian)1658 3940 y(y)m(ear\))277 4053 y Fn(P2000)490 b Fy(D)565 b FA(J2000.0)33 b(parallax)c(\(arcsec\))277 4166 y Fn(V2000)484 b Fy(D)565 b FA(J2000)24 b(radial)c(v)m(elo)s(cit)m (y)i(\(km)g(s)2702 4133 y Fm(\000)p Fr(1)2796 4166 y FA(,)i(+v)m(e)f(=)e(mo)m(ving)h(a)m(w)m(a)m(y\))0 4626 y Fy(RETURNED)46 b FA(:)277 4772 y Fn(R1950)486 b Fy(D)565 b FA(B1950.0)33 b Fi(\013)e FA(\(radians\))277 4885 y Fn(D1950)483 b Fy(D)565 b FA(B1950.0)33 b Fi(\016)i FA(\(radians\))277 4998 y Fn(DR1950)417 b Fy(D)565 b FA(B1950.0)39 b(prop)s(er)c(motion)h (in)f Fi(\013)i FA(\(radians)f(p)s(er)f(tropical)1658 5111 y(y)m(ear\))277 5223 y Fn(DD1950)414 b Fy(D)565 b FA(B1950.0)41 b(prop)s(er)c(motion)i(in)e Fi(\016)42 b FA(\(radians)37 b(p)s(er)h(tropical)1658 5336 y(y)m(ear\))277 5449 y Fn(P1950)490 b Fy(D)565 b FA(B1950.0)33 b(parallax)d(\(arcsec\)) 277 5562 y Fn(V1950)484 b Fy(D)565 b FA(radial)29 b(v)m(elo)s(cit)m(y)i (\(km)f(s)2477 5529 y Fm(\000)p Fr(1)2571 5562 y FA(,)h(+v)m(e)g(=)f (mo)m(ving)g(a)m(w)m(a)m(y\))p eop %%Page: 75 77 75 76 bop 0 52 a Ft(SUN/67.45)3252 b FA(75)0 351 y Fy(NOTES)44 b FA(:)311 549 y(1.)i(The)37 b Fi(\013)h FA(prop)s(er)e(motions)h(are) 57 b(_)-45 b Fi(\013)38 b FA(rather)f(than)57 b(_)-44 b Fi(\013)15 b FA(cos)h Fi(\016)s FA(,)40 b(and)d(are)h(p)s(er)e(y)m (ear)i(rather)f(than)g(p)s(er)427 662 y(cen)m(tury)-8 b(.)311 813 y(2.)46 b(Note)f(that)e(con)m(v)m(ersion)h(from)e(Julian)f (ep)s(o)s(c)m(h)i(2000.0)j(to)d(Besselian)g(ep)s(o)s(c)m(h)g(1950.0)i (only)d(is)427 926 y(pro)m(vided)31 b(for.)46 b(Con)m(v)m(ersions)31 b(in)m(v)m(olving)g(other)h(ep)s(o)s(c)m(hs)g(will)d(require)i(use)h (of)g(the)g(appropriate)427 1039 y(precession,)c(prop)s(er)e(motion,)i (and)f(E-terms)g(routines)f(b)s(efore)h(and/or)h(after)g(FK524)h(is)d (called.)311 1190 y(3.)46 b(In)41 b(the)h(FK4)g(catalogue)h(the)f(prop) s(er)e(motions)h(of)h(stars)f(within)e(10)2905 1157 y Fm(\016)2987 1190 y FA(of)j(the)f(p)s(oles)g(do)g(not)427 1303 y(include)29 b(the)j Fn(di\013er)-5 b(ential)34 b(E-terms)39 b FA(e\013ect)33 b(and)d(should,)g(strictly)g(sp)s (eaking,)g(b)s(e)h(handled)e(in)h(a)427 1416 y(di\013eren)m(t)37 b(manner)f(from)g(stars)h(outside)f(these)h(regions.)60 b(Ho)m(w)m(ev)m(er,)40 b(giv)m(en)d(the)g(general)g(lac)m(k)427 1529 y(of)i(homogeneit)m(y)g(of)f(the)h(star)f(data)h(a)m(v)-5 b(ailable)38 b(for)g(routine)f(astrometry)-8 b(,)42 b(the)d (di\016culties)c(of)427 1642 y(handling)30 b(p)s(ositions)g(that)j(ma)m (y)g(ha)m(v)m(e)h(b)s(een)e(determined)f(from)h(astrometric)h(\014elds) d(spanning)427 1755 y(the)25 b(p)s(olar)e(and)h(non-p)s(olar)f (regions,)i(the)f(lik)m(eliho)s(o)s(d)d(that)k(the)g(di\013eren)m(tial) e(E-terms)h(e\013ect)i(w)m(as)427 1868 y(not)31 b(tak)m(en)h(in)m(to)f (accoun)m(t)h(when)d(allo)m(wing)h(for)g(prop)s(er)f(motion)i(in)e (past)i(astrometry)-8 b(,)32 b(and)e(the)427 1981 y(undesirabilit)m(y)c (of)j(a)h(discon)m(tin)m(uit)m(y)d(in)h(the)i(algorithm,)f(the)g (decision)f(has)h(b)s(een)f(made)i(in)e(this)427 2094 y(routine)c(to)h(include)d(the)j(e\013ect)h(of)f(di\013eren)m(tial)e (E-terms)h(on)h(the)f(prop)s(er)f(motions)h(for)h(all)e(stars,)427 2207 y(whether)k(p)s(olar)f(or)i(not.)40 b(A)m(t)29 b(ep)s(o)s(c)m(h)e (2000,)j(and)d(measuring)f(on)i(the)f(sky)h(rather)f(than)g(in)g(terms) 427 2319 y(of)34 b(\001)p Fi(\013)p FA(,)h(the)e(errors)g(resulting)f (from)h(this)f(simpli\014cation)e(are)k(less)f(than)g(1)h (milliarcsecond)d(in)427 2432 y(p)s(osition)e(and)h(1)g(milliarcsecond) e(p)s(er)h(cen)m(tury)i(in)e(prop)s(er)g(motion.)311 2584 y(4.)46 b(See)31 b(also)f(sla)p Fq(_)p FA(FK425,)h(sla)p Fq(_)p FA(FK45Z,)g(sla)p Fq(_)p FA(FK54Z.)0 2971 y Fy(REFERENCES)44 b FA(:)311 3169 y(1.)i(Smith,)29 b(C.A.)i Fn(et)h(al.)p FA(,)g(1989.)g Fn(Astr.J.)e Fy(97)p FA(,)h(265.)311 3320 y(2.)46 b(Y)-8 b(allop,)30 b(B.D.)i Fn(et)h(al.)p FA(,)e(1989.)h Fn(Astr.J.)e Fy(97)p FA(,)h(274.)311 3472 y(3.)46 b(Seidelmann,)27 b(P)-8 b(.K.)28 b(\(ed\),)i(1992.)41 b Fn(Explanatory)34 b(Supplement)e(to)f(the)g(Astr)-5 b(onomic)g(al)33 b(A)n(lmanac,)427 3585 y FA(ISBN)d(0-935702-68-7.)p 0 3710 3780 8 v 0 3823 a Fu(SLA)p Fk(_)p Fu(FK52H)681 b Fj(FK5)39 b(to)f(Hipparcos)680 b Fu(SLA)p Fk(_)p Fu(FK52H)0 4173 y Fy(A)m(CTION)44 b FA(:)68 b(T)-8 b(ransform)43 b(an)i(FK5)f(\(J2000\))j(p)s(osition)42 b(and)h(prop)s(er)g(motion)h(in)m(to)g(the)h(frame)f(of)g(the)227 4286 y(Hipparcos)30 b(catalogue.)0 4474 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_FK52H)g(\(R5,D5,DR5,DD5,RH,DH,DR)o(H,DD)o (H\))0 4839 y Fy(GIVEN)f FA(:)277 4985 y Fn(R5)624 b Fy(D)565 b FA(J2000.0)33 b(FK5)e Fi(\013)f FA(\(radians\))277 5098 y Fn(D5)621 b Fy(D)565 b FA(J2000.0)33 b(FK5)e Fi(\016)j FA(\(radians\))277 5211 y Fn(DR5)555 b Fy(D)565 b FA(J2000.0)36 b(FK5)f(prop)s(er)e(motion)g(in)g Fi(\013)i FA(\(radians)e(p)s(er)g (Ju-)1658 5323 y(lian)c(y)m(ear\))277 5436 y Fn(DD5)552 b Fy(D)565 b FA(J2000.0)24 b(FK5)e(prop)s(er)d(motion)j(in)e Fi(\016)25 b FA(\(radians)20 b(p)s(er)g(Julian)1658 5549 y(y)m(ear\))p eop %%Page: 76 78 76 77 bop 0 52 a FA(76)0 351 y Fy(RETURNED)46 b FA(:)277 497 y Fn(RH)602 b Fy(D)565 b FA(Hipparcos)30 b Fi(\013)g FA(\(radians\))277 610 y Fn(DH)599 b Fy(D)565 b FA(Hipparcos)30 b Fi(\016)k FA(\(radians\))277 723 y Fn(DRH)533 b Fy(D)565 b FA(Hipparcos)33 b(prop)s(er)f(motion)h(in)f Fi(\013)i FA(\(radians)e(p)s(er)g(Julian)1658 836 y(y)m(ear\))277 949 y Fn(DDH)530 b Fy(D)565 b FA(Hipparcos)35 b(prop)s(er)f(motion)h (in)f Fi(\016)40 b FA(\(radians)34 b(p)s(er)g(Julian)1658 1062 y(y)m(ear\))0 1404 y Fy(NOTES)44 b FA(:)311 1590 y(1.)i(The)37 b Fi(\013)h FA(prop)s(er)e(motions)h(are)57 b(_)-45 b Fi(\013)38 b FA(rather)f(than)57 b(_)-44 b Fi(\013)15 b FA(cos)h Fi(\016)s FA(,)40 b(and)d(are)h(p)s(er)e(y)m(ear) i(rather)f(than)g(p)s(er)427 1703 y(cen)m(tury)-8 b(.)311 1847 y(2.)46 b(The)41 b(FK5)g(to)g(Hipparcos)f(transformation)g (consists)g(of)h(a)g(pure)f(rotation)h(and)f(spin;)k(zonal)427 1960 y(errors)30 b(in)f(the)i(FK5)g(catalogue)h(are)e(not)h(tak)m(en)g (in)m(to)g(accoun)m(t.)311 2104 y(3.)46 b(The)c(adopted)h(ep)s(o)s(c)m (h)g(J2000.0)h(FK5)g(to)f(Hipparcos)f(orien)m(tation)g(and)g(spin)f(v) -5 b(alues)42 b(are)h(as)427 2217 y(follo)m(ws)30 b(\(see)h (reference\):)p 821 2346 1115 4 v 819 2459 4 113 v 971 2459 V 971 2459 V 1023 2425 a Fn(orientation)p 1509 2459 V 199 w(spin)p 1934 2459 V 821 2462 1115 4 v 819 2575 4 113 v 871 2541 a Fi(x)p 971 2575 V 184 w Fl(\000)p FA(19)p Fi(:)p FA(9)p 1509 2575 V 254 w Fl(\000)p FA(0)p Fi(:)p FA(30)p 1934 2575 V 819 2688 V 875 2654 a Fi(y)p 971 2688 V 232 w Fl(\000)p FA(9)p Fi(:)p FA(1)p 1509 2688 V 254 w(+0)p Fi(:)p FA(60)p 1934 2688 V 819 2801 V 877 2767 a Fi(z)p 971 2801 V 188 w FA(+22)p Fi(:)p FA(9)p 1509 2801 V 254 w(+0)p Fi(:)p FA(70)p 1934 2801 V 821 2804 1115 4 v 819 2917 4 113 v 971 2917 V 1151 2883 a Fn(mas)p 1509 2917 V 299 w(mas/y)p 1934 2917 V 821 2920 1115 4 v 427 3125 a FA(These)40 b(orien)m(tation)h(and)e(spin) f(comp)s(onen)m(ts)j(are)g(in)m(terpreted)e(as)i Fn(axial)h(ve)-5 b(ctors.)71 b FA(An)40 b(axial)427 3238 y(v)m(ector)35 b(p)s(oin)m(ts)d(at)i(the)g(p)s(ole)e(of)i(the)f(rotation)h(and)f(its)f (length)h(is)f(the)i(amoun)m(t)g(of)f(rotation)h(in)427 3351 y(radians.)311 3495 y(4.)46 b(See)31 b(also)f(sla)p Fq(_)p FA(FK5HZ,)g(sla)p Fq(_)p FA(H2FK5,)h(sla)p Fq(_)p FA(HFK5Z.)0 3845 y Fy(REFERENCE)44 b FA(:)d(F)-8 b(eissel,)30 b(M.)h(&)f(Mignard,)g(F.,)h(1998.,)h Fn(Astr)-5 b(on.Astr)g(ophys.)34 b Fy(331)p FA(,)d(L33-L36.)p 0 3973 3780 8 v 0 4086 a Fu(SLA)p Fk(_)p Fu(FK54Z)305 b Fj(FK5)39 b(to)f(FK4,)h(no)f(P)-10 b(.M.)39 b(or)f(P)m(arallax)302 b Fu(SLA)p Fk(_)p Fu(FK54Z)0 4436 y Fy(A)m(CTION)44 b FA(:)i(Con)m(v)m(ert)34 b(a)g(J2000.0)h(FK5)f (star)f(p)s(osition)f(to)i(B1950.0)i(FK4)d(assuming)f(FK5)i(zero)g (prop)s(er)227 4549 y(motion)e(and)f(parallax.)43 b(This)30 b(routine)g(con)m(v)m(erts)k(star)d(p)s(ositions)f(from)h(the)h(new,)g (IA)m(U)g(1976,)i(FK5,)227 4662 y(F)-8 b(ric)m(k)m(e)32 b(system)e(to)i(the)e(old,)g(Bessel-New)m(com)m(b,)i(FK4)f(system.)0 4850 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_FK54Z)g (\(R2000,D2000,BEPOCH,R19)o(50,D)o(195)o(0,DR)o(1950)o(,DD)o(1950)o(\)) 0 5193 y Fy(GIVEN)f FA(:)277 5339 y Fn(R2000)486 b Fy(D)565 b FA(J2000.0)33 b(FK5)e Fi(\013)f FA(\(radians\))277 5452 y Fn(D2000)483 b Fy(D)565 b FA(J2000.0)33 b(FK5)e Fi(\016)j FA(\(radians\))277 5565 y Fn(BEPOCH)345 b Fy(D)565 b FA(Besselian)30 b(ep)s(o)s(c)m(h)g(\()p Fn(e.g.)g FA(1950D0\))p eop %%Page: 77 79 77 78 bop 0 52 a Ft(SUN/67.45)3252 b FA(77)0 351 y Fy(RETURNED)46 b FA(:)277 497 y Fn(R1950)486 b Fy(D)565 b FA(B1950.0)33 b(FK4)e Fi(\013)g FA(at)g(ep)s(o)s(c)m(h)f(BEPOCH)g(\(radians\))277 610 y Fn(D1950)483 b Fy(D)565 b FA(B1950.0)33 b(FK4)e Fi(\016)j FA(at)d(ep)s(o)s(c)m(h)g(BEPOCH)f(\(radians\))277 723 y Fn(DR1950)417 b Fy(D)565 b FA(B1950.0)26 b(FK4)e(prop)s(er)d (motion)i(in)f Fi(\013)i FA(\(radians)e(p)s(er)g(trop-)1658 836 y(ical)30 b(y)m(ear\))277 949 y Fn(DD1950)414 b Fy(D)565 b FA(B1950.0)28 b(FK4)d(prop)s(er)f(motion)h(in)e Fi(\016)29 b FA(\(radians)24 b(p)s(er)g(trop-)1658 1062 y(ical)30 b(y)m(ear\))0 1435 y Fy(NOTES)44 b FA(:)311 1630 y(1.)i(The)37 b Fi(\013)h FA(prop)s(er)e(motions)h(are)57 b(_)-45 b Fi(\013)38 b FA(rather)f(than)57 b(_)-44 b Fi(\013)15 b FA(cos)h Fi(\016)s FA(,)40 b(and)d(are)h(p)s(er)e(y)m(ear)i(rather)f (than)g(p)s(er)427 1743 y(cen)m(tury)-8 b(.)311 1893 y(2.)46 b(Con)m(v)m(ersion)31 b(from)f(Julian)f(ep)s(o)s(c)m(h)h (2000.0)j(to)f(Besselian)e(ep)s(o)s(c)m(h)h(1950.0)i(only)d(is)g(pro)m (vided)f(for.)427 2006 y(Con)m(v)m(ersions)44 b(in)m(v)m(olving)f (other)i(ep)s(o)s(c)m(hs)f(will)d(require)j(use)g(of)g(the)h (appropriate)e(precession)427 2119 y(routines)30 b(b)s(efore)f(and)h (after)h(this)e(routine)h(is)f(called.)311 2269 y(3.)46 b(Unlik)m(e)24 b(in)f(the)h(sla)p Fq(_)p FA(FK524)h(routine,)g(the)f (FK5)h(prop)s(er)e(motions,)i(the)g(parallax)e(and)h(the)g(radial)427 2381 y(v)m(elo)s(cit)m(y)31 b(are)g(presumed)e(zero.)311 2531 y(4.)46 b(It)25 b(w)m(as)g(the)f(in)m(ten)m(tion)g(that)h(FK5)g (should)d(b)s(e)i(a)h(close)f(appro)m(ximation)g(to)h(an)f(inertial)e (frame,)k(so)427 2644 y(that)i(distan)m(t)e(ob)5 b(jects)28 b(ha)m(v)m(e)f(zero)h(prop)s(er)d(motion;)j(suc)m(h)f(ob)5 b(jects)27 b(ha)m(v)m(e)h(\(in)e(general\))h(non-zero)427 2757 y(prop)s(er)i(motion)h(in)f(FK4,)i(and)f(this)f(routine)h(returns) f(those)i Fn(\014ctitious)i(pr)-5 b(op)g(er)35 b(motions)p FA(.)311 2907 y(5.)46 b(The)25 b(p)s(osition)e(returned)h(b)m(y)g(this) g(routine)g(is)g(in)g(the)h(B1950)i(reference)e(frame)g(but)f(at)i (Besselian)427 3020 y(ep)s(o)s(c)m(h)36 b(BEPOCH.)h(F)-8 b(or)37 b(comparison)f(with)f(catalogues)j(the)f(BEPOCH)f(argumen)m(t)h (will)c(fre-)427 3133 y(quen)m(tly)d(b)s(e)g(1950D0.)311 3283 y(6.)46 b(See)31 b(also)f(sla)p Fq(_)p FA(FK425,)h(sla)p Fq(_)p FA(FK45Z,)g(sla)p Fq(_)p FA(FK524.)p 0 3423 3780 8 v 0 3536 a Fu(SLA)p Fk(_)p Fu(FK5HZ)428 b Fj(FK5)39 b(to)f(Hipparcos,)f(no)h(P)-10 b(.M.)428 b Fu(SLA)p Fk(_)p Fu(FK5HZ)0 3887 y Fy(A)m(CTION)44 b FA(:)38 b(T)-8 b(ransform)24 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y(cen)m(tury)-8 b(.)311 850 y(2.)46 b(The)41 b(FK5)g(to)g(Hipparcos)f(transformation)g (consists)g(of)h(a)g(pure)f(rotation)h(and)f(spin;)k(zonal)427 963 y(errors)30 b(in)f(the)i(FK5)g(catalogue)h(are)e(not)h(tak)m(en)g (in)m(to)g(accoun)m(t.)311 1127 y(3.)46 b(The)c(adopted)h(ep)s(o)s(c)m (h)g(J2000.0)h(FK5)g(to)f(Hipparcos)f(orien)m(tation)g(and)g(spin)f(v) -5 b(alues)42 b(are)h(as)427 1240 y(follo)m(ws)30 b(\(see)h (reference\):)p 821 1378 1115 4 v 819 1491 4 113 v 971 1491 V 971 1491 V 1023 1457 a Fn(orientation)p 1509 1491 V 199 w(spin)p 1934 1491 V 821 1494 1115 4 v 819 1607 4 113 v 871 1573 a Fi(x)p 971 1607 V 184 w Fl(\000)p FA(19)p Fi(:)p FA(9)p 1509 1607 V 254 w Fl(\000)p FA(0)p Fi(:)p FA(30)p 1934 1607 V 819 1720 V 875 1686 a Fi(y)p 971 1720 V 232 w Fl(\000)p FA(9)p Fi(:)p FA(1)p 1509 1720 V 254 w(+0)p Fi(:)p FA(60)p 1934 1720 V 819 1833 V 877 1799 a Fi(z)p 971 1833 V 188 w FA(+22)p Fi(:)p FA(9)p 1509 1833 V 254 w(+0)p Fi(:)p FA(70)p 1934 1833 V 821 1836 1115 4 v 819 1949 4 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b(sla_FLOTIN)f(\(STRING,)h(NSTRT,)g(RESLT,)g (JFLAG\))0 4227 y Fy(GIVEN)f FA(:)277 4373 y Fn(STRING)381 b Fy(C)569 b FA(string)29 b(con)m(taining)h(n)m(um)m(b)s(er)f(to)j(b)s (e)d(deco)s(ded)277 4486 y Fn(NSTR)-7 b(T)428 b Fy(I)605 b FA(p)s(oin)m(ter)30 b(to)h(where)f(deco)s(ding)f(is)g(to)i(commence) 277 4598 y Fn(RESL)-7 b(T)442 b Fy(R)567 b FA(curren)m(t)30 b(v)-5 b(alue)30 b(of)h(result)0 5040 y Fy(RETURNED)46 b FA(:)277 5186 y Fn(NSTR)-7 b(T)428 b Fy(I)605 b FA(adv)-5 b(anced)31 b(to)g(next)f(n)m(um)m(b)s(er)277 5299 y Fn(RESL)-7 b(T)442 b Fy(R)567 b FA(result)277 5412 y Fn(JFLA)n(G)436 b Fy(I)605 b FA(status:)65 b Fl(\000)p FA(1)43 b(=)f Fl(\000)p FA(OK,)f(0)i(=)f(+OK,)g(1)h(=)f(n)m(ull)e(result,)1658 5524 y(2)31 b(=)f(error)p eop %%Page: 79 81 79 80 bop 0 52 a Ft(SUN/67.45)3252 b FA(79)0 351 y Fy(NOTES)44 b FA(:)311 549 y(1.)i(The)36 b(reason)h(sla)p Fq(_)p FA(FLOTIN)f(has)g(separate)i(`OK')e(status)h(v)-5 b(alues)36 b(for)g(+)h(and)f Fl(\000)g FA(is)g(to)h(enable)427 662 y(min)m(us)28 b(zero)j(to)g(b)s(e)e(detected.)42 b(This)28 b(is)g(of)i(crucial)f(imp)s(ortance)g(when)g(deco)s(ding)g(mixed-radix) 427 774 y(n)m(um)m(b)s(ers.)68 b(F)-8 b(or)40 b(example,)j(an)c(angle)h (expressed)f(as)i(degrees,)i(arcmin)m(utes)c(and)g(arcseconds)427 887 y(ma)m(y)31 b(ha)m(v)m(e)h(a)f(leading)e(min)m(us)f(sign)i(but)f(a) i(zero)g(degrees)g(\014eld.)311 1038 y(2.)46 b(A)32 b(T)-8 b(AB)32 b(is)f(in)m(terpreted)g(as)h(a)g(space,)h(and)e(lo)m(w)m (ercase)i(c)m(haracters)g(are)f(in)m(terpreted)f(as)h(upp)s(er-)427 1151 y(case.)42 b Fn(n.b.)30 b FA(The)g(test)h(for)f(T)-8 b(AB)31 b(is)f(ASCI)s(I-sp)s(eci\014c.)311 1302 y(3.)46 b(The)38 b(basic)f(format)h(is)f(the)h(sequence)h(of)f(\014elds)e Fl(\006)p Fi(n:nx)24 b Fl(\006)h Fi(n)p FA(,)40 b(where)d Fl(\006)h FA(is)f(a)h(sign)f(c)m(haracter)427 1415 y(`+')f(or)g(`)p Fl(\000)p FA(',)i Fi(n)e FA(means)f(a)i(string)e(of)h(decimal)f (digits,)h(`.')58 b(is)35 b(a)h(decimal)f(p)s(oin)m(t,)i(and)e Fi(x)p FA(,)j(whic)m(h)427 1528 y(indicates)30 b(an)h(exp)s(onen)m(t,)h (means)f(`D')h(or)f(`E'.)h(V)-8 b(arious)31 b(com)m(binations)f(of)h (these)h(\014elds)e(can)h(b)s(e)427 1641 y(omitted,)g(and)f(em)m(b)s (edded)f(blanks)g(are)i(p)s(ermissible)26 b(in)j(certain)h(places.)311 1792 y(4.)46 b(Spaces:)506 1943 y Fl(\017)g FA(Leading)30 b(spaces)h(are)g(ignored.)506 2075 y Fl(\017)46 b FA(Em)m(b)s(edded)38 b(spaces)i(are)g(allo)m(w)m(ed)f(only)f(after)i(+,)i Fl(\000)p FA(,)g(D)d(or)h(E,)f(and)g(after)h(the)f(decimal)597 2188 y(p)s(oin)m(t)30 b(if)f(the)i(\014rst)e(sequence)i(of)f(digits)f (is)h(absen)m(t.)506 2320 y Fl(\017)46 b FA(T)-8 b(railing)38 b(spaces)i(are)h(ignored;)j(the)c(\014rst)f(signi\014es)f(end)h(of)h (deco)s(ding)f(and)g(subsequen)m(t)597 2433 y(ones)31 b(are)g(skipp)s(ed.)311 2584 y(5.)46 b(Delimiters:)506 2735 y Fl(\017)g FA(An)m(y)32 b(c)m(haracter)h(other)f(than)f(+,)p Fl(\000)p FA(,0-9,.,D,E)j(or)e(space)g(ma)m(y)g(b)s(e)f(used)g(to)h (signal)e(the)i(end)597 2847 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b(\(JFLA)m(G=2\))i(o)s(ccur)e (when:)506 5299 y Fl(\017)46 b FA(a)31 b(+,)f Fl(\000)p FA(,)h(D)f(or)h(E)f(is)f(left)h(unsatis\014ed;)f(or)506 5430 y Fl(\017)46 b FA(the)30 b(decimal)e(p)s(oin)m(t)h(is)f(presen)m (t)i(without)f(at)h(least)g(one)f(decimal)g(digit)f(b)s(efore)h(or)h (after)g(it;)597 5543 y(or)506 5675 y Fl(\017)46 b FA(an)31 b(exp)s(onen)m(t)f(more)g(than)h(100)g(has)f(b)s(een)g(presen)m(ted.)p eop %%Page: 80 82 80 81 bop 0 52 a FA(80)266 351 y(15.)46 b(When)31 b(an)f(error)h(has)f (b)s(een)g(detected,)j(NSTR)-8 b(T)30 b(is)g(left)g(p)s(oin)m(ting)f (to)j(the)f(c)m(haracter)h(follo)m(wing)427 464 y(the)41 b(last)g(one)g(used)g(b)s(efore)f(the)h(error)g(came)h(to)f(ligh)m(t.) 72 b(This)39 b(ma)m(y)j(b)s(e)e(after)i(the)f(p)s(oin)m(t)f(at)427 577 y(whic)m(h)g(a)h(more)f(sophisticated)g(program)h(could)e(ha)m(v)m (e)j(detected)g(the)f(error.)71 b(F)-8 b(or)42 b(example,)427 690 y(sla)p Fq(_)p FA(FLOTIN)26 b(do)s(es)i(not)f(detect)i(that)f 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FA(:)d(F)-8 b(eissel,)30 b(M.)h(&)f(Mignard,)g(F.,)h(1998.,)h Fn(Astr)-5 b(on.Astr)g(ophys.)34 b Fy(331)p FA(,)d(L33-L36.)p 0 469 3780 8 v 0 582 a Fu(SLA)p Fk(_)p Fu(HFK5Z)428 b Fj(Hipparcos)37 b(to)h(FK5,)h(no)f(P)-10 b(.M.)428 b Fu(SLA)p Fk(_)p Fu(HFK5Z)0 932 y Fy(A)m(CTION)44 b FA(:)53 b(T)-8 b(ransform)36 b(a)h(Hipparcos)f(star)h(p)s(osition)e(in)m(to)i(the)g(FK5)g(\(J2000\)) i(frame)d(assuming)g(zero)227 1045 y(Hipparcos)30 b(prop)s(er)f (motion.)0 1232 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_HFK5Z)g (\(RH,DH,EPOCH,R5,D5,DR5,)o(DD5\))0 1562 y Fy(GIVEN)f FA(:)277 1708 y Fn(RH)602 b Fy(D)565 b FA(Hipparcos)30 b Fi(\013)g FA(\(radians\))277 1821 y Fn(DH)599 b Fy(D)565 b FA(Hipparcos)30 b Fi(\016)k FA(\(radians\))277 1934 y Fn(EPOCH)409 b Fy(D)565 b FA(Julian)28 b(ep)s(o)s(c)m(h)i(\(TDB\))0 2252 y Fy(RETURNED)46 b FA(:)277 2398 y Fn(R5)624 b Fy(D)565 b FA(J2000.0)33 b(FK5)e Fi(\013)f FA(\(radians\))277 2510 y Fn(D5)621 b Fy(D)565 b FA(J2000.0)33 b(FK5)e Fi(\016)j FA(\(radians\))277 2623 y Fn(DR5)555 b Fy(D)565 b FA(J2000.0)36 b(FK5)f(prop)s(er)e(motion)g(in)g Fi(\013)i FA(\(radians)e(p)s(er)g (Ju-)1658 2736 y(lian)c(y)m(ear\))277 2849 y Fn(DD5)552 b Fy(D)565 b FA(FK5)22 b(J2000.0)i(prop)s(er)19 b(motion)j(in)e Fi(\016)25 b FA(\(radians)20 b(p)s(er)g(Julian)1658 2962 y(y)m(ear\))0 3280 y Fy(NOTES)44 b FA(:)311 3463 y(1.)i(The)37 b Fi(\013)h FA(prop)s(er)e(motions)h(are)57 b(_)-45 b Fi(\013)38 b FA(rather)f(than)57 b(_)-44 b Fi(\013)15 b FA(cos)h Fi(\016)s FA(,)40 b(and)d(are)h(p)s(er)e(y)m(ear)i(rather)f (than)g(p)s(er)427 3575 y(cen)m(tury)-8 b(.)311 3716 y(2.)46 b(The)41 b(FK5)g(to)g(Hipparcos)f(transformation)g(consists)g (of)h(a)g(pure)f(rotation)h(and)f(spin;)k(zonal)427 3829 y(errors)30 b(in)f(the)i(FK5)g(catalogue)h(are)e(not)h(tak)m(en)g(in)m (to)g(accoun)m(t.)311 3970 y(3.)46 b(The)c(adopted)h(ep)s(o)s(c)m(h)g (J2000.0)h(FK5)g(to)f(Hipparcos)f(orien)m(tation)g(and)g(spin)f(v)-5 b(alues)42 b(are)h(as)427 4083 y(follo)m(ws)30 b(\(see)h(reference\):)p 821 4210 1115 4 v 819 4323 4 113 v 971 4323 V 971 4323 V 1023 4289 a Fn(orientation)p 1509 4323 V 199 w(spin)p 1934 4323 V 821 4326 1115 4 v 819 4439 4 113 v 871 4405 a Fi(x)p 971 4439 V 184 w Fl(\000)p FA(19)p Fi(:)p FA(9)p 1509 4439 V 254 w Fl(\000)p FA(0)p Fi(:)p FA(30)p 1934 4439 V 819 4552 V 875 4518 a Fi(y)p 971 4552 V 232 w Fl(\000)p FA(9)p Fi(:)p FA(1)p 1509 4552 V 254 w(+0)p Fi(:)p FA(60)p 1934 4552 V 819 4665 V 877 4631 a Fi(z)p 971 4665 V 188 w FA(+22)p Fi(:)p FA(9)p 1509 4665 V 254 w(+0)p Fi(:)p FA(70)p 1934 4665 V 821 4668 1115 4 v 819 4781 4 113 v 971 4781 V 1151 4747 a Fn(mas)p 1509 4781 V 299 w(mas/y)p 1934 4781 V 821 4785 1115 4 v 427 4987 a FA(These)40 b(orien)m(tation)h(and)e(spin)f(comp)s(onen)m(ts)j(are)g (in)m(terpreted)e(as)i Fn(axial)h(ve)-5 b(ctors.)71 b FA(An)40 b(axial)427 5100 y(v)m(ector)35 b(p)s(oin)m(ts)d(at)i(the)g(p) s(ole)e(of)i(the)f(rotation)h(and)f(its)f(length)h(is)f(the)i(amoun)m (t)g(of)f(rotation)h(in)427 5213 y(radians.)40 b(The)29 b(order)h(of)h(the)f(rotations,)h(whic)m(h)e(are)i(v)m(ery)g(small,)311 5354 y(4.)46 b(It)37 b(w)m(as)g(the)g(in)m(ten)m(tion)f(that)h (Hipparcos)f(should)f(b)s(e)h(a)h(close)g(appro)m(ximation)e(to)j(an)e (inertial)427 5467 y(frame,)c(so)f(that)h(distan)m(t)f(ob)5 b(jects)31 b(ha)m(v)m(e)i(zero)f(prop)s(er)d(motion;)j(suc)m(h)f(ob)5 b(jects)31 b(ha)m(v)m(e)i(\(in)d(gener-)427 5580 y(al\))36 b(non-zero)h(prop)s(er)d(motion)i(in)f(FK5,)j(and)d(this)g(routine)g (returns)g(those)i Fn(\014ctitious)h(pr)-5 b(op)g(er)427 5693 y(motions.)p eop %%Page: 87 89 87 88 bop 0 52 a Ft(SUN/67.45)3252 b FA(87)311 351 y(5.)46 b(The)39 b(p)s(osition)f(returned)h(b)m(y)g(this)g(routine)f(is)h(in)f (the)i(FK5)g(J2000)h(reference)f(frame)g(but)f(at)427 464 y(Julian)28 b(ep)s(o)s(c)m(h)i(EPOCH.)311 601 y(6.)46 b(See)31 b(also)f(sla)p Fq(_)p FA(FK52H,)h(sla)p Fq(_)p FA(FK5HZ,)f(sla)p Fq(_)p FA(H2FK5.)0 896 y Fy(REFERENCE)44 b FA(:)d(F)-8 b(eissel,)30 b(M.)h(&)f(Mignard,)g(F.,)h(1998.,)h Fn(Astr)-5 b(on.Astr)g(ophys.)34 b Fy(331)p FA(,)d(L33-L36.)p 0 1000 3780 8 v 0 1113 a Fu(SLA)p Fk(_)p Fu(IMXV)478 b Fj(Apply)38 b(3D)h(Rev)m(erse)f(Rotation)478 b Fu(SLA)p Fk(_)p Fu(IMXV)0 1463 y Fy(A)m(CTION)44 b FA(:)c(Multiply)28 b(a)j(3-v)m(ector)i(b)m(y)d(the)h(in)m(v)m(erse)f(of)g(a)h(rotation)g (matrix)f(\(single)f(precision\).)0 1651 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_IMXV)g(\(RM,)h(VA,)f(VB\))0 1962 y Fy(GIVEN)f FA(:)277 2108 y Fn(RM)588 b Fy(R\(3,3\))352 b FA(rotation)31 b(matrix)277 2221 y Fn(V)-9 b(A)609 b Fy(R\(3\))433 b FA(v)m(ector)32 b(to)f(b)s(e)f(rotated)0 2508 y Fy(RETURNED)46 b FA(:)277 2679 y Fn(VB)604 b Fy(R\(3\))433 b FA(result)29 b(v)m(ector)0 2974 y Fy(NOTES)44 b FA(:)311 3152 y(1.)i(This)29 b(routine)g(p)s(erforms)g(the)i(op)s(eration:)597 3289 y Fy(b)g FA(=)f Fy(M)886 3256 y Fc(T)941 3289 y Fl(\001)p Fy(a)427 3425 y FA(where)g Fy(a)f FA(and)g Fy(b)h FA(are)g(the)g(3-v)m(ectors)i(V)-10 b(A)30 b(and)f(VB)i(resp)s (ectiv)m(ely)-8 b(,)30 b(and)f Fy(M)h FA(is)f(the)h(3)19 b Fl(\002)g FA(3)30 b(matrix)427 3538 y(RM.)311 3675 y(2.)46 b(The)34 b(main)g(function)f(of)i(this)e(routine)h(is)f(apply)g (an)i(in)m(v)m(erse)f(rotation;)j(under)c(these)i(circum-)427 3788 y(stances,)d Fy(M)e FA(is)g Fn(ortho)-5 b(gonal)p FA(,)34 b(with)29 b(its)g(in)m(v)m(erse)i(the)f(same)h(as)g(its)e (transp)s(ose.)311 3924 y(3.)46 b(T)-8 b(o)25 b(comply)f(with)g(the)h (ANSI)f(F)-8 b(ortran)26 b(77)f(standard,)g(V)-10 b(A)25 b(and)f(VB)i(m)m(ust)e Fy(not)h FA(b)s(e)f(the)h(same)g(ar-)427 4037 y(ra)m(y)-8 b(.)40 b(The)25 b(routine)f(is,)i(in)e(fact,)k(co)s (ded)d(so)g(as)h(to)g(w)m(ork)f(prop)s(erly)f(on)h(the)g(V)-10 b(AX)26 b(and)f(man)m(y)g(other)427 4150 y(systems)31 b(ev)m(en)g(if)e(this)g(rule)g(is)h(violated,)g(something)g(that)h(is)e Fy(not)p FA(,)i(ho)m(w)m(ev)m(er,)h(recommended.)p 0 4254 V 0 4367 a Fu(SLA)p Fk(_)p Fu(INTIN)474 b Fj(Deco)s(de)39 b(an)g(In)m(teger)f(Num)m(b)s(er)473 b Fu(SLA)p Fk(_)p Fu(INTIN)0 4717 y Fy(A)m(CTION)44 b FA(:)c(Con)m(v)m(ert)32 b(free-format)f(input)d(in)m(to)j(an)f(in)m(teger.)0 4905 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_INTIN)g(\(STRING,)f (NSTRT,)h(IRESLT,)g(JFLAG\))0 5216 y Fy(GIVEN)f FA(:)277 5362 y Fn(STRING)381 b Fy(C)569 b FA(string)29 b(con)m(taining)h(n)m (um)m(b)s(er)f(to)j(b)s(e)d(deco)s(ded)277 5475 y Fn(NSTR)-7 b(T)428 b Fy(I)605 b FA(p)s(oin)m(ter)30 b(to)h(where)f(deco)s(ding)f (is)g(to)i(commence)277 5588 y Fn(IRESL)-7 b(T)407 b Fy(I)605 b FA(curren)m(t)30 b(v)-5 b(alue)30 b(of)h(result)p eop %%Page: 88 90 88 89 bop 0 52 a FA(88)0 351 y Fy(RETURNED)46 b FA(:)277 497 y Fn(NSTR)-7 b(T)428 b Fy(I)605 b FA(adv)-5 b(anced)31 b(to)g(next)f(n)m(um)m(b)s(er)277 610 y Fn(IRESL)-7 b(T)407 b Fy(I)605 b FA(result)277 723 y Fn(JFLA)n(G)436 b Fy(I)605 b FA(status:)65 b Fl(\000)p FA(1)43 b(=)f Fl(\000)p FA(OK,)f(0)i(=)f (+OK,)g(1)h(=)f(n)m(ull)e(result,)1658 836 y(2)31 b(=)f(error)0 1221 y Fy(NOTES)44 b FA(:)311 1421 y(1.)i(The)d(reason)g(sla)p Fq(_)p FA(INTIN)e(has)i(separate)g(`OK')g(status)g(v)-5 b(alues)42 b(for)h(+)f(and)g Fl(\000)h FA(is)e(to)j(enable)427 1534 y(min)m(us)28 b(zero)j(to)g(b)s(e)e(detected.)42 b(This)28 b(is)g(of)i(crucial)f(imp)s(ortance)g(when)g(deco)s(ding)g (mixed-radix)427 1647 y(n)m(um)m(b)s(ers.)68 b(F)-8 b(or)40 b(example,)j(an)c(angle)h(expressed)f(as)i(degrees,)i(arcmin)m(utes)c (and)g(arcseconds)427 1760 y(ma)m(y)31 b(ha)m(v)m(e)h(a)f(leading)e (min)m(us)f(sign)i(but)f(a)i(zero)g(degrees)g(\014eld.)311 1912 y(2.)46 b(A)31 b(T)-8 b(AB)31 b(is)e(in)m(terpreted)h(as)g(a)h (space.)41 b Fn(n.b.)30 b FA(The)g(test)i(for)e(T)-8 b(AB)31 b(is)e(ASCI)s(I-sp)s(eci\014c.)311 2064 y(3.)46 b(The)29 b(basic)f(format)h(is)f(the)h(sequence)h(of)f(\014elds)e Fl(\006)p Fi(n)p FA(,)i(where)f Fl(\006)h FA(is)e(a)j(sign)e(c)m (haracter)i(`+')f(or)g(`)p Fl(\000)p FA(',)427 2177 y(and)h Fi(n)g FA(means)g(a)h(string)e(of)i(decimal)e(digits.)311 2329 y(4.)46 b(Spaces:)506 2482 y Fl(\017)g FA(Leading)30 b(spaces)h(are)g(ignored.)506 2614 y Fl(\017)46 b FA(Spaces)31 b(b)s(et)m(w)m(een)g(the)f(sign)g(and)f(the)i(n)m(um)m(b)s(er)e(are)i (allo)m(w)m(ed.)506 2747 y Fl(\017)46 b FA(T)-8 b(railing)38 b(spaces)i(are)h(ignored;)j(the)c(\014rst)f(signi\014es)f(end)h(of)h (deco)s(ding)f(and)g(subsequen)m(t)597 2860 y(ones)31 b(are)g(skipp)s(ed.)311 3012 y(5.)46 b(Delimiters:)506 3165 y Fl(\017)g FA(An)m(y)30 b(c)m(haracter)h(other)f(than)f(+,)p Fl(\000)p FA(,0-9)i(or)e(space)h(ma)m(y)h(b)s(e)e(used)f(to)j(signal)d (the)i(end)f(of)g(the)597 3277 y(n)m(um)m(b)s(er)g(and)h(terminate)g (deco)s(ding.)506 3410 y Fl(\017)46 b FA(Comma)34 b(is)g(recognized)g (b)m(y)g(sla)p Fq(_)p FA(INTIN)f(as)i(a)f(sp)s(ecial)f(case;)38 b(it)33 b(is)h(skipp)s(ed,)e(lea)m(ving)i(the)597 3523 y(p)s(oin)m(ter)c(on)g(the)g(next)h(c)m(haracter.)42 b(See)31 b(9,)g(b)s(elo)m(w.)506 3656 y Fl(\017)46 b FA(Deco)s(ding)31 b(will)c(in)i(all)h(cases)h(terminate)f(if)g(end)f (of)i(string)e(is)h(reac)m(hed.)311 3808 y(6.)46 b(The)30 b(sign)g(is)f(optional.)40 b(The)30 b(default)f(is)h(+.)311 3960 y(7.)46 b(A)28 b Fn(nul)5 b(l)30 b(r)-5 b(esult)37 b FA(o)s(ccurs)28 b(when)e(the)i(string)f(of)h(c)m(haracters)h(b)s (eing)d(deco)s(ded)h(do)s(es)h(not)g(b)s(egin)e(with)427 4073 y(+,)p Fl(\000)34 b FA(or)f(0-9,)k(or)c(consists)h(en)m(tirely)f (of)h(spaces.)51 b(When)34 b(this)e(condition)h(is)f(detected,)37 b(JFLA)m(G)427 4186 y(is)30 b(set)h(to)g(1)f(and)g(IRESL)-8 b(T)30 b(is)f(left)h(un)m(touc)m(hed.)311 4338 y(8.)46 b(NSTR)-8 b(T)30 b(=)g(1)h(for)f(the)g(\014rst)g(c)m(haracter)i(in)d (the)i(string.)311 4491 y(9.)46 b(On)26 b(return)g(from)g(sla)p Fq(_)p FA(INTIN,)g(NSTR)-8 b(T)26 b(is)g(set)h(ready)g(for)f(the)h (next)g(deco)s(de)g({)g(follo)m(wing)e(trail-)427 4604 y(ing)31 b(blanks)g(and)g(an)m(y)h(comma.)47 b(If)31 b(a)i(delimiter)c(other)j(than)g(comma)h(is)e(b)s(eing)f(used,)i(NSTR) -8 b(T)427 4717 y(m)m(ust)25 b(b)s(e)f(incremen)m(ted)g(b)s(efore)g (the)h(next)g(call)f(to)i(sla)p Fq(_)p 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3785 y(3.)46 b(T)-8 b(o)37 b(comply)e(with)g(the)h (ANSI)g(F)-8 b(ortran)36 b(77)h(standard,)g(FWDS)f(and)g(BKWDS)g(m)m (ust)g Fy(not)g FA(b)s(e)427 3898 y(the)h(same)g(arra)m(y)-8 b(.)61 b(The)36 b(routine)g(is,)h(in)e(fact,)40 b(co)s(ded)c(so)h(as)g (to)g(w)m(ork)g(prop)s(erly)e(on)h(the)h(V)-10 b(AX)427 4011 y(and)28 b(man)m(y)g(other)g(systems)g(ev)m(en)h(if)d(this)h(rule) g(is)g(violated,)h(something)g(that)g(is)f Fy(not)p FA(,)i(ho)m(w)m(ev) m(er,)427 4124 y(recommended.)311 4261 y(4.)46 b(See)31 b(also)f(sla)p Fq(_)p FA(FITXY,)g(sla)p Fq(_)p FA(PXY,)g(sla)p Fq(_)p FA(XY2XY,)h(sla)p Fq(_)p FA(DCMPF.)p 0 4365 V 0 4478 a Fu(SLA)p Fk(_)p Fu(KBJ)797 b Fj(Select)39 b(Ep)s(o)s(c)m(h)f (Pre\014x)798 b Fu(SLA)p Fk(_)p Fu(KBJ)0 4829 y Fy(A)m(CTION)44 b FA(:)c(Select)31 b(ep)s(o)s(c)m(h)f(pre\014x)g(`B')h(or)f(`J'.)0 5016 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_KBJ)g(\(JB,)h(E,)g(K,)g (J\))0 5329 y Fy(GIVEN)e FA(:)277 5475 y Fn(JB)624 b Fy(I)605 b FA(sla)p Fq(_)p FA(DBJIN)30 b(pre\014x)g(status:)41 b(0=none,)30 b(1=`B',)i(2=`J')277 5588 y Fn(E)674 b Fy(D)565 b FA(ep)s(o)s(c)m(h)30 b({)h(Besselian)f(or)g(Julian)p eop %%Page: 90 92 90 91 bop 0 52 a FA(90)0 351 y Fy(RETURNED)46 b FA(:)277 497 y Fn(K)666 b Fy(C)569 b FA(`B')31 b(or)g(`J')277 610 y Fn(J)688 b Fy(I)605 b FA(status:)41 b(0=OK)0 967 y Fy(NOTE)j FA(:)51 b(The)35 b(routine)f(is)h(mainly)e(in)m(tended)h (for)i(use)f(in)f(conjunction)g(with)g(the)i(sla)p Fq(_)p FA(DBJIN)f(routine.)227 1080 y(If)f(the)g(v)-5 b(alue)34 b(of)g(JB)g(indicates)f(that)h(an)g(explicit)f(B)h(or)g(J)g(pre\014x)e (w)m(as)j(detected)g(b)m(y)f(sla)p Fq(_)p FA(DBJIN,)g(a)227 1193 y(`B')h(or)e(`J')h(is)e(returned)g(to)i(matc)m(h.)51 b(If)33 b(JB)h(indicates)e(that)i(no)f(explicit)f(B)i(or)f(J)g(w)m(as)h (supplied,)d(the)227 1306 y(c)m(hoice)g(is)f(made)g(on)h(the)f(basis)f (of)i(the)f(ep)s(o)s(c)m(h)h(itself;)e(B)i(is)e(assumed)h(for)g(E)g Fi(<)25 b FA(1984,)32 b(otherwise)e(J.)p 0 1440 3780 8 v 0 1553 a Fu(SLA)p Fk(_)p Fu(M2A)-15 b(V)353 b Fj(Rotation)36 b(Matrix)h(to)h(Axial)f(V)-10 b(ector)354 b Fu(SLA)p Fk(_)p Fu(M2A)-15 b(V)0 1903 y Fy(A)m(CTION)44 b FA(:)36 b(F)-8 b(rom)21 b(a)h(rotation)f(matrix,)h(determine)f(the)g(corresp)s (onding)e(axial)h(v)m(ector)j(\(single)d(precision\).)0 2091 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_M2AV)g(\(RMAT,)g (AXVEC\))0 2442 y Fy(GIVEN)f FA(:)277 2614 y Fn(RMA)-7 b(T)462 b Fy(R\(3,3\))352 b FA(rotation)31 b(matrix)0 2978 y Fy(RETURNED)46 b FA(:)277 3150 y Fn(AXVEC)405 b Fy(R\(3\))433 b FA(axial)30 b(v)m(ector)i(\(radians\))0 3515 y Fy(NOTES)44 b FA(:)311 3704 y(1.)i(A)32 b(rotation)f(matrix)g (describ)s(es)e(a)i(rotation)h(ab)s(out)f(some)g(arbitrary)f(axis.)43 b(The)30 b(axis)h(is)f(called)427 3816 y(the)g Fn(Euler)i(axis)p FA(,)f(and)e(the)h(angle)g(through)f(whic)m(h)g(the)h(reference)g (frame)g(rotates)h(is)e(called)g(the)427 3929 y Fn(Euler)k(angle)p FA(.)42 b(The)30 b Fn(axial)k(ve)-5 b(ctor)41 b FA(returned)30 b(b)m(y)g(this)g(routine)g(has)g(the)h(same)g(direction)e(as)i(the)427 4042 y(Euler)e(axis,)h(and)g(its)g(magnitude)f(is)h(the)g(Euler)f (angle)i(in)e(radians.)311 4189 y(2.)46 b(The)35 b(magnitude)g(and)g (direction)f(of)i(the)g(axial)f(v)m(ector)i(can)f(b)s(e)f(separated)h (b)m(y)f(means)h(of)f(the)427 4302 y(routine)30 b(sla)p Fq(_)p FA(VN.)311 4448 y(3.)46 b(The)28 b(reference)g(frame)g(rotates)h (clo)s(c)m(kwise)e(as)i(seen)f(lo)s(oking)e(along)i(the)g(axial)f(v)m (ector)j(from)d(the)427 4561 y(origin.)311 4708 y(4.)46 b(If)30 b(RMA)-8 b(T)31 b(is)e(n)m(ull,)g(so)i(is)e(the)i(result.)p 0 4842 V 0 4955 a Fu(SLA)p Fk(_)p Fu(MAP)775 b Fj(Mean)39 b(to)f(Apparen)m(t)775 b Fu(SLA)p Fk(_)p Fu(MAP)0 5305 y Fy(A)m(CTION)44 b FA(:)66 b(T)-8 b(ransform)43 b(star)g([)15 b Fi(\013;)g(\016)21 b FA(])43 b(from)g(mean)g(place)h(to)g(geo)s(cen)m (tric)g(apparen)m(t.)80 b(The)43 b(reference)227 5418 y(frames)30 b(and)g(timescales)h(used)e(are)i(p)s(ost)f(IA)m(U)h(1976.) 0 5606 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_MAP)g(\(RM,)h(DM,)g (PR,)g(PD,)g(PX,)f(RV,)h(EQ,)g(DATE,)g(RA,)g(DA\))p eop %%Page: 91 93 91 92 bop 0 52 a Ft(SUN/67.45)3252 b FA(91)0 351 y Fy(GIVEN)45 b FA(:)277 497 y Fn(RM,DM)409 b Fy(D)565 b FA(mean)31 b([)15 b Fi(\013;)g(\016)20 b FA(])30 b(\(radians\))277 610 y Fn(PR,PD)449 b Fy(D)565 b FA(prop)s(er)29 b(motions:)40 b([)15 b Fi(\013;)g(\016)21 b FA(])30 b(c)m(hanges)i(p)s(er)d(Julian)f (y)m(ear)277 723 y Fn(PX)606 b Fy(D)565 b FA(parallax)29 b(\(arcsec\))277 836 y Fn(R)-9 b(V)611 b Fy(D)565 b FA(radial)29 b(v)m(elo)s(cit)m(y)i(\(km)f(s)2477 803 y Fm(\000)p Fr(1)2571 836 y FA(,)h(+v)m(e)g(if)e(receding\))277 949 y Fn(EQ)604 b Fy(D)565 b FA(ep)s(o)s(c)m(h)30 b(and)g(equino)m(x)g(of)g(star)h (data)g(\(Julian\))277 1062 y Fn(D)n(A)-7 b(TE)481 b Fy(D)565 b FA(TDB)31 b(for)f(apparen)m(t)h(place)f(\(JD)p Fl(\000)p FA(2400000.5\))0 1432 y Fy(RETURNED)46 b FA(:)277 1604 y Fn(RA,D)n(A)439 b Fy(D)565 b FA(apparen)m(t)31 b([)15 b Fi(\013;)g(\016)20 b FA(])31 b(\(radians\))0 1982 y Fy(NOTES)44 b FA(:)311 2177 y(1.)i(EQ)41 b(is)f(the)i(Julian)d (ep)s(o)s(c)m(h)i(sp)s(ecifying)e(b)s(oth)i(the)g(reference)h(frame)f (and)g(the)h(ep)s(o)s(c)m(h)f(of)g(the)427 2290 y(p)s(osition)26 b({)j(usually)c(2000.)42 b(F)-8 b(or)29 b(p)s(ositions)d(where)h(the)i (ep)s(o)s(c)m(h)e(and)h(equino)m(x)f(are)i(di\013eren)m(t,)f(use)427 2403 y(the)j(routine)e(sla)p Fq(_)p FA(PM)h(to)h(apply)e(prop)s(er)g (motion)h(corrections)h(b)s(efore)f(using)f(this)g(routine.)311 2552 y(2.)46 b(The)35 b(distinction)e(b)s(et)m(w)m(een)k(the)e (required)f(TDB)i(and)f(TT)g(is)f(alw)m(a)m(ys)i(negligible.)54 b(Moreo)m(v)m(er,)427 2665 y(for)30 b(all)g(but)f(the)i(most)g (critical)e(applications)f(UTC)i(is)g(adequate.)311 2814 y(3.)46 b(The)37 b Fi(\013)h FA(prop)s(er)e(motions)h(are)57 b(_)-45 b Fi(\013)38 b FA(rather)f(than)57 b(_)-44 b Fi(\013)15 b FA(cos)h Fi(\016)s FA(,)40 b(and)d(are)h(p)s(er)e(y)m(ear) i(rather)f(than)g(p)s(er)427 2927 y(cen)m(tury)-8 b(.)311 3077 y(4.)46 b(This)28 b(routine)h(ma)m(y)h(b)s(e)f(w)m(asteful)g(for)h (some)g(applications)d(b)s(ecause)j(it)f(recomputes)h(the)g(Earth)427 3190 y(p)s(osition/v)m(elo)s(cit)m(y)23 b(and)g(the)g(precession/n)m (utation)g(matrix)g(eac)m(h)i(time,)g(and)e(b)s(ecause)g(it)g(allo)m (ws)427 3303 y(for)37 b(parallax)f(and)h(prop)s(er)f(motion.)61 b(Where)37 b(m)m(ultiple)e(transformations)h(are)i(to)g(b)s(e)e (carried)427 3416 y(out)c(for)g(one)g(ep)s(o)s(c)m(h,)g(a)g(faster)h (metho)s(d)e(is)g(to)h(call)f(the)h(sla)p Fq(_)p FA(MAPP)-8 b(A)32 b(routine)f(once)i(and)e(then)427 3528 y(either)39 b(the)h(sla)p Fq(_)p FA(MAPQK)f(routine)f(\(whic)m(h)h(includes)e (parallax)h(and)h(prop)s(er)f(motion\))i(or)f(s-)427 3641 y(la)p Fq(_)p FA(MAPQKZ)29 b(\(whic)m(h)h(assumes)g(zero)h (parallax)e(and)h(FK5)h(prop)s(er)e(motion\).)0 4020 y Fy(REFERENCES)44 b FA(:)311 4214 y(1.)i(1984)32 b Fn(Astr)-5 b(onomic)g(al)36 b(A)n(lmanac)p FA(,)31 b(pp)e(B39-B41.)311 4364 y(2.)46 b(Lederle)30 b(&)g(Sc)m(h)m(w)m(an,)h(1984.)h 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b(of)h(mean)f(equino) m(x)g(to)h(b)s(e)f(used)g(\(Julian\))277 610 y Fn(D)n(A)-7 b(TE)481 b Fy(D)565 b FA(TDB)31 b(\(JD)p Fl(\000)p FA(2400000.5\))0 1025 y Fy(RETURNED)46 b FA(:)277 1171 y Fn(AMPRMS)325 b Fy(D\(21\))379 b FA(star-indep)s(enden)m(t)29 b(mean-to-apparen)m(t)j (parameters:)537 1283 y(\(1\))1006 b(time)30 b(in)m(terv)-5 b(al)30 b(for)g(prop)s(er)f(motion)h(\(Julian)e(y)m(ears\))499 1396 y(\(2-4\))969 b(barycen)m(tric)30 b(p)s(osition)f(of)h(the)h (Earth)f(\(A)m(U\))499 1509 y(\(5-7\))969 b(helio)s(cen)m(tric)29 b(direction)g(of)i(the)f(Earth)g(\(unit)g(v)m(ector\))537 1622 y(\(8\))1006 b(\(gra)m(vitational)52 b(radius)e(of)i(Sun\))p Fl(\002)p FA(2)p Fi(=)p FA(\(Sun-Earth)e(dis-)1658 1735 y(tance\))477 1848 y(\(9-11\))946 b Fy(v)p FA(:)41 b(barycen)m(tric)30 b(Earth)g(v)m(elo)s(cit)m(y)h(in)e(units)g(of)i(c)514 1995 y(\(12\))1658 1889 y Ff(q)p 1741 1889 302 4 v 106 x FA(1)21 b Fl(\000)f(j)p Fy(v)p Fl(j)2003 1953 y Fr(2)454 2114 y FA(\(13-21\))924 b(precession/n)m(utation)30 b(3)21 b Fl(\002)f FA(3)30 b(matrix)0 2528 y Fy(NOTES)44 b FA(:)311 2740 y(1.)i(F)-8 b(or)36 b(D)m(A)-8 b(TE,)37 b(the)e(distinction)e(b)s (et)m(w)m(een)j(the)f(required)f(TDB)h(and)g(TT)f(is)h(alw)m(a)m(ys)h (negligible.)427 2853 y(Moreo)m(v)m(er,)d(for)d(all)f(but)h(the)h(most) f(critical)g(applications)e(UTC)i(is)f(adequate.)311 3011 y(2.)46 b(The)23 b(accuracy)h(of)f(the)g(routines)f(using)g(the)h (parameters)g(AMPRMS)g(is)g(limited)d(b)m(y)j(the)g(routine)427 3124 y(sla)p Fq(_)p FA(EVP)-8 b(,)36 b(used)g(here)g(to)h(compute)f (the)h(Earth)f(p)s(osition)e(and)i(v)m(elo)s(cit)m(y)g(b)m(y)g(the)h (metho)s(ds)e(of)427 3237 y(Stump\013.)69 b(The)40 b(maxim)m(um)f (error)h(in)f(the)i(resulting)d(ab)s(erration)h(corrections)i(is)e(ab)s (out)h(0.3)427 3350 y(milliarcsecond.)311 3508 y(3.)46 b(The)23 b(v)m(ectors)j(AMPRMS\(2-4\))f(and)e(AMPRMS\(5-7\))j(are)e (referred)f(to)h(the)g(mean)g(equino)m(x)f(and)427 3621 y(equator)31 b(of)g(ep)s(o)s(c)m(h)f(EQ.)311 3779 y(4.)46 b(The)20 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FA(of)g(the)g(cen)m(tre)h(of)g(the)f(Sun's) f(disc.)39 b(The)29 b(term)g(has)g(a)h(maxim)m(um)e(v)-5 b(alue)28 b(of)427 4785 y(ab)s(out)23 b(1)720 4749 y Fh(0)m(0)724 4785 y Fi(:)p FA(85)i(at)f(this)e(radius,)i(and)e (decreases)i(to)h(zero)f(as)f(the)h(cen)m(tre)g(of)g(the)f(disc)g(is)f (approac)m(hed.)0 5269 y Fy(REFERENCES)44 b FA(:)311 5505 y(1.)i(1984)32 b Fn(Astr)-5 b(onomic)g(al)36 b(A)n(lmanac)p FA(,)31 b(pp)e(B39-B41.)311 5675 y(2.)46 b(Lederle)30 b(&)g(Sc)m(h)m(w)m(an,)h(1984.)h Fn(Astr.Astr)-5 b(ophys.)33 b Fy(134)p FA(,)e(1-6.)p eop %%Page: 94 96 94 95 bop 0 52 a FA(94)p 0 267 3780 8 v 0 380 a Fu(SLA)p Fk(_)p Fu(MAPQKZ)170 b Fj(Quic)m(k)39 b(Mean-Appt,)e(no)i(PM)g Fg(etc.)184 b Fu(SLA)p Fk(_)p Fu(MAPQKZ)0 730 y Fy(A)m(CTION)44 b FA(:)39 b(Quic)m(k)26 b(mean)g(to)i(apparen)m(t)f(place:)39 b(transform)26 b(a)h(star)g([)15 b Fi(\013;)g(\016)20 b FA(])27 b(from)f(mean)h(place)g(to)g(geo)s(cen-)227 843 y(tric)37 b(apparen)m(t)h(place,)h(giv)m(en)f(the)f(star-indep)s 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b(barycen)m(tric)30 b(Earth)g(v)m(elo)s(cit)m(y)h(in)e(units)g (of)i(c)514 2629 y(\(12\))1658 2523 y Ff(q)p 1741 2523 302 4 v 106 x FA(1)21 b Fl(\000)f(j)p Fy(v)p Fl(j)2003 2587 y Fr(2)454 2748 y FA(\(13-21\))924 b(precession/n)m(utation)30 b(3)21 b Fl(\002)f FA(3)30 b(matrix)0 3189 y Fy(RETURNED)46 b FA(:)277 3360 y Fn(RA,D)n(A)439 b Fy(D)565 b FA(apparen)m(t)31 b([)15 b Fi(\013;)g(\016)20 b FA(])31 b(\(radians\))0 3810 y Fy(NOTES)44 b FA(:)311 4032 y(1.)i(Use)32 b(of)f(this)g(routine) f(is)g(appropriate)h(when)f(e\016ciency)h(is)g(imp)s(ortan)m(t)f(and)h (where)g(man)m(y)g(star)427 4145 y(p)s(ositions,)c(all)g(with)f (parallax)h(and)g(prop)s(er)f(motion)i(either)f(zero)i(or)f(already)f (allo)m(w)m(ed)h(for,)g(and)427 4258 y(all)34 b(referred)h(to)h(the)f (same)h(equator)g(and)e(equino)m(x,)i(are)g(to)g(b)s(e)f(transformed)f (for)h(one)g(ep)s(o)s(c)m(h.)427 4371 y(The)23 b(star-indep)s(enden)m (t)g(parameters)h(can)g(b)s(e)f(obtained)g(b)m(y)g(calling)g(the)g(sla) p Fq(_)p FA(MAPP)-8 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b(lapse)h(rate)i(\(degrees)f(K)g(p)s (er)f(metre,)i Fn(e.g.)1658 4019 y FA(0.0065D0\))0 4387 y Fy(RETURNED)46 b FA(:)277 4559 y Fn(RAP,D)n(AP)315 b Fy(D)565 b FA(geo)s(cen)m(tric)32 b(apparen)m(t)e([)15 b Fi(\013;)g(\016)21 b FA(])0 4935 y Fy(NOTES)44 b FA(:)311 5128 y(1.)i(Only)39 b(the)h(\014rst)g(c)m(haracter)i(of)e(the)g(TYPE)g (argumen)m(t)h(is)e(signi\014can)m(t.)69 b(`R')41 b(or)f(`r')h (indicates)427 5241 y(that)35 b(OBS1)f(and)g(OBS2)g(are)h(the)f(observ) m(ed)h(Righ)m(t)f(Ascension)f(and)h(Declination;)h(`H')g(or)g(`h')427 5354 y(indicates)27 b(that)h(they)g(are)g(Hour)f(Angle)g(\(w)m(est)i (+v)m(e\))f(and)f(Declination;)h(an)m(ything)f(else)h(\(`A')g(or)427 5467 y(`a')h(is)f(recommended\))g(indicates)f(that)i(OBS1)f(and)g(OBS2) g(are)h(Azim)m(uth)e(\(north)h(zero,)i(east)f(is)427 5580 y(90)517 5547 y Fm(\016)558 5580 y FA(\))i(and)g(Zenith)f (Distance.)44 b(\(Zenith)31 b(distance)g(is)f(used)h(rather)g(than)g (elev)-5 b(ation)32 b(in)e(order)h(to)427 5693 y(re\015ect)g(the)g (fact)g(that)g(no)f(allo)m(w)m(ance)h(is)f(made)g(for)g(depression)f (of)i(the)f(horizon.\))p eop %%Page: 99 101 99 100 bop 0 52 a Ft(SUN/67.45)3252 b FA(99)311 351 y(2.)46 b(The)30 b(accuracy)i(of)f(the)g(result)e(is)h(limited)e(b)m(y)j(the)g (corrections)g(for)f(refraction.)41 b(Pro)m(viding)29 b(the)427 464 y(meteorological)j(parameters)f(are)g(kno)m(wn)f (accurately)h(and)f(there)h(are)g(no)f(gross)h(lo)s(cal)f(e\013ects,) 427 577 y(the)f(predicted)e(azim)m(uth)h(and)g(elev)-5 b(ation)28 b(should)e(b)s(e)i(within)e(ab)s(out)i(0)2869 540 y Fh(0)l(0)2873 577 y Fi(:)p FA(1)h(for)f Fi(\020)k(<)25 b FA(70)3367 544 y Fm(\016)3407 577 y FA(.)40 b(Ev)m(en)29 b(at)427 690 y(a)i(top)s(o)s(cen)m(tric)f(zenith)g(distance)g(of)g(90) 1800 657 y Fm(\016)1840 690 y FA(,)h(the)f(accuracy)i(in)c(elev)-5 b(ation)31 b(should)d(b)s(e)h(b)s(etter)i(than)427 803 y(1)21 b(arcmin)m(ute;)j(useful)19 b(results)g(are)i(a)m(v)-5 b(ailable)20 b(for)g(a)h(further)f(3)2512 770 y Fm(\016)2551 803 y FA(,)j(b)s(ey)m(ond)d(whic)m(h)f(the)i(sla)p Fq(_)p FA(REFR)m(O)427 916 y(routine)26 b(returns)f(a)i(\014xed)f(v)-5 b(alue)27 b(of)f(the)h(refraction.)39 b(The)27 b(complemen)m(tary)f (routines)g(sla)p Fq(_)p FA(A)m(OP)427 1029 y(\(or)39 b(sla)p Fq(_)p FA(A)m(OPQK\))f(and)g(sla)p Fq(_)p FA(O)m(AP)g(\(or)h (sla)p Fq(_)p FA(O)m(APQK\))f(are)h(self-consisten)m(t)g(to)g(b)s (etter)g(than)427 1142 y(1)31 b(microarcsecond)f(all)g(o)m(v)m(er)h (the)g(celestial)f(sphere.)311 1273 y(3.)46 b(It)c(is)e(advisable)h(to) h(tak)m(e)h(great)g(care)f(with)e(units,)j(as)f(ev)m(en)g(unlik)m(ely)d (v)-5 b(alues)41 b(of)h(the)f(input)427 1386 y(parameters)31 b(are)g(accepted)g(and)f(pro)s(cessed)g(in)f(accordance)j(with)d(the)i (mo)s(dels)e(used.)311 1517 y(4.)46 b Fn(Observe)-5 b(d)49 b FA([)15 b Fi(Az)t(;)g(E)5 b(l)42 b FA(])d(means)g(the)g(p)s(osition)d (that)k(w)m(ould)d(b)s(e)i(seen)f(b)m(y)h(a)g(p)s(erfect)g(theo)s (dolite)427 1630 y(lo)s(cated)46 b(at)g(the)g(observ)m(er.)86 b(This)44 b(is)h(related)g(to)h(the)g(observ)m(ed)g([)15 b Fi(h;)g(\016)20 b FA(])45 b(via)h(the)f(standard)427 1743 y(rotation,)30 b(using)c(the)j(geo)s(detic)g(latitude)e (\(corrected)j(for)e(p)s(olar)f(motion\),)i(while)e(the)h(observ)m(ed) 427 1856 y(HA)39 b(and)e(RA)h(are)h(related)f(simply)d(through)j(the)g (lo)s(cal)f(apparen)m(t)i(ST.)e Fn(Observe)-5 b(d)48 b FA([)15 b Fi(\013;)g(\016)20 b FA(])38 b(or)427 1969 y([)15 b Fi(h;)g(\016)20 b FA(])32 b(th)m(us)f(means)g(the)g(p)s (osition)e(that)j(w)m(ould)e(b)s(e)h(seen)g(b)m(y)g(a)g(p)s(erfect)g (equatorial)g(lo)s(cated)h(at)427 2082 y(the)25 b(observ)m(er)g(and)f (with)g(its)g(p)s(olar)g(axis)g(aligned)f(to)j(the)f(Earth's)g(axis)f (of)h(rotation)g(\()p Fn(n.b.)g FA(not)g(to)427 2195 y(the)32 b(refracted)g(p)s(ole\).)44 b(By)32 b(remo)m(ving)f(from)g (the)h(observ)m(ed)g(place)f(the)h(e\013ects)h(of)f(atmospheric)427 2308 y(refraction)e(and)g(diurnal)e(ab)s(erration,)h(the)i(geo)s(cen)m (tric)g(apparen)m(t)g([)15 b Fi(\013;)g(\016)20 b FA(])31 b(is)e(obtained.)311 2439 y(5.)46 b(F)-8 b(requen)m(tly)g(,)32 b Fn(me)-5 b(an)38 b FA(rather)30 b(than)g Fn(app)-5 b(ar)g(ent)49 b FA([)15 b Fi(\013;)g(\016)20 b FA(])31 b(will)c(b)s(e)j(required,)f(in)g(whic)m(h)g(case)j(further)427 2552 y(transformations)37 b(will)d(b)s(e)j(necessary)-8 b(.)62 b(The)37 b(sla)p Fq(_)p FA(AMP)f Fn(etc.)h FA(routines)f(will)f (con)m(v)m(ert)k(the)e(ap-)427 2665 y(paren)m(t)k([)15 b Fi(\013;)g(\016)20 b FA(])41 b(pro)s(duced)d(b)m(y)j(the)f(presen)m (t)h(routine)e(in)m(to)h(an)h(FK5)f(J2000)i(mean)f(place,)i(b)m(y)427 2778 y(allo)m(wing)30 b(for)h(the)h(Sun's)e(gra)m(vitational)i(lens)e (e\013ect,)j(ann)m(ual)e(ab)s(erration,)g(n)m(utation)g(and)g(pre-)427 2891 y(cession.)46 b(Should)29 b(FK4)k(B1950)h(co)s(ordinates)e(b)s(e)f (needed,)i(the)f(routines)f(sla)p Fq(_)p FA(FK524)h Fn(etc.)g FA(will)427 3004 y(also)f(need)f(to)h(b)s(e)f(applied.)311 3135 y(6.)46 b(T)-8 b(o)31 b(con)m(v)m(ert)h(to)f(apparen)m(t)f([)15 b Fi(\013;)g(\016)21 b FA(])30 b(the)h(co)s(ordinates)f(read)g(from)g (a)g(real)g(telescop)s(e,)h(corrections)427 3248 y(w)m(ould)43 b(ha)m(v)m(e)i(to)g(b)s(e)f(applied)e(for)h(enco)s(der)h(zero)h(p)s (oin)m(ts,)i(gear)e(and)e(enco)s(der)h(errors,)j(tub)s(e)427 3361 y(\015exure,)e(the)d(p)s(osition)e(of)j(the)f(rotator)h(axis)f (and)g(the)g(p)s(oin)m(ting)e(axis)i(relativ)m(e)g(to)h(it,)i(non-)427 3474 y(p)s(erp)s(endicularit)m(y)22 b(b)s(et)m(w)m(een)k(the)g(moun)m (ting)f(axes,)i(and)e(\014nally)f(for)h(the)h(tilt)f(of)g(the)h(azim)m (uth)f(or)427 3587 y(p)s(olar)32 b(axis)g(of)h(the)h(moun)m(ting)e (\(with)g(appropriate)g(corrections)h(for)g(moun)m(t)f(\015exures\).)48 b(Some)427 3700 y(telescop)s(es)22 b(w)m(ould,)g(of)f(course,)i (exhibit)d(other)h(prop)s(erties)e(whic)m(h)h(w)m(ould)g(need)h(to)h(b) s(e)e(accoun)m(ted)427 3813 y(for)30 b(at)i(the)e(appropriate)f(p)s (oin)m(t)h(in)f(the)h(sequence.)311 3944 y(7.)46 b(The)40 b(star-indep)s(enden)m(t)f(apparen)m(t-to-observ)m(ed-place)k (parameters)e(in)e(A)m(OPRMS)i(ma)m(y)g(b)s(e)427 4057 y(computed)31 b(b)m(y)f(means)g(of)h(the)g(sla)p Fq(_)p FA(A)m(OPP)-8 b(A)30 b(routine.)40 b(If)30 b(nothing)g(has)g(c)m (hanged)h(signi\014can)m(tly)427 4170 y(except)45 b(the)g(time,)i(the)d (sla)p Fq(_)p FA(A)m(OPP)-8 b(A)g(T)45 b(routine)e(ma)m(y)h(b)s(e)g (used)f(to)i(p)s(erform)e(the)h(requisite)427 4283 y(partial)29 b(recomputation)i(of)f(A)m(OPRMS.)311 4414 y(8.)46 b(The)26 b(D)m(A)-8 b(TE)27 b(argumen)m(t)g(is)e(UTC)h(expressed)g(as)g(an)g (MJD.)h(This)e(is,)h(strictly)f(sp)s(eaking,)i(wrong,)427 4527 y(b)s(ecause)33 b(of)g(leap)g(seconds.)48 b(Ho)m(w)m(ev)m(er,)35 b(as)e(long)g(as)g(the)g(\001UT)f(and)h(the)g(UTC)f(are)h(consisten)m (t)427 4640 y(there)j(are)h(no)f(di\016culties,)f(except)i(during)d(a)i (leap)g(second.)57 b(In)36 b(this)f(case,)j(the)f(start)f(of)g(the)427 4753 y(61st)i(second)f(of)g(the)g(\014nal)f(min)m(ute)g(should)f(b)s (egin)g(a)j(new)e(MJD)h(da)m(y)h(and)e(the)h(old)f(pre-leap)427 4866 y(\001UT)i(should)e(con)m(tin)m(ue)i(to)h(b)s(e)e(used.)63 b(As)38 b(the)g(61st)h(second)f(completes,)j(the)d(MJD)g(should)427 4979 y(rev)m(ert)31 b(to)h(the)e(start)h(of)g(the)f(da)m(y)h(as,)g(sim) m(ultaneously)-8 b(,)29 b(the)h(\001UT)g(c)m(hanges)h(b)m(y)g(one)f (second)h(to)427 5091 y(its)f(p)s(ost-leap)g(new)g(v)-5 b(alue.)311 5223 y(9.)46 b(The)27 b(\001UT)h(\(UT1)p Fl(\000)p FA(UTC\))g(is)e(tabulated)i(in)e(IERS)h(circulars)f(and)h (elsewhere.)39 b(It)28 b(increases)g(b)m(y)427 5336 y(exactly)k(one)f (second)f(at)i(the)f(end)f(of)h(eac)m(h)g(UTC)f(leap)h(second,)g(in)m (tro)s(duced)e(in)g(order)h(to)i(k)m(eep)427 5449 y(\001UT)e(within)e Fl(\006)p FA(0)1066 5416 y Fr(s)1071 5449 y Fi(:)p FA(9.)266 5580 y(10.)46 b(IMPOR)-8 b(T)g(ANT)39 b({)g(T)-8 b(AKE)38 b(CARE)g(WITH)h(THE)f(LONGITUDE)h(SIGN)f(CONVENTION.)427 5693 y(The)33 b(longitude)f(required)g(b)m(y)h(the)g(presen)m(t)h (routine)e(is)h Fy(east-p)s(ositiv)m(e)p FA(,)h(in)e(accordance)j(with) p eop %%Page: 100 102 100 101 bop 0 52 a FA(100)427 351 y(geographical)34 b(con)m(v)m(en)m (tion)g(\(and)f(righ)m(t-handed\).)49 b(In)32 b(particular,)h(note)h (that)g(the)f(longitudes)427 464 y(returned)d(b)m(y)i(the)f(sla)p Fq(_)p FA(OBS)f(routine)h(are)h(w)m(est-p)s(ositiv)m(e)f(\(as)h(in)e (the)i Fn(Astr)-5 b(onomic)g(al)36 b(A)n(lmanac)427 577 y FA(b)s(efore)30 b(1984\))j(and)c(m)m(ust)i(b)s(e)e(rev)m(ersed)i(in)e (sign)g(b)s(efore)h(use)h(in)e(the)h(presen)m(t)h(routine.)266 871 y(11.)46 b(The)37 b(p)s(olar)f(co)s(ordinates)h(XP)-8 b(,YP)38 b(can)f(b)s(e)g(obtained)f(from)h(IERS)f(circulars)f(and)i (equiv)-5 b(alen)m(t)427 984 y(publications.)36 b(The)24 b(maxim)m(um)f(amplitude)g(is)g(ab)s(out)h(0)2373 947 y Fh(0)m(0)2377 984 y Fi(:)p FA(3.)40 b(If)24 b(XP)-8 b(,YP)25 b(v)-5 b(alues)24 b(are)h(una)m(v)-5 b(ailable,)427 1097 y(use)31 b(XP=YP=0D0.)43 b(See)32 b(page)g(B60)g(of)f(the)g(1988)i Fn(Astr)-5 b(onomic)g(al)36 b(A)n(lmanac)h FA(for)30 b(a)i(de\014nition)427 1210 y(of)f(the)f(t)m(w)m(o)i(angles.)266 1503 y(12.)46 b(The)35 b(heigh)m(t)g(ab)s(o)m(v)m(e)h(sea)f(lev)m(el)g (of)g(the)g(observing)f(station,)i(HM,)g(can)f(b)s(e)g(obtained)f(from) g(the)427 1616 y Fn(Astr)-5 b(onomic)g(al)39 b(A)n(lmanac)h FA(\(Section)35 b(J)f(in)f(the)i(1988)h(edition\),)f(or)f(via)g(the)h (routine)e(sla)p Fq(_)p FA(OBS.)427 1729 y(If)h(P)-8 b(,)34 b(the)g(pressure)e(in)h(mB,)h(is)f(a)m(v)-5 b(ailable,)34 b(an)f(adequate)i(estimate)g(of)f(HM)g(can)g(b)s(e)f(obtained)427 1842 y(from)d(the)h(follo)m(wing)e(expression:)597 2136 y Fq(HM=-29.3D0*TSL*LOG\(P/1013)o(.25D)o(0\))427 2430 y FA(where)c(TSL)g(is)f(the)i(appro)m(ximate)f(sea-lev)m(el)h(air)f (temp)s(erature)g(in)f(degrees)i(K)f(\(see)i Fn(Astr)-5 b(ophysi-)427 2543 y(c)g(al)27 b(Quantities)p FA(,)f(C.W.Allen,)e(3rd)f (edition,)h Fl(x)p FA(52\).)40 b(Similarly)-8 b(,)22 b(if)g(the)i(pressure)e(P)h(is)g(not)h(kno)m(wn,)427 2656 y(it)30 b(can)h(b)s(e)f(estimated)g(from)g(the)h(heigh)m(t)f(of)g (the)h(observing)e(station,)i(HM)g(as)g(follo)m(ws:)597 2949 y Fq(P=1013.25D0*EXP\(-HM/\(29.3)o(D0*T)o(SL\)\))427 3243 y FA(Note,)26 b(ho)m(w)m(ev)m(er,)f(that)e(the)f(refraction)g(is)f (prop)s(ortional)f(to)j(the)g(pressure)e(and)g(that)i(an)f(accurate)427 3356 y(P)30 b(v)-5 b(alue)30 b(is)g(imp)s(ortan)m(t)f(for)h(precise)g (w)m(ork.)266 3650 y(13.)46 b(The)31 b(azim)m(uths)g Fn(etc.)g FA(used)g(b)m(y)g(the)h(presen)m(t)f(routine)g(are)h(with)e (resp)s(ect)h(to)h(the)g(celestial)f(p)s(ole.)427 3763 y(Corrections)f(from)g(the)h(terrestrial)e(p)s(ole)g(can)i(b)s(e)f (computed)g(using)f(sla)p Fq(_)p FA(POLMO.)p 0 4191 3780 8 v 0 4304 a Fu(SLA)p Fk(_)p Fu(O)l(APQK)334 b Fj(Quic)m(k)39 b(Observ)m(ed)f(to)g(Apparen)m(t)334 b Fu(SLA)p Fk(_)p Fu(O)l(APQK)0 4654 y Fy(A)m(CTION)44 b FA(:)c(Quic)m(k)30 b(observ)m(ed)h(to)g(apparen)m(t)f(place.)0 4842 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_OAPQK)g(\(TYPE,)g(OB1,)g(OB2,)h(AOPRMS,)f (RAP,)g(DAP\))0 5634 y Fy(GIVEN)f FA(:)p eop %%Page: 101 103 101 102 bop 0 52 a Ft(SUN/67.45)3206 b FA(101)277 339 y Fn(TYPE)479 b Fy(C*\(*\))383 b FA(t)m(yp)s(e)31 b(of)f(co)s (ordinates)g({)h(`R',)g(`H')g(or)f(`A')h(\(see)h(b)s(elo)m(w\))277 452 y Fn(OB1)556 b Fy(D)565 b FA(observ)m(ed)53 b(Az,)60 b(HA)53 b(or)g(RA)g(\(radians;)64 b(Az)53 b(is)g(N=0,)1658 565 y(E=90)1881 532 y Fm(\016)1921 565 y FA(\))277 678 y Fn(OB2)556 b Fy(D)565 b FA(observ)m(ed)31 b(zenith)e(distance)h(or)h Fi(\016)j FA(\(radians\))277 791 y Fn(A)n(OPRMS)339 b Fy(D\(14\))379 b FA(star-indep)s(enden)m(t)29 b(apparen)m(t-to-observ)m (ed)j(parameter-)1658 904 y(s:)537 1016 y(\(1\))1006 b(geo)s(detic)31 b(latitude)f(\(radians\))502 1129 y(\(2,3\))971 b(sine)29 b(and)h(cosine)g(of)h(geo)s(detic)g(latitude)537 1242 y(\(4\))1006 b(magnitude)30 b(of)g(diurnal)e(ab)s(erration)h(v)m (ector)537 1355 y(\(5\))1006 b(heigh)m(t)30 b(\(HM\))537 1468 y(\(6\))1006 b(am)m(bien)m(t)31 b(temp)s(erature)f(\(TDK\))537 1581 y(\(7\))1006 b(pressure)29 b(\(PMB\))537 1694 y(\(8\))1006 b(relativ)m(e)31 b(h)m(umidit)m(y)d(\(RH\))537 1807 y(\(9\))1006 b(w)m(a)m(v)m(elength)32 b(\(WL\))514 1920 y(\(10\))984 b(lapse)30 b(rate)h(\(TLR\))456 2033 y(\(11,12\))927 b(refraction)30 b(constan)m(ts)i(A)e(and)g(B)h(\(radians\))514 2146 y(\(13\))984 b(longitude)41 b(+)h(eqn)h(of)f(equino)m(xes)g(+)h (\\sidereal)e(\001UT")1658 2258 y(\(radians\))514 2371 y(\(14\))984 b(lo)s(cal)30 b(apparen)m(t)g(sidereal)f(time)h (\(radians\))0 2726 y Fy(RETURNED)46 b FA(:)277 2897 y Fn(RAP,D)n(AP)315 b Fy(D)565 b FA(geo)s(cen)m(tric)32 b(apparen)m(t)e([)15 b Fi(\013;)g(\016)21 b FA(])0 3260 y Fy(NOTES)44 b FA(:)311 3448 y(1.)i(Only)39 b(the)h(\014rst)g(c)m (haracter)i(of)e(the)g(TYPE)g(argumen)m(t)h(is)e(signi\014can)m(t.)69 b(`R')41 b(or)f(`r')h(indicates)427 3561 y(that)35 b(OBS1)f(and)g(OBS2) g(are)h(the)f(observ)m(ed)h(Righ)m(t)f(Ascension)f(and)h(Declination;)h (`H')g(or)g(`h')427 3674 y(indicates)27 b(that)h(they)g(are)g(Hour)f (Angle)g(\(w)m(est)i(+v)m(e\))f(and)f(Declination;)h(an)m(ything)f (else)h(\(`A')g(or)427 3786 y(`a')h(is)f(recommended\))g(indicates)f (that)i(OBS1)f(and)g(OBS2)g(are)h(Azim)m(uth)e(\(north)h(zero,)i(east)f (is)427 3899 y(90)517 3866 y Fm(\016)558 3899 y FA(\))i(and)g(Zenith)f (Distance.)44 b(\(Zenith)31 b(distance)g(is)f(used)h(rather)g(than)g (elev)-5 b(ation)32 b(in)e(order)h(to)427 4012 y(re\015ect)g(the)g (fact)g(that)g(no)f(allo)m(w)m(ance)h(is)f(made)g(for)g(depression)f (of)i(the)f(horizon.\))311 4159 y(2.)46 b(The)30 b(accuracy)i(of)f(the) g(result)e(is)h(limited)e(b)m(y)j(the)g(corrections)g(for)f (refraction.)41 b(Pro)m(viding)29 b(the)427 4271 y(meteorological)j (parameters)f(are)g(kno)m(wn)f(accurately)h(and)f(there)h(are)g(no)f (gross)h(lo)s(cal)f(e\013ects,)427 4384 y(the)f(predicted)e(azim)m(uth) h(and)g(elev)-5 b(ation)28 b(should)e(b)s(e)i(within)e(ab)s(out)i(0) 2869 4347 y Fh(0)l(0)2873 4384 y Fi(:)p FA(1)h(for)f Fi(\020)k(<)25 b FA(70)3367 4351 y Fm(\016)3407 4384 y FA(.)40 b(Ev)m(en)29 b(at)427 4497 y(a)i(top)s(o)s(cen)m(tric)f (zenith)g(distance)g(of)g(90)1800 4464 y Fm(\016)1840 4497 y FA(,)h(the)f(accuracy)i(in)c(elev)-5 b(ation)31 b(should)d(b)s(e)h(b)s(etter)i(than)427 4610 y(1)21 b(arcmin)m(ute;)j (useful)19 b(results)g(are)i(a)m(v)-5 b(ailable)20 b(for)g(a)h(further) f(3)2512 4577 y Fm(\016)2551 4610 y FA(,)j(b)s(ey)m(ond)d(whic)m(h)f (the)i(sla)p Fq(_)p FA(REFR)m(O)427 4723 y(routine)26 b(returns)f(a)i(\014xed)f(v)-5 b(alue)27 b(of)f(the)h(refraction.)39 b(The)27 b(complemen)m(tary)f(routines)g(sla)p Fq(_)p FA(A)m(OP)427 4836 y(\(or)39 b(sla)p Fq(_)p FA(A)m(OPQK\))f(and)g(sla)p Fq(_)p FA(O)m(AP)g(\(or)h(sla)p Fq(_)p FA(O)m(APQK\))f(are)h (self-consisten)m(t)g(to)g(b)s(etter)g(than)427 4949 y(1)31 b(microarcsecond)f(all)g(o)m(v)m(er)h(the)g(celestial)f(sphere.) 311 5095 y(3.)46 b(It)c(is)e(advisable)h(to)h(tak)m(e)h(great)g(care)f (with)e(units,)j(as)f(ev)m(en)g(unlik)m(ely)d(v)-5 b(alues)41 b(of)h(the)f(input)427 5208 y(parameters)31 b(are)g(accepted)g(and)f (pro)s(cessed)g(in)f(accordance)j(with)d(the)i(mo)s(dels)e(used.)311 5354 y(4.)46 b Fn(Observe)-5 b(d)49 b FA([)15 b Fi(Az)t(;)g(E)5 b(l)42 b FA(])d(means)g(the)g(p)s(osition)d(that)k(w)m(ould)d(b)s(e)i (seen)f(b)m(y)h(a)g(p)s(erfect)g(theo)s(dolite)427 5467 y(lo)s(cated)46 b(at)g(the)g(observ)m(er.)86 b(This)44 b(is)h(related)g(to)h(the)g(observ)m(ed)g([)15 b Fi(h;)g(\016)20 b FA(])45 b(via)h(the)f(standard)427 5580 y(rotation,)30 b(using)c(the)j(geo)s(detic)g(latitude)e(\(corrected)j(for)e(p)s(olar)f (motion\),)i(while)e(the)h(observ)m(ed)427 5693 y(HA)39 b(and)e(RA)h(are)h(related)f(simply)d(through)j(the)g(lo)s(cal)f (apparen)m(t)i(ST.)e Fn(Observe)-5 b(d)48 b FA([)15 b Fi(\013;)g(\016)20 b FA(])38 b(or)p eop %%Page: 102 104 102 103 bop 0 52 a FA(102)427 351 y([)15 b Fi(h;)g(\016)20 b FA(])32 b(th)m(us)f(means)g(the)g(p)s(osition)e(that)j(w)m(ould)e(b)s (e)h(seen)g(b)m(y)g(a)g(p)s(erfect)g(equatorial)g(lo)s(cated)h(at)427 464 y(the)25 b(observ)m(er)g(and)f(with)g(its)g(p)s(olar)g(axis)g (aligned)f(to)j(the)f(Earth's)g(axis)f(of)h(rotation)g(\()p Fn(n.b.)g FA(not)g(to)427 577 y(the)32 b(refracted)g(p)s(ole\).)44 b(By)32 b(remo)m(ving)f(from)g(the)h(observ)m(ed)g(place)f(the)h (e\013ects)h(of)f(atmospheric)427 690 y(refraction)e(and)g(diurnal)e (ab)s(erration,)h(the)i(geo)s(cen)m(tric)g(apparen)m(t)g([)15 b Fi(\013;)g(\016)20 b FA(])31 b(is)e(obtained.)311 833 y(5.)46 b(F)-8 b(requen)m(tly)g(,)32 b Fn(me)-5 b(an)38 b FA(rather)30 b(than)g Fn(app)-5 b(ar)g(ent)49 b FA([)15 b Fi(\013;)g(\016)20 b FA(])31 b(will)c(b)s(e)j(required,)f(in)g(whic)m (h)g(case)j(further)427 946 y(transformations)37 b(will)d(b)s(e)j (necessary)-8 b(.)62 b(The)37 b(sla)p Fq(_)p FA(AMP)f Fn(etc.)h FA(routines)f(will)f(con)m(v)m(ert)k(the)e(ap-)427 1059 y(paren)m(t)k([)15 b Fi(\013;)g(\016)20 b FA(])41 b(pro)s(duced)d(b)m(y)j(the)f(presen)m(t)h(routine)e(in)m(to)h(an)h (FK5)f(J2000)i(mean)f(place,)i(b)m(y)427 1171 y(allo)m(wing)30 b(for)h(the)h(Sun's)e(gra)m(vitational)i(lens)e(e\013ect,)j(ann)m(ual)e (ab)s(erration,)g(n)m(utation)g(and)g(pre-)427 1284 y(cession.)46 b(Should)29 b(FK4)k(B1950)h(co)s(ordinates)e(b)s(e)f(needed,)i(the)f (routines)f(sla)p Fq(_)p FA(FK524)h Fn(etc.)g FA(will)427 1397 y(also)f(need)f(to)h(b)s(e)f(applied.)311 1540 y(6.)46 b(T)-8 b(o)31 b(con)m(v)m(ert)h(to)f(apparen)m(t)f([)15 b Fi(\013;)g(\016)21 b FA(])30 b(the)h(co)s(ordinates)f(read)g(from)g (a)g(real)g(telescop)s(e,)h(corrections)427 1653 y(w)m(ould)43 b(ha)m(v)m(e)i(to)g(b)s(e)f(applied)e(for)h(enco)s(der)h(zero)h(p)s (oin)m(ts,)i(gear)e(and)e(enco)s(der)h(errors,)j(tub)s(e)427 1766 y(\015exure,)e(the)d(p)s(osition)e(of)j(the)f(rotator)h(axis)f (and)g(the)g(p)s(oin)m(ting)e(axis)i(relativ)m(e)g(to)h(it,)i(non-)427 1879 y(p)s(erp)s(endicularit)m(y)22 b(b)s(et)m(w)m(een)k(the)g(moun)m (ting)f(axes,)i(and)e(\014nally)f(for)h(the)h(tilt)f(of)g(the)h(azim)m (uth)f(or)427 1992 y(p)s(olar)32 b(axis)g(of)h(the)h(moun)m(ting)e (\(with)g(appropriate)g(corrections)h(for)g(moun)m(t)f(\015exures\).)48 b(Some)427 2105 y(telescop)s(es)22 b(w)m(ould,)g(of)f(course,)i (exhibit)d(other)h(prop)s(erties)e(whic)m(h)h(w)m(ould)g(need)h(to)h(b) s(e)e(accoun)m(ted)427 2218 y(for)30 b(at)i(the)e(appropriate)f(p)s (oin)m(t)h(in)f(the)h(sequence.)311 2360 y(7.)46 b(The)40 b(star-indep)s(enden)m(t)f(apparen)m(t-to-observ)m(ed-place)k (parameters)e(in)e(A)m(OPRMS)i(ma)m(y)g(b)s(e)427 2473 y(computed)31 b(b)m(y)f(means)g(of)h(the)g(sla)p Fq(_)p FA(A)m(OPP)-8 b(A)30 b(routine.)40 b(If)30 b(nothing)g(has)g(c)m (hanged)h(signi\014can)m(tly)427 2586 y(except)45 b(the)g(time,)i(the)d (sla)p Fq(_)p FA(A)m(OPP)-8 b(A)g(T)45 b(routine)e(ma)m(y)h(b)s(e)g (used)f(to)i(p)s(erform)e(the)h(requisite)427 2699 y(partial)29 b(recomputation)i(of)f(A)m(OPRMS.)311 2842 y(8.)46 b(The)31 b(azim)m(uths)g Fn(etc.)g FA(used)g(b)m(y)g(the)h(presen)m(t)f(routine) g(are)h(with)e(resp)s(ect)h(to)h(the)g(celestial)f(p)s(ole.)427 2955 y(Corrections)f(from)g(the)h(terrestrial)e(p)s(ole)g(can)i(b)s(e)f (computed)g(using)f(sla)p Fq(_)p FA(POLMO.)p 0 3077 3780 8 v 0 3190 a Fu(SLA)p Fk(_)p Fu(OBS)677 b Fj(Observ)-7 b(atory)37 b(P)m(arameters)675 b Fu(SLA)p Fk(_)p Fu(OBS)0 3541 y Fy(A)m(CTION)44 b FA(:)39 b(Lo)s(ok)27 b(up)f(an)h(en)m(try)h (in)e(a)h(standard)g(list)e(of)j(groundbased)e(observing)g(stations)h (parameters.)0 3728 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_OBS)g(\(N,)h(C,)g(NAME,)g(W,)g(P,)g(H\))0 4065 y Fy(GIVEN)e FA(:)277 4236 y Fn(N)668 b Fy(I)605 b FA(n)m(um)m(b)s(er) 29 b(sp)s(ecifying)f(observing)i(station)0 4575 y Fy(GIVEN)k(or)h (RETURNED)46 b FA(:)277 4746 y Fn(C)671 b Fy(C*\(*\))383 b FA(iden)m(ti\014er)29 b(sp)s(ecifying)f(observing)h(station)0 5085 y Fy(RETURNED)46 b FA(:)277 5231 y Fn(NAME)456 b Fy(C*\(*\))383 b FA(name)31 b(of)f(sp)s(eci\014ed)f(observing)g (station)277 5344 y Fn(W)645 b Fy(D)565 b FA(longitude)29 b(\(radians,)h(w)m(est)h(+v)m(e\))277 5457 y Fn(P)674 b Fy(D)565 b FA(geo)s(detic)31 b(latitude)f(\(radians,)f(north)h(+v)m (e\))277 5570 y Fn(H)668 b Fy(D)565 b FA(heigh)m(t)30 b(ab)s(o)m(v)m(e)i(sea)f(lev)m(el)f(\(metres\))p eop %%Page: 103 105 103 104 bop 0 52 a Ft(SUN/67.45)3206 b FA(103)0 351 y Fy(NOTES)44 b FA(:)311 542 y(1.)i(Station)26 b(iden)m(ti\014ers)f(C)h (ma)m(y)h(b)s(e)e(up)h(to)h(10)g(c)m(haracters)h(long,)f(and)e(station) i(names)f(NAME)h(ma)m(y)427 655 y(b)s(e)j(up)f(to)i(40)h(c)m(haracters) f(long.)311 802 y(2.)46 b(C)23 b(and)f(N)h(are)h Fn(alternative)31 b FA(w)m(a)m(ys)24 b(of)f(sp)s(ecifying)e(the)i(observing)f(station.)38 b(The)23 b(C)g(option,)h(whic)m(h)427 915 y(is)k(the)h(most)g (generally)e(useful,)h(ma)m(y)h(b)s(e)f(selected)h(b)m(y)g(sp)s (ecifying)d(an)i(N)h(v)-5 b(alue)28 b(of)h(zero)g(or)g(less.)427 1028 y(If)34 b(N)f(is)g(1)h(or)g(more,)h(the)f(parameters)g(of)g(the)g (Nth)g(station)g(in)e(the)i(curren)m(tly)f(supp)s(orted)f(list)427 1141 y(are)c(in)m(terrogated,)h(and)e(the)g(station)h(iden)m(ti\014er)d 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(names)g(and)f(other)i(details)e(are)h(sub)5 b(ject)22 b(to)h(c)m(hange)g(and)e(should)427 2261 y(not)31 b(b)s(e)f(hardwired)d (in)m(to)k(application)d(programs.)311 2408 y(6.)46 b(All)29 b(station)h(iden)m(ti\014ers)e(C)h(are)h(upp)s(ercase)f(only;)h(lo)m(w) m(er)g(case)h(c)m(haracters)g(m)m(ust)f(b)s(e)f(con)m(v)m(erted)427 2521 y(to)j(upp)s(ercase)e(b)m(y)h(the)g(calling)f(program.)42 b(The)30 b(station)i(names)e(returned)g(ma)m(y)i(con)m(tain)f(b)s(oth) 427 2634 y(upp)s(er-)44 b(and)h(lo)m(w)m(ercase.)87 b(All)44 b(c)m(haracters)i(up)f(to)h(the)f(\014rst)g(space)h(are)g(c)m(hec)m(k)m (ed;)55 b(th)m(us)45 b(an)427 2747 y(abbreviated)20 b(ID)h(will)d (return)h(the)i(parameters)g(for)f(the)h(\014rst)e(station)i(in)e(the)i (list)e(whic)m(h)g(matc)m(hes)427 2860 y(the)i(abbreviation)e (supplied,)h(and)g(no)g(station)h(in)e(the)i(list)e(will)f(ev)m(er)j (con)m(tain)g(em)m(b)s(edded)f(spaces.)427 2973 y(C)30 b(m)m(ust)g(not)h(ha)m(v)m(e)h(leading)d(spaces.)311 3121 y(7.)46 b(IMPOR)-8 b(T)g(ANT)28 b({)f(BEW)-10 b(ARE)28 b(OF)f(THE)g(LONGITUDE)h(SIGN)f(CONVENTION.)f(The)h(lon-)427 3233 y(gitude)34 b(returned)g(b)m(y)h(sla)p Fq(_)p FA(OBS)e(is)h Fy(w)m(est-p)s(ositiv)m(e)p FA(,)h(follo)m(wing)f(the)g(pre-1984)j Fn(Astr)-5 b(onomic)g(al)427 3346 y(A)n(lmanac)p FA(.)41 b(Ho)m(w)m(ev)m(er,)31 b(this)c(sign)h(con)m(v)m(en)m(tion)h(is)f (left-handed)f(and)h(is)f(the)h(opp)s(osite)g(of)h(the)f(one)427 3459 y(no)m(w)37 b(used;)i(elsewhere)d(in)g(SLALIB)g(the)g(preferable)g (east-p)s(ositiv)m(e)h(con)m(v)m(en)m(tion)h(is)d(used.)59 b(In)427 3572 y(particular,)36 b(note)g(that)g(for)f(use)g(in)f(sla)p Fq(_)p FA(A)m(OP)-8 b(,)36 b(sla)p Fq(_)p FA(A)m(OPP)-8 b(A)35 b(and)g(sla)p Fq(_)p FA(O)m(AP)g(the)g(sign)g(of)g(the)427 3685 y(longitude)29 b(m)m(ust)i(b)s(e)e(rev)m(ersed.)311 3833 y(8.)46 b(Users)40 b(are)g(urged)f(to)h(inform)e(the)i(author)f (of)h(an)m(y)g(impro)m(v)m(emen)m(ts)g(they)f(w)m(ould)g(lik)m(e)g(to)h (see)427 3946 y(made.)h(F)-8 b(or)31 b(example:)506 4093 y 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105 107 105 106 bop 0 52 a Ft(SUN/67.45)3206 b FA(105)227 351 y(P)-8 b(ALOMAR48)288 b(P)m(alomar)31 b(48-inc)m(h)g(Sc)m(hmidt)227 464 y(P)-8 b(ALOMAR60)288 b(P)m(alomar)31 b(60)g(inc)m(h)227 577 y(P)-8 b(ARKES)473 b(P)m(ark)m(es)32 b(64)f(metre)227 690 y(QUEBEC1.6)338 b(Queb)s(ec)30 b(1.6)h(metre)227 803 y(SAA)m(O74)501 b(Sutherland)28 b(74)j(inc)m(h)227 916 y(SANPM83)424 b(San)30 b(P)m(edro)h(Martir)f(83)h(inc)m(h)227 1029 y(ST.ANDREWS)226 b(St)30 b(Andrews)f(Univ)m(ersit)m(y)h(Observ)-5 b(atory)227 1142 y(STEW)-10 b(ARD90)290 b(Stew)m(ard)30 b(90)i(inc)m(h)227 1255 y(STR)m(OMLO74)293 b(Moun)m(t)31 b(Stromlo)f(74)h(inc)m(h)227 1367 y(SUBAR)m(U)463 b(Subaru)29 b(8)h(metre)227 1480 y(SUGAR)m(GR)m(O)m(VE)191 b(Sugar)30 b(Gro)m(v)m(e)i(150)g(fo)s(ot)227 1593 y(T)-8 b(A)m(UTNBG)386 b(T)-8 b(auten)m(burg)30 b(2)h(metre)227 1706 y(T)-8 b(A)m(UTSCHM)321 b(T)-8 b(auten)m(b)s(erg)31 b(1.34)h(metre)f(Sc)m (hmidt)227 1819 y(TIDBINBLA)324 b(Tidbin)m(billa)25 b(64)32 b(metre)227 1932 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b([)p Fi(\025;)15 b(\036)p FA(])31 b Fn(etc.)p FA(.)311 3024 y(2.)46 b(The)30 b(result)e(is)h(the) h(b)s(earing)f(\(p)s(osition)f(angle\),)j(in)d(radians,)h(of)h(p)s(oin) m(t)f(V2)h(as)g(seen)g(from)f(p)s(oin)m(t)427 3137 y(V1.)48 b(It)33 b(is)f(in)f(the)i(range)g Fl(\006)p Fi(\031)s FA(.)47 b(The)33 b(sense)f(is)g(suc)m(h)g(that)h(if)f(V2)h(is)f(a)h (small)e(distance)h(due)g(east)427 3250 y(of)f(V1)g(the)f(result)g(is)f (ab)s(out)h(+)p Fi(\031)s(=)p FA(2.)41 b(Zero)31 b(is)e(returned)g(if)h (the)g(t)m(w)m(o)i(p)s(oin)m(ts)d(are)i(coinciden)m(t.)311 3406 y(3.)46 b(The)37 b(routine)g(sla)p Fq(_)p FA(BEAR)g(p)s(erforms)f (an)h(equiv)-5 b(alen)m(t)37 b(function)f(except)j(that)f(the)g(p)s (oin)m(ts)e(are)427 3519 y(sp)s(eci\014ed)29 b(in)g(the)i(form)e(of)i (spherical)e(co)s(ordinates.)p 0 3672 V 0 3785 a Fu(SLA)p Fk(_)p Fu(PCD)656 b Fj(Apply)39 b(Radial)e(Distortion)655 b Fu(SLA)p Fk(_)p Fu(PCD)0 4136 y Fy(A)m(CTION)44 b FA(:)c(Apply)29 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Fn(J1)642 b Fy(I)605 b FA(\015ag:)41 b(0)31 b(=)f(solution)f(1)i(is)e(v)-5 b(alid)277 4689 y Fn(H2)622 b Fy(D)565 b FA(hour)30 b(angle:)40 b(second)31 b(solution)e(if)g(an)m(y)277 4802 y Fn(J2)642 b Fy(I)605 b FA(\015ag:)41 b(0)31 b(=)f(solution)f(2)i(is)e(v)-5 b(alid)p 0 4955 V 0 5068 a Fu(SLA)p Fk(_)p Fu(PDQ2H)543 b Fj(H.A.)38 b(for)f(a)i(Giv)m(en)f(P)-10 b(.A.)543 b Fu(SLA)p Fk(_)p Fu(PDQ2H)0 5418 y Fy(A)m(CTION)44 b FA(:)c(Hour)31 b(Angle)f(corresp)s(onding)e(to)j(a)g(giv)m(en)f(parallactic)g(angle)g (\(double)g(precision\).)0 5606 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_PDQ2H)g(\(P,)h(D,)g(Q,)g(H1,)g(J1,)g(H2,)g(J2\))p eop %%Page: 108 110 108 109 bop 0 52 a FA(108)0 351 y Fy(GIVEN)45 b FA(:)277 497 y Fn(P)674 b Fy(D)565 b FA(latitude)277 610 y Fn(D)667 b Fy(D)565 b FA(declination)277 723 y Fn(Q)666 b Fy(D)565 b FA(azim)m(uth)0 1088 y Fy(RETURNED)46 b FA(:)277 1234 y Fn(H1)622 b Fy(D)565 b FA(hour)30 b(angle:)40 b(\014rst)30 b(solution)f(if)g(an)m(y)277 1347 y Fn(J1)642 b 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(eed)f(without)p eop %%Page: 113 115 113 114 bop 0 52 a Ft(SUN/67.45)3206 b FA(113)427 351 y(signi\014can)m(tly)39 b(degrading)h(accuracy)-8 b(.)72 b(A)m(t)42 b(a)e(lo)m(w)h(frequency)-8 b(,)43 b(the)e(routine)e(sla)p Fq(_)p FA(PLANET)g(is)427 464 y(called)30 b(to)h(generate)g(up)s(dated) e(p)s(osition+v)m(elo)s(cit)m(y)g(\\state)j(v)m(ectors".)42 b(The)30 b(only)f(task)i(remain-)427 577 y(ing)38 b(to)i(b)s(e)e (carried)g(out)h(at)h(the)f(full)e(frequency)h(\()p Fn(i.e.)g FA(at)i(eac)m(h)g(in)m(tegration)f(step\))g(is)f(to)i(use)427 690 y(the)33 b(state)h(v)m(ectors)g(to)f(extrap)s(olate)h(the)e (planetary)g(p)s(ositions.)46 b(In)31 b(place)i(of)g(a)g(strictly)e (linear)427 803 y(extrap)s(olation,)g(some)g(allo)m(w)m(ance)g(is)f (made)g(for)h(the)g(curv)-5 b(ature)30 b(of)h(the)g(orbit)e(b)m(y)i (scaling)f(bac)m(k)427 916 y(the)h(radius)d(v)m(ector)k(as)f(the)f (linear)f(extrap)s(olation)h(go)s(es)h(o\013)g(at)g(a)g(tangen)m(t.)427 1134 y(V)-8 b(arious)37 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b(AD)46 b(and)f(exceed)h(1000)2305 3914 y Fh(0)m(0)2392 3951 y FA(outside)e(6800)17 b(BC)45 b(to)h(8200)17 b(AD.)46 b(The)427 4064 y(SLALIB)37 b(routine)f(sla)p Fq(_)p FA(PRECL)g (implemen)m(ts)f(a)j(more)f(elab)s(orate)h(mo)s(del)e(whic)m(h)g(is)g (suitable)427 4177 y(for)30 b(problems)f(spanning)f(sev)m(eral)j (thousand)f(y)m(ears.)0 4444 y Fy(REFERENCES)44 b FA(:)311 4618 y(1.)i(Liesk)m(e,)31 b(J.H.,)g(1979.)h Fn(Astr.Astr)-5 b(ophys.)33 b Fy(73)p FA(,)e(282;)h(equations)e(6)h(&)f(7,)h(p283.)311 4750 y(2.)46 b(Kaplan,)30 b(G.H.,)h(1981.)i Fn(USNO)e(cir)-5 b(cular)34 b(no.)f(163)p FA(,)f(pA2.)p 0 4842 V 0 4955 a Fu(SLA)p Fk(_)p Fu(PRECES)765 b Fj(Precession)f Fu(SLA)p Fk(_)p Fu(PRECES)0 5305 y Fy(A)m(CTION)44 b FA(:)39 b(Precession)26 b({)h(either)f(the)g(old)g(\\FK4")i(\(Bessel-New)m(com)m(b,)i(pre)c(IA) m(U)h(1976\))i(or)d(new)g(\\FK5")227 5418 y(\(F)-8 b(ric)m(k)m(e,)33 b(p)s(ost)d(IA)m(U)h(1976\))h(as)f(required.)0 5606 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_PRECES)f(\(SYSTEM,)h(EP0,)h (EP1,)f(RA,)h(DC\))p eop %%Page: 123 125 123 124 bop 0 52 a Ft(SUN/67.45)3206 b FA(123)0 351 y Fy(GIVEN)45 b FA(:)277 497 y Fn(SYSTEM)357 b Fy(C)569 b FA(precession)30 b(to)h(b)s(e)f(applied:)38 b(`FK4')31 b(or)g(`FK5')277 610 y Fn(EP0,EP1)368 b Fy(D)565 b FA(starting)30 b(and)g(ending)f(ep)s(o)s(c)m(h)277 723 y Fn(RA,DC)440 b Fy(D)565 b FA([)15 b Fi(\013;)g(\016)20 b FA(],)31 b(mean)g(equator)g(&)f(equino)m(x)g(of)g(ep)s(o)s(c)m(h)g(EP0)0 1184 y Fy(RETURNED)46 b FA(:)277 1356 y Fn(RA,DC)440 b Fy(D)565 b FA([)15 b Fi(\013;)g(\016)20 b FA(],)31 b(mean)g(equator)g(&)f(equino)m(x)g(of)g(ep)s(o)s(c)m(h)g(EP1)0 1825 y Fy(NOTES)44 b FA(:)311 2055 y(1.)i(Lo)m(w)m(ercase)33 b(c)m(haracters)e(in)e(SYSTEM)h(are)h(acceptable.)311 2223 y(2.)46 b(The)36 b(ep)s(o)s(c)m(hs)g(are)g(Besselian)g(if)f (SYSTEM=`FK4')h(and)f(Julian)f(if)h(`FK5'.)59 b(F)-8 b(or)37 b(example,)h(to)427 2336 y(precess)d(co)s(ordinates)g(in)e(the) 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b(the)i(inclination)c(\(radians\))602 464 y(\012)348 b(is)29 b(the)i(longitude)e(of)h(the)h(ascending)e(no)s (de)h(\(radians\))602 577 y Fi($)339 b FA(is)29 b(the)i(longitude)e(of) h(p)s(erihelion)d(\(radians\))602 690 y Fi(!)357 b FA(is)29 b(the)i(argumen)m(t)f(of)h(p)s(erihelion)c(\(radians\))602 803 y Fi(a)366 b FA(is)29 b(the)i(mean)f(distance)g(\(A)m(U\))602 916 y Fi(q)373 b FA(is)29 b(the)i(p)s(erihelion)c(distance)j(\(A)m(U\)) 602 1029 y Fi(e)372 b FA(is)29 b(the)i(eccen)m(tricit)m(y)602 1142 y Fi(L)352 b FA(is)29 b(the)i(longitude)e(\(radians,)g(0)21 b Fl(\000)f FA(2)p Fi(\031)s FA(\))602 1255 y Fi(M)326 b FA(is)29 b(the)i(mean)f(anomaly)g(\(radians,)g(0)20 b Fl(\000)g FA(2)p Fi(\031)s FA(\))602 1367 y Fi(n)359 b FA(is)29 b(the)i(daily)d(motion)i(\(radians\))602 1480 y(-)384 b(means)30 b(no)g(v)-5 b(alue)30 b(is)f(set)311 1736 y(6.)46 b(A)m(t)c(v)m(ery)g(small)e(inclinations,)h(the)h (longitude)e(of)h(the)g(ascending)g(no)s(de)g(ANODE)g(b)s(ecomes)427 1849 y(indeterminate)36 b(and)g(under)f(some)i(circumstances)f(ma)m(y)h (b)s(e)f(set)h(arbitrarily)d(to)j(zero.)60 b(Simi-)427 1962 y(larly)-8 b(,)38 b(if)d(the)i(orbit)f(is)f(close)i(to)h (circular,)e(the)h(true)g(anomaly)f(b)s(ecomes)h(indeterminate)e(and) 427 2075 y(under)h(some)i(circumstances)g(ma)m(y)g(b)s(e)f(set)h (arbitrarily)d(to)j(zero.)63 b(In)37 b(suc)m(h)g(cases,)j(the)e(other) 427 2188 y(elemen)m(ts)h(are)g(automatically)g(adjusted)f(to)i(comp)s (ensate,)h(and)d(so)h(the)g(elemen)m(ts)g(remain)f(a)427 2301 y(v)-5 b(alid)29 b(description)f(of)j(the)f(orbit.)0 2958 y Fy(REFERENCE)44 b FA(:)55 b(Sterne,)40 b(Theo)s(dore)d(E.,)j Fn(A)n(n)e(Intr)-5 b(o)g(duction)42 b(to)e(Celestial)g(Me)-5 b(chanics,)40 b FA(In)m(terscience)227 3071 y(Publishers,)27 b(1960.)p 0 3322 3780 8 v 0 3435 a Fu(SLA)p Fk(_)p Fu(PV2UE)91 b Fj(P)m(osition/V)-10 b(elo)s(cit)m(y)34 b(to)k(Univ)m(ersal)e(Elemen) m(ts)90 b Fu(SLA)p Fk(_)p Fu(PV2UE)0 3785 y Fy(A)m(CTION)44 b FA(:)39 b(Construct)26 b(a)g(univ)m(ersal)f(elemen)m(t)i(set)g(based) f(on)g(an)h(instan)m(taneous)f(p)s(osition)e(and)i(v)m(elo)s(cit)m(y)-8 b(.)0 3973 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_PV2UE)g(\(PV,)g (DATE,)h(PMASS,)f(U,)h(JSTAT\))0 4500 y Fy(GIVEN)e FA(:)277 4646 y Fn(PV)606 b Fy(D\(6\))431 b FA(helio)s(cen)m(tric)29 b([)15 b Fi(x;)g(y)s(;)g(z)t(;)33 b FA(_)-43 b Fi(x)r(;)32 b FA(_)-42 b Fi(y)s(;)31 b FA(_)-41 b Fi(z)20 b FA(],)31 b(equatorial,)f(J2000)1825 4759 y(\(A)m(U,)i(A)m(U/s;)f(Note)h(1\))277 4872 y Fn(D)n(A)-7 b(TE)481 b Fy(D)565 b FA(date)29 b(\(TT)f(Mo)s (di\014ed)e(Julian)g(Date)k(=)e(JD)p Fl(\000)p FA(2400000.5\))277 4985 y Fn(PMASS)422 b Fy(D)565 b FA(mass)30 b(of)h(the)f(planet)g (\(Sun)f(=)h(1;)h(Note)h(2\))0 5634 y Fy(RETURNED)46 b FA(:)p eop %%Page: 128 130 128 129 bop 0 52 a FA(128)277 339 y Fn(U)668 b Fy(D\(13\))379 b FA(univ)m(ersal)29 b(orbital)g(elemen)m(ts)i(\(Note)h(3\))537 452 y(\(1\))1006 b(com)m(bined)30 b(mass)g(\()p Fi(M)h FA(+)20 b Fi(m)p FA(\))537 565 y(\(2\))1006 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FA(3)f(=)g(to)s(o)h(slo)m(w)0 2383 y Fy(NOTES)44 b FA(:)311 2615 y(1.)i(The)30 b(PV)h(6-v)m(ector)i(can)e(b) s(e)e(with)h(resp)s(ect)g(to)h(an)m(y)g(c)m(hosen)g(inertial)e(frame,)i (and)f(the)g(resulting)427 2728 y(univ)m(ersal-elemen)m(t)h(set)h(will) d(b)s(e)h(with)h(resp)s(ect)g(to)h(the)g(same)g(frame.)44 b(A)31 b(common)h(c)m(hoice)g(will)427 2841 y(b)s(e)e(mean)g(equator)h (and)f(ecliptic)f(of)i(ep)s(o)s(c)m(h)f(J2000.)311 3009 y(2.)46 b(The)e(mass,)j(PMASS,)c(is)g(imp)s(ortan)m(t)g(only)g(for)g (the)h(larger)g(planets.)80 b(F)-8 b(or)44 b(most)g(purp)s(oses)427 3122 y(\()p Fn(e.g.)30 b FA(asteroids\))h(use)f(0D0.)42 b(V)-8 b(alues)30 b(less)g(than)g(zero)h(are)g(illegal.)311 3290 y(3.)46 b(The)40 b(\\univ)m(ersal")f(elemen)m(ts)h(are)g(those)h (whic)m(h)d(de\014ne)h(the)h(orbit)f(for)h(the)g(purp)s(oses)e(of)i (the)427 3403 y(metho)s(d)32 b(of)g(univ)m(ersal)e(v)-5 b(ariables)31 b(\(see)i(reference\).)47 b(They)32 b(consist)f(of)i(the) f(com)m(bined)f(mass)h(of)427 3516 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w(48.81)p 2864 831 V 759 944 V 856 910 a(45)p 995 944 V 371 w(58.16)p 1572 944 V 441 w(58.18)p 2219 944 V 441 w(58.16)p 2864 944 V 759 1057 V 856 1023 a(50)p 995 1057 V 371 w(69.28)p 1572 1057 V 441 w(69.30)p 2219 1057 V 441 w(69.27)p 2864 1057 V 759 1170 V 856 1136 a(55)p 995 1170 V 371 w(82.97)p 1572 1170 V 441 w(82.99)p 2219 1170 V 441 w(82.95)p 2864 1170 V 759 1283 V 856 1249 a(60)p 995 1283 V 325 w(100.51)p 1572 1283 V 397 w(100.54)p 2219 1283 V 396 w(100.50)p 2864 1283 V 759 1396 V 856 1362 a(65)p 995 1396 V 325 w(124.23)p 1572 1396 V 397 w(124.26)p 2219 1396 V 396 w(124.20)p 2864 1396 V 759 1509 V 856 1475 a(70)p 995 1509 V 325 w(158.63)p 1572 1509 V 397 w(158.68)p 2219 1509 V 396 w(158.61)p 2864 1509 V 759 1621 V 856 1588 a(72)p 995 1621 V 325 w(177.32)p 1572 1621 V 397 w(177.37)p 2219 1621 V 396 w(177.31)p 2864 1621 V 759 1734 V 856 1701 a(74)p 995 1734 V 325 w(200.35)p 1572 1734 V 397 w(200.38)p 2219 1734 V 396 w(200.32)p 2864 1734 V 759 1847 V 856 1813 a(76)p 995 1847 V 325 w(229.45)p 1572 1847 V 397 w(229.43)p 2219 1847 V 396 w(229.42)p 2864 1847 V 759 1960 V 856 1926 a(78)p 995 1960 V 325 w(267.44)p 1572 1960 V 397 w(267.29)p 2219 1960 V 396 w(267.41)p 2864 1960 V 759 2073 V 856 2039 a(80)p 995 2073 V 325 w(319.13)p 1572 2073 V 397 w(318.55)p 2219 2073 V 396 w(319.10)p 2864 2073 V 761 2076 2106 4 v 759 2189 4 113 v 810 2155 a(deg)p 995 2189 V 340 w(arcsec)p 1572 2189 V 409 w(arcsec)p 2219 2189 V 409 w(arcsec)p 2864 2189 V 761 2193 2106 4 v 427 2408 a(The)33 b(v)-5 b(alues)33 b(for)h(Saastamoinen's)f(form)m(ula)g(\(whic)m(h)g(includes)e(terms)j (up)e(to)j(tan)3299 2375 y Fr(5)3338 2408 y FA(\))f(are)g(tak)m(en)427 2521 y(from)c(Hohenk)m(erk)h(and)f(Sinclair)d(\(1985\).)427 2647 y(The)36 b(results)f(from)h(the)g(m)m(uc)m(h)g(slo)m(w)m(er)h(but) e(more)h(accurate)i(sla)p Fq(_)p FA(REF)m(CO)e(routine)f(ha)m(v)m(e)i (not)427 2760 y(b)s(een)k(included)e(in)i(the)h(tabulation)f(as)h(they) g(are)g(iden)m(tical)f(to)h(those)g(in)f(the)h(sla)p Fq(_)p FA(REFR)m(O)427 2873 y(column)29 b(to)j(the)e(0)1053 2836 y Fh(0)l(0)1057 2873 y Fi(:)p FA(01)i(resolution)d(used.)311 3013 y(6.)46 b(Outlandish)25 b(input)h(parameters)i(are)h(silen)m(tly)d (limited)g(to)i(mathematically)g(safe)g(v)-5 b(alues.)40 b(Zero)427 3126 y(pressure)29 b(is)h(p)s(ermissible,)c(and)k(causes)h (zero)s(es)g(to)g(b)s(e)f(returned.)311 3265 y(7.)46 b(The)30 b(algorithm)g(dra)m(ws)f(on)i(sev)m(eral)f(sources,)h(as)g (follo)m(ws:)506 3405 y Fl(\017)46 b FA(The)27 b(form)m(ula)g(for)g (the)g(saturation)h(v)-5 b(ap)s(our)26 b(pressure)g(of)h(w)m(ater)i(as) e(a)h(function)e(of)i(temp)s(er-)597 3518 y(ature)j(and)f(temp)s (erature)g(is)f(tak)m(en)j(from)e(expressions)f(A4.5-A4.7)k(of)d(Gill)f (\(1982\).)506 3645 y Fl(\017)46 b FA(The)25 b(form)m(ula)g(for)h(the)g (w)m(ater)g(v)-5 b(ap)s(our)25 b(pressure,)h(giv)m(en)f(the)h (saturation)g(pressure)e(and)h(the)597 3758 y(relativ)m(e)31 b(h)m(umidit)m(y)d(is)i(from)f(Crane)h(\(1976\),)j(expression)d(2.5.5.) 506 3884 y Fl(\017)46 b FA(The)30 b(refractivit)m(y)f(of)h(air)f(is)g (a)h(function)f(of)h(temp)s(erature,)g(total)g(pressure,)f(w)m(ater-v) -5 b(ap)s(our)597 3997 y(pressure)29 b(and,)i(in)e(the)h(case)i(of)f (optical/IR)f(but)g(not)g(radio,)g(w)m(a)m(v)m(elength.)43 b(The)30 b(form)m(ulae)597 4110 y(for)g(the)f(t)m(w)m(o)i(cases)g(are)f (dev)m(elop)s(ed)f(from)g(the)h(Essen)f(and)g(F)-8 b(ro)s(ome)30 b(expressions)e(adopted)597 4223 y(in)e(Resolution)g(1)i(of)g(the)f (12th)h(In)m(ternational)f(Geo)s(desy)g(Asso)s(ciation)g(General)g (Assem)m(bly)597 4336 y(\(1963\).)427 4475 y(The)j(ab)s(o)m(v)m(e)i (three)e(items)g(are)h(as)g(used)e(in)g(the)i(sla)p Fq(_)p FA(REFR)m(O)f(routine.)506 4615 y Fl(\017)46 b FA(The)33 b(form)m(ula)f(for)h Fi(\014)38 b FA(\(=)30 b Fi(H)1566 4629 y Fr(0)1605 4615 y Fi(=r)1691 4629 y Fr(0)1731 4615 y FA(\))j(is)f(an)h(adaption)g(of)g(expression)f(9)h(from)g(Stone)g (\(1996\).)597 4728 y(The)e(adaptations,)i(arriv)m(ed)d(at)j (empirically)-8 b(,)29 b(consist)i(of)h(\(i\))g(a)f(small)g(adjustmen)m (t)g(to)h(the)597 4841 y(co)s(e\016cien)m(t)g(and)d(\(ii\))h(a)h(h)m (umidit)m(y)d(term)i(for)g(the)h(radio)f(case)h(only)-8 b(.)506 4968 y Fl(\017)46 b FA(The)32 b(form)m(ulae)f(for)h(the)g (refraction)f(constan)m(ts)i(as)g(a)f(function)e(of)i Fi(n)21 b Fl(\000)g FA(1)32 b(and)g Fi(\014)37 b FA(are)32 b(from)597 5080 y(Green)f(\(1987\),)i(expression)c(4.31.)0 5399 y Fy(REFERENCES)44 b FA(:)311 5580 y(1.)i(Crane,)h(R.K.,)h(Meeks,) g(M.L.)c(\(ed\),)k(\\Refraction)d(E\013ects)f(in)f(the)h(Neutral)f(A)m (tmosphere",)427 5693 y Fn(Metho)-5 b(ds)34 b(of)f(Exp)-5 b(erimental)34 b(Physics:)43 b(Astr)-5 b(ophysics)34 b(12B,)d FA(Academic)g(Press,)f(1976.)p eop %%Page: 137 139 137 138 bop 0 52 a Ft(SUN/67.45)3206 b FA(137)311 351 y(2.)46 b(Gill,)29 b(Adrian)g(E.,)h Fn(A)n(tmospher)-5 b(e-Oc)g(e)g(an)35 b(Dynamics,)c FA(Academic)f(Press,)g(1982.)311 488 y(3.)46 b(Hohenk)m(erk,)31 b(C.Y.,)g(&)f(Sinclair,)e(A.T.,)j(NA)m (O)g(T)-8 b(ec)m(hnical)30 b(Note)i(No.)f(63,)g(1985.)311 626 y(4.)46 b(In)m(ternational)32 b(Geo)s(desy)h(Asso)s(ciation)f (General)g(Assem)m(bly)-8 b(,)32 b(Bulletin)f(G)m(\023)-43 b(eo)s(d)m(\023)g(esique)34 b Fy(70)e FA(p390,)427 739 y(1963.)311 876 y(5.)46 b(Stone,)31 b(Ronald)e(C.,)i(P)-8 b(.A.S.P)g(.)31 b Fy(108)h FA(1051-1058,)i(1996.)311 1013 y(6.)46 b(Green,)31 b(R.M.,)g Fn(Spheric)-5 b(al)35 b(Astr)-5 b(onomy,)32 b FA(Cam)m(bridge)e(Univ)m(ersit)m(y)f(Press,)h (1987.)p 0 1119 3780 8 v 0 1232 a Fu(SLA)p Fk(_)p Fu(REFR)l(O)834 b Fj(Refraction)e Fu(SLA)p Fk(_)p Fu(REFR)l(O)0 1582 y Fy(A)m(CTION)44 b FA(:)c(A)m(tmospheric)31 b(refraction,)f(for)g (radio)g(or)g(optical/IR)g(w)m(a)m(v)m(elengths.)0 1770 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_REFRO)g(\(ZOBS,)g(HM,)h(TDK,) f(PMB,)h(RH,)g(WL,)g(PHI,)f(TLR,)h(EPS,)g(REF\))0 2083 y Fy(GIVEN)e FA(:)277 2230 y Fn(ZOBS)495 b Fy(D)565 b FA(observ)m(ed)31 b(zenith)e(distance)h(of)h(the)g(source)f (\(radians\))277 2342 y Fn(HM)586 b Fy(D)565 b FA(heigh)m(t)30 b(of)h(the)g(observ)m(er)f(ab)s(o)m(v)m(e)i(sea)f(lev)m(el)f(\(metre\)) 277 2455 y Fn(TDK)532 b Fy(D)565 b FA(am)m(bien)m(t)31 b(temp)s(erature)f(at)h(the)g(observ)m(er)f(\(degrees)h(K\))277 2568 y Fn(PMB)528 b Fy(D)565 b FA(pressure)29 b(at)i(the)g(observ)m(er) f(\(mB\))277 2681 y Fn(RH)602 b Fy(D)565 b FA(relativ)m(e)31 b(h)m(umidit)m(y)d(at)j(the)g(observ)m(er)f(\(range)h(0)16 b({)g(1\))277 2794 y Fn(WL)588 b Fy(D)565 b FA(e\013ectiv)m(e)32 b(w)m(a)m(v)m(elength)g(of)e(the)h(source)g(\()p Fi(\026)p FA(m\))277 2907 y Fn(PHI)571 b Fy(D)565 b FA(latitude)30 b(of)g(the)h(observ)m(er)f(\(radian,)g(astronomical\))277 3020 y Fn(TLR)548 b Fy(D)565 b FA(temp)s(erature)27 b(lapse)g(rate)h (in)e(the)i(trop)s(osphere)e(\(degrees)1658 3133 y(K)k(p)s(er)g (metre\))277 3246 y Fn(EPS)561 b Fy(D)k FA(precision)27 b(required)f(to)j(terminate)f(iteration)g(\(radian\))0 3537 y Fy(RETURNED)46 b FA(:)277 3683 y Fn(REF)549 b Fy(D)565 b FA(refraction:)42 b Fn(in)34 b(vacuo)j FA(ZD)31 b(min)m(us)e(observ)m(ed)j(ZD)f(\(radi-)1658 3796 y(ans\))0 4087 y Fy(NOTES)44 b FA(:)311 4265 y(1.)i(A)30 b(suggested)h(v)-5 b(alue)30 b(for)g(the)g(TLR)f(argumen)m(t)i(is)e(0.0065D0.)44 b(The)29 b(refraction)h(is)f(signi\014can)m(tly)427 4378 y(a\013ected)d(b)m(y)f(TLR,)f(and)h(if)e(studies)h(of)h(the)f(lo)s(cal) g(atmosphere)h(ha)m(v)m(e)h(b)s(een)e(carried)g(out)h(a)g(b)s(etter)427 4491 y(TLR)30 b(v)-5 b(alue)30 b(ma)m(y)h(b)s(e)f(a)m(v)-5 b(ailable.)311 4628 y(2.)46 b(A)31 b(suggested)h(v)-5 b(alue)30 b(for)g(the)h(EPS)f(argumen)m(t)h(is)f(1D)p Fl(\000)p FA(8.)43 b(The)30 b(result)f(is)h(usually)f(at)i(least)g(t)m (w)m(o)427 4741 y(orders)f(of)h(magnitude)e(more)i(computationally)e (precise)h(than)g(the)g(supplied)d(EPS)j(v)-5 b(alue.)311 4878 y(3.)46 b(The)36 b(routine)g(computes)g(the)h(refraction)f(for)h (zenith)e(distances)h(up)g(to)h(and)f(a)h(little)e(b)s(ey)m(ond)427 4991 y(90)517 4958 y Fm(\016)598 4991 y FA(using)k(the)i(metho)s(d)g (of)f(Hohenk)m(erk)i(&)e(Sinclair)e(\(NA)m(O)j(T)-8 b(ec)m(hnical)41 b(Notes)h(59)f(and)f(63,)427 5104 y(subsequen)m(tly)31 b(adopted)h(in)f(the)h Fn(Explanatory)37 b(Supplement)e(to)g(the)f (Astr)-5 b(onomic)g(al)37 b(A)n(lmanac,)427 5217 y FA(1992)32 b({)f(see)g(section)g(3.281\).)311 5354 y(4.)46 b(The)39 b(co)s(de)h(is)f(based)g(on)h(the)g(AREF)g(optical/IR)f(refraction)h (subroutine)d(of)j(C.)15 b(Hohenk)m(erk)427 5467 y(\(HMNA)m(O,)37 b(Septem)m(b)s(er)d(1984\),)k(with)33 b(extensions)h(to)h(supp)s(ort)e (the)i(radio)f(case.)55 b(The)34 b(mo)s(di-)427 5580 y(\014cations)f(to)g(the)g(original)e(HMNA)m(O)i(optical/IR)g (refraction)f(co)s(de)h(whic)m(h)f(a\013ect)i(the)f(results)427 5693 y(are:)p eop %%Page: 138 140 138 139 bop 0 52 a FA(138)506 351 y Fl(\017)46 b FA(Murra)m(y's)f(v)-5 b(alues)45 b(for)f(the)i(gas)f(constan)m(ts)h(ha)m(v)m(e)h(b)s(een)d (used)g(\()p Fn(V)-7 b(e)i(ctorial)48 b(Astr)-5 b(ometry,)597 464 y FA(Adam)30 b(Hilger,)g(1983\).)506 603 y Fl(\017)46 b FA(A)29 b(b)s(etter)f(mo)s(del)f(for)i Fi(P)1426 617 y Fc(s)1463 603 y FA(\()p Fi(T)13 b FA(\))29 b(has)f(b)s(een)f(adopted) i(\(tak)m(en)h(from)e(Gill,)f Fn(A)n(tmospher)-5 b(e-Oc)g(e)g(an)597 716 y(Dynamics,)31 b FA(Academic)g(Press,)f(1982\).)506 854 y Fl(\017)46 b FA(More)31 b(accurate)h(expressions)d(for)h Fi(P)13 b(w)1945 868 y Fc(o)2014 854 y FA(ha)m(v)m(e)32 b(b)s(een)d(adopted)i(\(again)g(from)e(Gill)g(1982\).)506 993 y Fl(\017)46 b FA(Pro)m(vision)c(for)i(radio)e(w)m(a)m(v)m (elengths)j(has)e(b)s(een)g(added)f(using)g(expressions)g(devised)h(b)m (y)597 1106 y(A.)16 b(T.)f(Sinclair,)23 b(R)m(GO)h(\(priv)-5 b(ate)24 b(comm)m(unication)g(1989\),)k(based)c(on)g(the)g(Essen)g(&)g (F)-8 b(ro)s(ome)597 1219 y(refractivit)m(y)35 b(form)m(ula)g(adopted)g (in)f(Resolution)h(1)g(of)h(the)f(12th)h(In)m(ternational)f(Geo)s(desy) 597 1332 y(Asso)s(ciation)30 b(General)g(Assem)m(bly)g(\(Bulletin)f(G)m (\023)-43 b(eo)s(d)m(\023)g(esique)31 b Fy(70)g FA(p390,)h(1963\).)427 1496 y(None)39 b(of)f(the)g(c)m(hanges)h(signi\014can)m(tly)d (a\013ects)j(the)f(optical/IR)g(results)e(with)h(resp)s(ect)h(to)g(the) 427 1609 y(algorithm)i(giv)m(en)g(in)g(the)g(1992)j Fn(Explanatory)h (Supplement.)73 b FA(F)-8 b(or)41 b(example,)i(at)e(70)3456 1576 y Fm(\016)3537 1609 y FA(zenith)427 1722 y(distance)f(the)g (presen)m(t)g(routine)f(agrees)i(with)e(the)h(ES)f(algorithm)g(to)i(b)s (etter)f(than)f(0)3510 1685 y Fh(0)m(0)3514 1722 y Fi(:)p FA(05)j(for)427 1835 y(an)m(y)j(reasonable)e(com)m(bination)h(of)g (parameters.)82 b(Ho)m(w)m(ev)m(er,)50 b(the)44 b(impro)m(v)m(ed)f(w)m (ater-v)-5 b(ap)s(our)427 1948 y(expressions)28 b(do)h(mak)m(e)h(a)g (signi\014can)m(t)e(di\013erence)g(in)g(the)h(radio)g(band,)f(at)i(70) 3115 1915 y Fm(\016)3184 1948 y FA(zenith)f(distance)427 2061 y(reac)m(hing)e(almost)f(4)1114 2024 y Fh(0)l(0)1181 2061 y FA(for)g(a)h(hot,)g(h)m(umid,)f(lo)m(w-altitude)f(site)h(during) e(a)j(p)s(erio)s(d)d(of)i(lo)m(w)h(pressure.)311 2225 y(5.)46 b(The)34 b(radio)g(refraction)g(is)f(c)m(hosen)i(b)m(y)f(sp)s (ecifying)e(WL)j Fi(>)c FA(100)36 b Fi(\026)p FA(m.)52 b(Because)36 b(the)e(algorithm)427 2338 y(tak)m(es)23 b(no)f(accoun)m(t)h(of)f(the)g(ionosphere,)h(the)e(accuracy)i (deteriorates)g(at)f(lo)m(w)g(frequencies,)g(b)s(elo)m(w)427 2451 y(ab)s(out)30 b(30)16 b(MHz.)311 2616 y(6.)46 b(Before)38 b(use,)g(the)f(v)-5 b(alue)37 b(of)g(ZOBS)e(is)h(expressed)g(in)g(the)h (range)g Fl(\006)p Fi(\031)s FA(.)60 b(If)36 b(this)g(ranged)g(ZOBS)427 2729 y(is)f(negativ)m(e,)k(the)d(result)f(REF)h(is)e(computed)i(from)f (its)h(absolute)f(v)-5 b(alue)36 b(b)s(efore)f(b)s(eing)f(made)427 2842 y(negativ)m(e)g(to)g(matc)m(h.)50 b(In)32 b(addition,)g(if)g(it)h (has)f(an)h(absolute)g(v)-5 b(alue)33 b(greater)h(than)f(93)3413 2809 y Fm(\016)3453 2842 y FA(,)h(a)f(\014xed)427 2955 y(REF)e(v)-5 b(alue)30 b(equal)f(to)j(the)e(result)f(for)i(ZOBS)e(=)c (93)2238 2922 y Fm(\016)2309 2955 y FA(is)k(returned,)g(appropriately)g (signed.)311 3119 y(7.)46 b(As)27 b(in)e(the)i(original)e(Hohenk)m(erk) i(and)f(Sinclair)e(algorithm,)j(\014xed)f(v)-5 b(alues)26 b(of)h(the)g(w)m(ater)h(v)-5 b(ap)s(our)427 3232 y(p)s(olytrop)s(e)27 b(exp)s(onen)m(t,)i(the)g(heigh)m(t)f(of)h(the)f(trop)s(opause,)h(and)f (the)g(heigh)m(t)g(at)i(whic)m(h)d(refraction)427 3345 y(is)j(negligible)e(are)i(used.)311 3509 y(8.)46 b(The)27 b(radio)f(refraction)h(has)g(b)s(een)g(tested)g(against)h(w)m(ork)f (done)g(b)m(y)g(Iain)f(Coulson,)h(JA)m(CH,)h(\(pri-)427 3622 y(v)-5 b(ate)32 b(comm)m(unication)e(1995\))j(for)e(the)f(James)h (Clerk)f(Maxw)m(ell)g(T)-8 b(elescop)s(e,)32 b(Mauna)e(Kea.)43 b(F)-8 b(or)427 3735 y(t)m(ypical)27 b(conditions,)g(agreemen)m(t)i(at) g(the)e(0)1916 3698 y Fh(0)l(0)1920 3735 y Fi(:)p FA(1)i(lev)m(el)e(is) f(ac)m(hiev)m(ed)j(for)e(mo)s(derate)h(ZD,)f(w)m(orsening)427 3848 y(to)h(p)s(erhaps)d(0)913 3811 y Fh(0)m(0)917 3848 y Fi(:)p FA(5)17 b({)e(1)1104 3811 y Fh(0)l(0)1108 3848 y Fi(:)p FA(0)28 b(at)g(ZD)f(80)1556 3815 y Fm(\016)1596 3848 y FA(.)40 b(A)m(t)28 b(hot)f(and)g(h)m(umid)e(sea-lev)m(el)j (sites)e(the)i(accuracy)g(will)c(not)427 3961 y(b)s(e)30 b(as)h(go)s(o)s(d.)311 4126 y(9.)46 b(It)d(should)d(b)s(e)h(noted)h (that)h(the)f(relativ)m(e)h(h)m(umidit)m(y)d(RH)i(is)f(formally)g (de\014ned)f(in)h(terms)h(of)427 4238 y(\\mixing)36 b(ratio")h(rather)g (than)g(pressures)e(or)i(densities)e(as)j(is)e(often)h(stated.)61 b(It)37 b(is)f(the)i(mass)427 4351 y(of)45 b(w)m(ater)h(p)s(er)d(unit)h (mass)g(of)h(dry)f(air)g(divided)e(b)m(y)j(that)g(for)g(saturated)g (air)f(at)h(the)g(same)427 4464 y(temp)s(erature)c(and)e(pressure)h (\(see)h(Gill)d(1982\).)73 b(The)40 b(familiar)f Fi(\027)47 b FA(=)42 b Fi(p)2995 4478 y Fc(w)3051 4464 y Fi(=p)3142 4478 y Fc(s)3220 4464 y FA(or)e Fi(\027)48 b FA(=)42 b Fi(\032)3594 4478 y Fc(w)3650 4464 y Fi(=\032)3742 4478 y Fc(s)427 4577 y FA(expressions)27 b(can)i(di\013er)e(from)h(the) h(formal)e(de\014nition)f(b)m(y)j(sev)m(eral)g(p)s(ercen)m(t,)g (signi\014can)m(t)e(in)g(the)427 4690 y(radio)j(case.)p 0 4842 3780 8 v 0 4955 a Fu(SLA)p Fk(_)p Fu(REFV)497 b Fj(Apply)38 b(Refraction)e(to)i(V)-10 b(ector)497 b Fu(SLA)p Fk(_)p Fu(REFV)0 5305 y Fy(A)m(CTION)44 b FA(:)39 b(Adjust)26 b(an)h(unrefracted)g(Cartesian)f(v)m(ector)j(to)f(include)d (the)i(e\013ect)i(of)e(atmospheric)g(refrac-)227 5418 y(tion,)j(using)f(the)i(simple)d(\001)p Fi(\020)k FA(=)25 b Fi(a)15 b FA(tan)g Fi(\020)27 b FA(+)20 b Fi(b)15 b FA(tan)1913 5385 y Fr(3)1968 5418 y Fi(\020)37 b FA(mo)s(del.)0 5606 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_REFV)g(\(VU,)h(REFA,)f (REFB,)g(VR\))p eop %%Page: 139 141 139 140 bop 0 52 a Ft(SUN/67.45)3206 b FA(139)0 351 y Fy(GIVEN)45 b FA(:)277 497 y Fn(VU)600 b Fy(D)565 b FA(unrefracted)50 b(p)s(osition)e(of)i(the)h(source)f(\([)15 b Fi(Az)t(;)g(E)5 b(l)54 b FA(])c(3-)1658 610 y(v)m(ector\))277 723 y Fn(REF)-9 b(A)490 b Fy(D)565 b FA(tan)16 b Fi(\020)36 b FA(co)s(e\016cien)m(t)c (\(radians\))277 836 y Fn(REFB)485 b Fy(D)565 b FA(tan)1789 803 y Fr(3)1844 836 y Fi(\020)37 b FA(co)s(e\016cien)m(t)31 b(\(radians\))0 1235 y Fy(RETURNED)46 b FA(:)277 1381 y Fn(VR)602 b Fy(D)565 b FA(refracted)25 b(p)s(osition)e(of)j(the)f (source)g(\([)15 b Fi(Az)t(;)g(E)5 b(l)28 b FA(])d(3-v)m(ector\))0 1893 y Fy(NOTES)44 b FA(:)311 2098 y(1.)i(This)30 b(routine)g(applies)g (the)h(adjustmen)m(t)g(for)g(refraction)g(in)f(the)i(opp)s(osite)e (sense)h(to)h(the)g(usual)427 2211 y(one)24 b({)f(it)g(tak)m(es)h(an)f (unrefracted)f(\()p Fn(in)27 b(vacuo)6 b FA(\))23 b(p)s(osition)e(and)i (pro)s(duces)e(an)i(observ)m(ed)g(\(refracted\))427 2324 y(p)s(osition,)28 b(whereas)g(the)h(\001)p Fi(\020)i FA(=)25 b Fi(a)15 b FA(tan)h Fi(\020)23 b FA(+)16 b Fi(b)f FA(tan)2083 2291 y Fr(3)2138 2324 y Fi(\020)35 b FA(mo)s(del)27 b(strictly)h(applies)e(to)k(the)e(case)i(where)427 2437 y(an)g(observ)m(ed)g(p)s(osition)e(is)h(to)i(ha)m(v)m(e)g(the)f (refraction)g(remo)m(v)m(ed.)41 b(The)30 b(unrefracted)f(to)i (refracted)427 2550 y(case)h(is)d(harder,)h(and)f(requires)g(an)i(in)m (v)m(erted)f(form)g(of)g(the)h(text-b)s(o)s(ok)g(refraction)f(mo)s (dels;)f(the)427 2663 y(algorithm)38 b(used)g(here)g(is)g(equiv)-5 b(alen)m(t)38 b(to)i(one)e(iteration)h(of)g(the)f(Newton-Raphson)h (metho)s(d)427 2776 y(applied)28 b(to)k(the)e(ab)s(o)m(v)m(e)i(form)m (ula.)311 2931 y(2.)46 b(Though)31 b(optimized)f(for)h(sp)s(eed)f (rather)h(than)g(precision,)f(the)i(presen)m(t)f(routine)f(ac)m(hiev)m (es)j(con-)427 3044 y(sistency)41 b(with)e(the)i (refracted-to-unrefracted)h(\001)p Fi(\020)49 b FA(=)43 b Fi(a)15 b FA(tan)g Fi(\020)34 b FA(+)27 b Fi(b)15 b FA(tan)2995 3011 y Fr(3)3050 3044 y Fi(\020)47 b FA(mo)s(del)40 b(at)h(b)s(etter)427 3157 y(than)32 b(1)g(microarcsecond)f(within)e(30) 1730 3124 y Fm(\016)1802 3157 y FA(of)j(the)g(zenith)f(and)g(remains)f (within)f(1)j(milliarcsecond)427 3270 y(to)j Fi(\020)j FA(=)31 b(70)812 3237 y Fm(\016)853 3270 y FA(.)52 b(The)33 b(inheren)m(t)h(accuracy)h(of)f(the)g(mo)s(del)f(is,)i(of)f(course,)i (far)e(w)m(orse)g(than)g(this)f({)427 3383 y(see)e(the)g(do)s(cumen)m (tation)f(for)g(sla)p Fq(_)p FA(REF)m(CO)g(for)g(more)g(information.) 311 3538 y(3.)46 b(A)m(t)34 b(lo)m(w)f(elev)-5 b(ations)33 b(\(b)s(elo)m(w)g(ab)s(out)g(3)1752 3505 y Fm(\016)1791 3538 y FA(\))h(the)f(refraction)g(correction)g(is)f(held)g(bac)m(k)i (to)g(prev)m(en)m(t)427 3651 y(arithmetic)28 b(problems)e(and)i(wildly) d(wrong)j(results.)39 b(Ov)m(er)28 b(a)h(wide)e(range)i(of)f(observ)m (er)h(heigh)m(ts)427 3764 y(and)36 b(corresp)s(onding)e(temp)s (eratures)i(and)f(pressures,)i(the)f(follo)m(wing)f(lev)m(els)g(of)i (accuracy)g(are)427 3876 y(ac)m(hiev)m(ed,)32 b(relativ)m(e)e(to)h(n)m (umerical)e(in)m(tegration)i(through)e(a)i(mo)s(del)e(atmosphere:)1519 4078 y Fi(\020)1559 4093 y Fc(obs)1769 4078 y Fn(err)-5 b(or)1525 4304 y FA(80)1615 4271 y Fm(\016)1811 4304 y FA(0)1851 4267 y Fh(0)l(0)1855 4304 y Fi(:)p FA(4)1525 4417 y(81)1615 4384 y Fm(\016)1811 4417 y FA(0)1851 4380 y Fh(0)l(0)1855 4417 y Fi(:)p FA(8)1525 4530 y(82)1615 4497 y Fm(\016)1811 4530 y FA(1)1851 4493 y Fh(0)l(0)1855 4530 y Fi(:)p FA(6)1525 4643 y(83)1615 4610 y Fm(\016)1828 4643 y FA(3)1868 4606 y Fh(0)l(0)1525 4756 y FA(84)1615 4723 y Fm(\016)1828 4756 y FA(7)1868 4719 y Fh(0)l(0)1525 4869 y FA(85)1615 4836 y Fm(\016)1805 4869 y FA(17)1890 4832 y Fh(0)m(0)1525 4982 y FA(86)1615 4949 y Fm(\016)1805 4982 y FA(45)1890 4945 y Fh(0)m(0)1525 5095 y FA(87)1615 5062 y Fm(\016)1782 5095 y FA(150)1912 5058 y Fh(0)n(0)1525 5207 y FA(88)1615 5175 y Fm(\016)1782 5207 y FA(340)1912 5171 y Fh(0)n(0)1525 5320 y FA(89)1615 5287 y Fm(\016)1782 5320 y FA(620)1912 5284 y Fh(0)n(0)1525 5433 y FA(90)1615 5400 y Fm(\016)1760 5433 y FA(1100)1935 5396 y Fh(0)m(0)1525 5546 y FA(91)1615 5513 y Fm(\016)1760 5546 y FA(1900)1935 5509 y Fh(0)m(0)2076 5546 y Fi(<)30 b FA(high-altitude)1525 5659 y(92)1615 5626 y Fm(\016)1760 5659 y FA(3200)1935 5622 y Fh(0)m(0)2076 5659 y Fi(<)g FA(sites)g(only)p eop %%Page: 140 142 140 141 bop 0 52 a FA(140)311 351 y(4.)46 b(See)27 b(also)f(the)g (routine)f(sla)p Fq(_)p FA(REFZ,)g(whic)m(h)g(p)s(erforms)g(the)h (adjustmen)m(t)g(to)h(the)f(zenith)g(distance)427 464 y(rather)40 b(than)f(in)f([)15 b Fi(x;)g(y)s(;)g(z)21 b FA(].)68 b(The)39 b(presen)m(t)h(routine)f(is)f(faster)i(than)f(sla)p Fq(_)p FA(REFZ)g(and,)i(except)427 577 y(v)m(ery)28 b(lo)m(w)f(do)m (wn,)g(is)g(equally)f(accurate)i(for)f(all)f(practical)h(purp)s(oses.) 38 b(Ho)m(w)m(ev)m(er,)30 b(b)s(ey)m(ond)d(ab)s(out)427 690 y Fi(\020)54 b FA(=)47 b(84)729 657 y Fm(\016)812 690 y FA(sla)p Fq(_)p FA(REFZ)c(should)e(b)s(e)i(used,)j(and)d(for)g (the)h(utmost)g(accuracy)g(iterativ)m(e)g(use)f(of)427 803 y(sla)p Fq(_)p FA(REFR)m(O)30 b(should)e(b)s(e)i(considered.)p 0 919 3780 8 v 0 1031 a Fu(SLA)p Fk(_)p Fu(REFZ)602 b Fj(Apply)38 b(Refraction)f(to)h(ZD)603 b Fu(SLA)p Fk(_)p Fu(REFZ)0 1382 y Fy(A)m(CTION)44 b FA(:)f(Adjust)31 b(an)h(unrefracted) f(zenith)h(distance)f(to)i(include)c(the)j(e\013ect)i(of)e(atmospheric) f(refrac-)227 1495 y(tion,)f(using)f(the)i(simple)d(\001)p Fi(\020)k FA(=)25 b Fi(a)15 b FA(tan)g Fi(\020)27 b FA(+)20 b Fi(b)15 b FA(tan)1913 1462 y Fr(3)1968 1495 y Fi(\020)37 b FA(mo)s(del.)0 1682 y Fy(CALL)45 b FA(:)77 b Fq(CALL)46 b(sla_REFZ)g(\(ZU,)h(REFA,)f(REFB,)g(ZR\))0 2021 y Fy(GIVEN)f FA(:)277 2167 y Fn(ZU)612 b Fy(D)565 b FA(unrefracted)29 b(zenith)f(distance)h(of)g(the)h(source)f(\(radians\))277 2393 y Fn(REF)-9 b(A)490 b Fy(D)565 b FA(tan)16 b Fi(\020)36 b FA(co)s(e\016cien)m(t)c(\(radians\))277 2506 y Fn(REFB)485 b Fy(D)565 b FA(tan)1789 2473 y Fr(3)1844 2506 y Fi(\020)37 b FA(co)s(e\016cien)m(t)31 b(\(radians\))0 2841 y Fy(RETURNED)46 b FA(:)277 3013 y Fn(ZR)614 b Fy(D)565 b FA(refracted)31 b(zenith)f(distance)g(\(radians\))0 3356 y Fy(NOTES)44 b FA(:)311 3541 y(1.)i(This)30 b(routine)g(applies)g(the)h(adjustmen)m (t)g(for)g(refraction)g(in)f(the)i(opp)s(osite)e(sense)h(to)h(the)g (usual)427 3654 y(one)24 b({)f(it)g(tak)m(es)h(an)f(unrefracted)f(\()p Fn(in)27 b(vacuo)6 b FA(\))23 b(p)s(osition)e(and)i(pro)s(duces)e(an)i (observ)m(ed)g(\(refracted\))427 3767 y(p)s(osition,)28 b(whereas)g(the)h(\001)p Fi(\020)i FA(=)25 b Fi(a)15 b FA(tan)h Fi(\020)23 b FA(+)16 b Fi(b)f FA(tan)2083 3734 y Fr(3)2138 3767 y Fi(\020)35 b FA(mo)s(del)27 b(strictly)h (applies)e(to)k(the)e(case)i(where)427 3879 y(an)g(observ)m(ed)g(p)s (osition)e(is)h(to)i(ha)m(v)m(e)g(the)f(refraction)g(remo)m(v)m(ed.)41 b(The)30 b(unrefracted)f(to)i(refracted)427 3992 y(case)h(is)d(harder,) h(and)f(requires)g(an)i(in)m(v)m(erted)f(form)g(of)g(the)h(text-b)s(o)s (ok)g(refraction)f(mo)s(dels;)f(the)427 4105 y(form)m(ula)21 b(used)f(here)h(is)f(based)g(on)h(the)h(Newton-Raphson)f(metho)s(d.)37 b(F)-8 b(or)21 b(the)h(utmost)f(n)m(umerical)427 4218 y(consistency)35 b(with)f(the)h(refracted)g(to)h(unrefracted)e(mo)s (del,)h(t)m(w)m(o)h(iterations)f(are)g(carried)f(out,)427 4331 y(ac)m(hieving)29 b(agreemen)m(t)h(at)g(the)f(10)1615 4298 y Fm(\000)p Fr(11)1774 4331 y FA(arcsecond)g(lev)m(el)g(for)f Fi(\020)k FA(=)25 b(80)2788 4298 y Fm(\016)2828 4331 y FA(.)40 b(The)29 b(inheren)m(t)e(accuracy)427 4444 y(of)d(the)g(mo)s(del)f(is,)h(of)g(course,)h(far)f(w)m(orse)g(than)f (this)g({)h(see)g(the)g(do)s(cumen)m(tation)g(for)f(sla)p Fq(_)p FA(REF)m(CO)427 4557 y(for)30 b(more)h(information.)311 4700 y(2.)46 b(A)m(t)28 b Fi(\020)k FA(=)25 b(83)813 4667 y Fm(\016)853 4700 y FA(,)j(the)f(rapidly-w)m(orsening)d(\001)p Fi(\020)31 b FA(=)25 b Fi(a)15 b FA(tan)h Fi(\020)k FA(+)13 b Fi(b)i FA(tan)2571 4667 y Fr(3)2626 4700 y Fi(\020)33 b FA(mo)s(del)26 b(is)g(abandoned)g(and)h(an)427 4813 y(empirical)h(form)m(ula)i(tak)m(es)i(o)m(v)m(er:)1201 5085 y(\001)p Fi(\020)g FA(=)25 b Fi(F)1531 4941 y Ff( )1607 5024 y FA(0)1652 4991 y Fm(\016)1658 5024 y Fi(:)r FA(55445)d Fl(\000)e FA(0)2068 4991 y Fm(\016)2074 5024 y Fi(:)r FA(01133)p Fi(E)29 b FA(+)19 b(0)2557 4991 y Fm(\016)2563 5024 y Fi(:)r FA(00202)p Fi(E)2887 4991 y Fr(2)p 1607 5064 1324 4 v 1744 5147 a FA(1)i(+)f(0)p Fi(:)p FA(28385)p Fi(E)28 b FA(+)20 b(0)p Fi(:)p FA(02390)p Fi(E)2749 5121 y Fr(2)2940 4941 y Ff(!)427 5354 y FA(where)33 b Fi(E)j FA(=)30 b(90)987 5321 y Fm(\016)1050 5354 y Fl(\000)22 b Fi(\020)1183 5368 y Fc(tr)r(ue)1353 5354 y FA(and)33 b Fi(F)47 b FA(is)32 b(a)i(factor)g(c)m(hosen)g(to)h(meet)f(the)g(\001) p Fi(\020)i FA(=)31 b Fi(a)15 b FA(tan)g Fi(\020)29 b FA(+)22 b Fi(b)15 b FA(tan)3678 5321 y Fr(3)3733 5354 y Fi(\020)427 5467 y FA(form)m(ula)34 b(at)h Fi(\020)j FA(=)32 b(83)1151 5434 y Fm(\016)1191 5467 y FA(.)53 b(Ov)m(er)34 b(a)h(wide)e(range)i(of)f(observ)m(er)h(heigh)m(ts)f(and)f (corresp)s(onding)g(tem-)427 5580 y(p)s(eratures)42 b(and)h(pressures,) i(the)e(follo)m(wing)f(lev)m(els)g(of)i(accuracy)g(are)f(ac)m(hiev)m (ed,)48 b(relativ)m(e)43 b(to)427 5693 y(n)m(umerical)29 b(in)m(tegration)i(through)e(a)i(mo)s(del)e(atmosphere:)p eop %%Page: 141 143 141 142 bop 0 52 a Ft(SUN/67.45)3206 b FA(141)1528 339 y Fi(\020)1568 354 y Fc(obs)1769 339 y Fn(err)-5 b(or)1534 565 y FA(80)1624 532 y Fm(\016)1811 565 y FA(0)1851 528 y Fh(0)l(0)1855 565 y Fi(:)p 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(mean)h(equator)g(and)e(equino)m(x)h(of)h(ep)s(o)s(c)m(h)427 3884 y(J2000.)40 b(The)23 b(orbital)f(elemen)m(ts)h(pro)s(duced)f(are)h (with)f(resp)s(ect)h(to)h(the)f(J2000)i(ecliptic)d(and)g(mean)427 3997 y(equino)m(x.)311 4176 y(3.)46 b(Three)30 b(di\013eren)m(t)g (elemen)m(t-format)i(options)d(are)i(supp)s(orted,)e(as)h(follo)m(ws.) 427 4452 y(JF)m(ORM=1,)h(suitable)e(for)i(the)f(ma)5 b(jor)30 b(planets:)602 4677 y(EPOCH)85 b(=)55 b(ep)s(o)s(c)m(h)30 b(of)h(elemen)m(ts)f Fi(t)1910 4691 y Fr(0)1980 4677 y FA(\(TT)g(MJD\))602 4790 y(ORBINC)45 b(=)55 b(inclination)27 b Fi(i)k FA(\(radians\))602 4903 y(ANODE)76 b(=)55 b(longitude)29 b(of)h(the)h(ascending)f(no)s(de)f(\012)h(\(radians\))602 5016 y(PERIH)122 b(=)55 b(longitude)29 b(of)h(p)s(erihelion)d Fi($)34 b FA(\(radians\))602 5129 y(A)m(OR)m(Q)143 b(=)55 b(mean)30 b(distance)g Fi(a)h FA(\(A)m(U\))602 5242 y(E)352 b(=)55 b(eccen)m(tricit)m(y)31 b Fi(e)g FA(\(0)26 b Fl(\024)f Fi(e)h(<)f FA(1\))602 5355 y(A)m(ORL)154 b(=)55 b(mean)30 b(longitude)f Fi(L)i FA(\(radians\))602 5468 y(DM)262 b(=)55 b(daily)29 b(motion)h Fi(n)g FA(\(radians\))427 5693 y(JF)m(ORM=2,)h(suitable)e(for)i(minor)d(planets:)p eop %%Page: 156 158 156 157 bop 0 52 a FA(156)602 351 y(EPOCH)85 b(=)55 b(ep)s(o)s(c)m(h)30 b(of)h(elemen)m(ts)f Fi(t)1910 365 y Fr(0)1980 351 y FA(\(TT)g(MJD\))602 464 y(ORBINC)45 b(=)55 b(inclination)27 b Fi(i)k FA(\(radians\))602 577 y(ANODE)76 b(=)55 b(longitude)29 b(of)h(the)h(ascending)f(no)s(de)f(\012)h(\(radians\))602 690 y(PERIH)122 b(=)55 b(argumen)m(t)31 b(of)f(p)s(erihelion)d Fi(!)33 b FA(\(radians\))602 803 y(A)m(OR)m(Q)143 b(=)55 b(mean)30 b(distance)g Fi(a)h FA(\(A)m(U\))602 916 y(E)352 b(=)55 b(eccen)m(tricit)m(y)31 b Fi(e)g FA(\(0)26 b Fl(\024)f Fi(e)h(<)f FA(1\))602 1029 y(A)m(ORL)154 b(=)55 b(mean)30 b(anomaly)h Fi(M)40 b FA(\(radians\))427 1260 y(JF)m(ORM=3,)31 b(suitable)e(for)i(comets:)602 1490 y(EPOCH)85 b(=)55 b(ep)s(o)s(c)m(h)30 b(of)h(p)s(erihelion)c Fi(T)43 b FA(\(TT)30 b(MJD\))602 1603 y(ORBINC)45 b(=)55 b(inclination)27 b Fi(i)k FA(\(radians\))602 1716 y(ANODE)76 b(=)55 b(longitude)29 b(of)h(the)h(ascending)f(no)s(de)f(\012)h(\(radians\))602 1829 y(PERIH)122 b(=)55 b(argumen)m(t)31 b(of)f(p)s(erihelion)d Fi(!)33 b FA(\(radians\))602 1942 y(A)m(OR)m(Q)143 b(=)55 b(p)s(erihelion)27 b(distance)j Fi(q)j FA(\(A)m(U\))602 2055 y(E)352 b(=)55 b(eccen)m(tricit)m(y)31 b Fi(e)g FA(\(0)26 b Fl(\024)f Fi(e)h Fl(\024)f FA(10\))311 2286 y(4.)46 b(It)26 b(ma)m(y)g(not)g(b)s(e)f(p)s(ossible)e(to)j(generate)h (elemen)m(ts)f(in)f(the)g(form)g(requested)h(through)f(JF)m(ORMR.)427 2399 y(The)45 b(caller)f(is)g(noti\014ed)g(of)h(the)g(form)f(of)h (elemen)m(ts)g(actually)g(returned)f(b)m(y)g(means)h(of)g(the)427 2512 y(JF)m(ORM)31 b(argumen)m(t:)554 2742 y(JF)m(ORMR)119 b(JF)m(ORM)234 b(meaning)705 2968 y(1)465 b(1)362 b(OK:)30 b(elemen)m(ts)g(are)h(in)e(the)i(requested)f(format)705 3081 y(1)465 b(2)362 b(nev)m(er)30 b(happ)s(ens)705 3194 y(1)465 b(3)362 b(orbit)29 b(not)i(elliptical)705 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FA(A)m(ORL)346 b Fi(L)256 b(M)230 b FA(-)602 5462 y(DM)454 b Fi(n)263 b FA(-)288 b(-)427 5693 y(where:)p eop %%Page: 157 159 157 158 bop 0 52 a Ft(SUN/67.45)3206 b FA(157)602 351 y Fi(t)635 365 y Fr(0)1016 351 y FA(is)29 b(the)i(ep)s(o)s(c)m(h)f(of)g (the)h(elemen)m(ts)g(\(MJD,)g(TT\))602 464 y Fi(T)361 b FA(is)29 b(the)i(ep)s(o)s(c)m(h)f(of)g(p)s(erihelion)d(\(MJD,)32 b(TT\))602 577 y Fi(i)383 b FA(is)29 b(the)i(inclination)c(\(radians\)) 602 690 y(\012)348 b(is)29 b(the)i(longitude)e(of)h(the)h(ascending)e (no)s(de)h(\(radians\))602 803 y Fi($)339 b FA(is)29 b(the)i(longitude)e(of)h(p)s(erihelion)d(\(radians\))602 916 y Fi(!)357 b FA(is)29 b(the)i(argumen)m(t)f(of)h(p)s(erihelion)c (\(radians\))602 1029 y Fi(a)366 b FA(is)29 b(the)i(mean)f(distance)g (\(A)m(U\))602 1142 y Fi(q)373 b FA(is)29 b(the)i(p)s(erihelion)c (distance)j(\(A)m(U\))602 1255 y Fi(e)372 b FA(is)29 b(the)i(eccen)m(tricit)m(y)602 1367 y Fi(L)352 b FA(is)29 b(the)i(longitude)e(\(radians,)g(0)21 b Fl(\000)f FA(2)p Fi(\031)s FA(\))602 1480 y Fi(M)326 b FA(is)29 b(the)i(mean)f(anomaly)g (\(radians,)g(0)20 b Fl(\000)g FA(2)p Fi(\031)s FA(\))602 1593 y Fi(n)359 b FA(is)29 b(the)i(daily)d(motion)i(\(radians\))602 1706 y(-)384 b(means)30 b(no)g(v)-5 b(alue)30 b(is)f(set)311 1962 y(6.)46 b(A)m(t)c(v)m(ery)g(small)e(inclinations,)h(the)h (longitude)e(of)h(the)g(ascending)g(no)s(de)g(ANODE)g(b)s(ecomes)427 2075 y(indeterminate)36 b(and)g(under)f(some)i(circumstances)f(ma)m(y)h (b)s(e)f(set)h(arbitrarily)d(to)j(zero.)60 b(Simi-)427 2187 y(larly)-8 b(,)38 b(if)d(the)i(orbit)f(is)f(close)i(to)h (circular,)e(the)h(true)g(anomaly)f(b)s(ecomes)h(indeterminate)e(and) 427 2300 y(under)h(some)i(circumstances)g(ma)m(y)g(b)s(e)f(set)h (arbitrarily)d(to)j(zero.)63 b(In)37 b(suc)m(h)g(cases,)j(the)e(other) 427 2413 y(elemen)m(ts)h(are)g(automatically)g(adjusted)f(to)i(comp)s (ensate,)h(and)d(so)h(the)g(elemen)m(ts)g(remain)f(a)427 2526 y(v)-5 b(alid)29 b(description)f(of)j(the)f(orbit.)0 3027 y Fy(REFERENCES)44 b 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Fy(GIVEN)i(and)h(RETURNED)46 b FA(:)p eop %%Page: 158 160 158 159 bop 0 52 a FA(158)277 339 y Fn(U)668 b Fy(D\(13\))379 b FA(univ)m(ersal)29 b(orbital)g(elemen)m(ts)i(\(up)s(dated;)e(Note)j (1\))537 452 y(\(1\))1006 b(com)m(bined)30 b(mass)g(\()p Fi(M)h FA(+)20 b Fi(m)p FA(\))537 565 y(\(2\))1006 b(total)31 b(energy)g(of)g(the)f(orbit)g(\()p Fi(\013)p FA(\))537 678 y(\(3\))1006 b(reference)31 b(\(osculating\))f(ep)s(o)s(c)m(h)h(\() p Fi(t)2869 692 y Fr(0)2908 678 y FA(\))499 791 y(\(4-6\))969 b(p)s(osition)29 b(at)i(reference)g(ep)s(o)s(c)m(h)f(\()p Fy(r)2836 805 y Fr(0)2876 791 y FA(\))499 904 y(\(7-9\))969 b(v)m(elo)s(cit)m(y)31 b(at)g(reference)g(ep)s(o)s(c)m(h)f(\()p Fy(v)2837 918 y Fr(0)2877 904 y FA(\))514 1016 y(\(10\))984 b(helio)s(cen)m(tric)29 b(distance)h(at)h(reference)g(ep)s(o)s(c)m(h) 514 1129 y(\(11\))984 b Fy(r)1701 1143 y Fr(0)1741 1129 y Fi(:)p Fy(v)1821 1143 y Fr(0)514 1242 y FA(\(12\))g(date)31 b(\()p Fi(t)p FA(\))514 1355 y(\(13\))984 b(univ)m(ersal)29 b(eccen)m(tric)i(anomaly)f(\()p Fi( )s FA(\))i(of)e(date,)i(appro)m(x)0 1631 y Fy(RETURNED)46 b FA(:)277 1777 y Fn(PV)606 b Fy(D\(6\))431 b FA(helio)s(cen)m(tric)29 b([)15 b Fi(x;)g(y)s(;)g(z)t(;)33 b FA(_)-43 b Fi(x)r(;)32 b FA(_)-42 b Fi(y)s(;)31 b FA(_)-41 b Fi(z)20 b FA(],)31 b(equatorial,)f(J2000)1825 1890 y(\(A)m(U,)i(A)m(U/s;)f(Note)h(1\))277 2003 y Fn(JST)-7 b(A)g(T)453 b Fy(I)605 b FA(status:)1866 2116 y(0)30 b(=)h(OK)1798 2229 y Fl(\000)p FA(1)f(=)g(radius)f(v)m(ector)i(zero) 1798 2342 y Fl(\000)p FA(2)f(=)g(failed)f(to)i(con)m(v)m(erge)0 2618 y Fy(NOTES)44 b FA(:)311 2795 y(1.)i(The)40 b(\\univ)m(ersal")f (elemen)m(ts)h(are)g(those)h(whic)m(h)d(de\014ne)h(the)h(orbit)f(for)h (the)g(purp)s(oses)e(of)i(the)427 2908 y(metho)s(d)32 b(of)g(univ)m(ersal)e(v)-5 b(ariables)31 b(\(see)i(reference\).)47 b(They)32 b(consist)f(of)i(the)f(com)m(bined)f(mass)h(of)427 3021 y(the)h(t)m(w)m(o)h(b)s(o)s(dies,)e(an)g(ep)s(o)s(c)m(h,)h(and)f (the)h(p)s(osition)e(and)h(v)m(elo)s(cit)m(y)h(v)m(ectors)h (\(arbitrary)e(reference)427 3134 y(frame\))j(at)g(that)g(ep)s(o)s(c)m (h.)53 b(The)34 b(parameter)h(set)g(used)f(here)g(includes)e(also)j(v) -5 b(arious)33 b(quan)m(tities)427 3247 y(that)i(can,)g(in)d(fact,)k(b) s(e)d(deriv)m(ed)f(from)i(the)f(other)h(information.)49 b(This)32 b(approac)m(h)i(is)f(tak)m(en)i(to)427 3359 y(a)m(v)m(oiding)d(unnecessary)f(computation)h(and)g(loss)f(of)h (accuracy)-8 b(.)48 b(The)31 b(supplemen)m(tary)g(quan)m(ti-)427 3472 y(ties)22 b(are)h(\(i\))f Fi(\013)p FA(,)i(whic)m(h)d(is)g(prop)s (ortional)f(to)j(the)g(total)g(energy)f(of)h(the)f(orbit,)h(\(ii\))e (the)i(helio)s(cen)m(tric)427 3585 y(distance)35 b(at)g(ep)s(o)s(c)m (h,)h(\(iii\))d(the)i(out)m(w)m(ards)g(comp)s(onen)m(t)g(of)g(the)g(v)m (elo)s(cit)m(y)g(at)h(the)f(giv)m(en)f(ep)s(o)s(c)m(h,)427 3698 y(\(iv\))29 b(an)f(estimate)h(of)g Fi( )s FA(,)h(the)e(\\univ)m (ersal)g(eccen)m(tric)h(anomaly")g(at)g(a)g(giv)m(en)g(date)g(and)f 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b(short,)i(is)d(the)i([)15 b Fi(\013;)g(\016)20 b FA(])25 b(if)f(view)m(ed)g(from)0 2705 y(the)32 b(cen)m(tre)i(of)e(the)h (Earth,)g(with)e(resp)s(ect)h(to)h(the)f(true)g(equator)h(and)f(equino) m(x)g(of)g(date.)47 b(T)-8 b(ransformation)0 2817 y(of)32 b(an)g(FK5)h(mean)f([)15 b Fi(\013;)g(\016)20 b FA(],)33 b(equino)m(x)e(J2000,)j(curren)m(t)e(ep)s(o)s(c)m(h,)h(to)g(apparen)m (t)f(place)g(in)m(v)m(olv)m(es)g(the)g(follo)m(wing)0 2930 y(e\013ects:)136 3189 y Fl(\017)46 b FA(Ligh)m(t)30 b(de\015ection)h({)f(the)h(gra)m(vitational)f(lens)g(e\013ect)i(of)e (the)h(sun.)136 3375 y Fl(\017)46 b FA(Ann)m(ual)29 b(ab)s(erration.) 136 3562 y Fl(\017)46 b FA(Precession/n)m(utation.)0 3820 y(The)30 b Fn(light)k(de\015e)-5 b(ction)39 b FA(is)31 b(seldom)f(signi\014can)m(t.)41 b(Its)31 b(v)-5 b(alue)31 b(at)g(the)h(lim)m(b)d(of)i(the)g(Sun)f(is)g(ab)s(out)g(1)3351 3784 y Fh(0)m(0)3355 3820 y Fi(:)p FA(74;)j(it)e(falls)0 3933 y(o\013)g(rapidly)d(with)h(distance)h(from)g(the)g(Sun)f(and)h 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FA(EPB2D)h(\(EPB\))472 5693 y(Besselian)f(Ep)s(o)s(c)m(h)g(to)h(Mo)s(di\014ed)e(Julian)f(Date) p eop %%Page: 206 208 206 207 bop 0 52 a FA(206)236 351 y(D)31 b(=)f(sla)p Fq(_)p FA(EPJ)f(\(D)m(A)-8 b(TE\))472 464 y(Mo)s(di\014ed)29 b(Julian)f(Date)k(to)f(Julian)d(Ep)s(o)s(c)m(h)236 640 y(D)j(=)f(sla)p Fq(_)p FA(EPJ2D)g(\(EPJ\))472 753 y(Julian)e(Ep)s(o)s (c)m(h)i(to)h(Mo)s(di\014ed)e(Julian)f(Date)0 1092 y Fs(Timescales)236 1331 y FA(D)j(=)f(sla)p Fq(_)p FA(GMST)f(\(UT1\))472 1444 y(Con)m(v)m(ersion)h(from)g(Univ)m(ersal)g(Time)f(to)i(sidereal)e (time)236 1620 y(D)i(=)f(sla)p Fq(_)p FA(GMST)-8 b(A)30 b(\(D)m(A)-8 b(TE,)32 b(UT1\))472 1732 y(Con)m(v)m(ersion)e(from)g (Univ)m(ersal)g(Time)f(to)i(sidereal)e(time,)h(rounding)e(errors)i (minimized)236 1908 y(D)h(=)f(sla)p Fq(_)p FA(EQEQX)f(\(D)m(A)-8 b(TE\))472 2021 y(Equation)30 b(of)h(the)f(equino)m(xes)236 2197 y(D)h(=)f(sla)p Fq(_)p FA(D)m(A)-8 b(T)31 b(\(DJU\))472 2310 y(O\013set)g(of)g(A)m(tomic)g(Time)e(from)h(Co)s(ordinated)f(Univ) 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b(matrix)g(\(IA)m(U\))236 4621 y(CALL)g(sla)p Fq(_)p FA(PRECL)f(\(EP0,)i(EP1,)g(RMA)-8 b(TP\))472 4734 y(Precession)30 b(matrix)g(\(suitable)f(for)h(long)g(p) s(erio)s(ds\))236 4909 y(CALL)g(sla)p Fq(_)p FA(PRENUT)f(\(EPOCH,)h(D)m (A)-8 b(TE,)32 b(RMA)-8 b(TPN\))472 5022 y(Com)m(bined)29 b(precession/n)m(utation)h(matrix)236 5198 y(CALL)g(sla)p Fq(_)p FA(PREBN)g(\(BEP0,)h(BEP1,)g(RMA)-8 b(TP\))472 5311 y(Precession)30 b(matrix,)g(old)g(system)236 5487 y(CALL)g(sla)p Fq(_)p FA(PRECES)e(\(SYSTEM,)i(EP0,)h(EP1,)g(RA,)f(DC\)) 472 5600 y(Precession,)h(in)e(either)h(the)g(old)g(or)g(the)h(new)e (system)p eop %%Page: 207 209 207 208 bop 0 52 a Ft(SUN/67.45)3206 b FA(207)0 351 y Fs(Prop)s(er)37 b(Motion)236 557 y FA(CALL)30 b(sla)p Fq(_)p FA(PM)g(\(R0,)h(D0,)h(PR,)e(PD,)h(PX,)f(R)-10 b(V,)31 b(EP0,)g(EP1,)f(R1,)h(D1\))472 670 y(Adjust)f(for)g(prop)s(er)f (motion)0 956 y Fs(FK4/FK5/Hipparcos)38 b(Con)m(v)m(ersions)236 1162 y FA(CALL)30 b(sla)p Fq(_)p FA(FK425)h(\(R1950,)i(D1950,)f (DR1950,)h(DD1950,)g(P1950,)g(V1950,)1000 1275 y(R2000,)g(D2000,)f (DR2000,)h(DD2000,)g(P2000,)g(V2000\))472 1369 y(Con)m(v)m(ert)f (B1950.0)h(FK4)e(star)f(data)h(to)g(J2000.0)i(FK5)236 1535 y(CALL)d(sla)p Fq(_)p FA(FK45Z)g(\(R1950,)j(D1950,)g(EPOCH,)c (R2000,)k(D2000\))472 1648 y(Con)m(v)m(ert)j(B1950.0)j(FK4)c(p)s (osition)f(to)h(J2000.0)j(FK5)e(assuming)d(zero)j(FK5)g(prop)s(er)e (motion)472 1761 y(and)c(no)g(parallax)236 1927 y(CALL)g(sla)p Fq(_)p FA(FK524)h(\(R2000,)i(D2000,)f(DR2000,)h(DD2000,)g(P2000,)g (V2000,)1000 2040 y(R1950,)g(D1950,)f(DR1950,)h(DD1950,)g(P1950,)g (V1950\))472 2134 y(Con)m(v)m(ert)f(J2000.0)g(FK5)f(star)g(data)g(to)g (B1950.0)i(FK4)236 2300 y(CALL)d(sla)p Fq(_)p FA(FK54Z)g(\(R2000,)j (D2000,)g(BEPOCH,)d(R1950,)i(D1950,)h(DR1950,)g(DD1950\))472 2413 y(Con)m(v)m(ert)j(J2000.0)i(FK5)e(p)s(osition)d(to)j(B1950.0)i (FK4)e(assuming)d(zero)j(FK5)g(prop)s(er)e(motion)472 2526 y(and)c(no)g(parallax)236 2692 y(CALL)g(sla)p Fq(_)p 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(detic)f(p)s(osition)d(to)j(geo)s(cen)m(tric)236 1124 y(CALL)f(sla)p Fq(_)p FA(POLMO)f(\(ELONGM,)i(PHIM,)g(XP)-8 b(,)31 b(YP)-8 b(,)31 b(ELONG,)f(PHI,)h(D)m(AZ\))472 1237 y(P)m(olar)g(motion)236 1404 y(CALL)f(sla)p Fq(_)p FA(PV)m(OBS)g(\(P)-8 b(,)31 b(H,)g(STL,)e(PV\))472 1517 y(P)m(osition)h(and)g(v)m(elo)s(cit)m(y)h(of)f(observ)-5 b(atory)0 1813 y Fs(Apparen)m(t)38 b(and)g(Observ)m(ed)g(Place)236 2024 y FA(CALL)30 b(sla)p Fq(_)p FA(MAP)g(\(RM,)h(DM,)g(PR,)g(PD,)g (PX,)f(R)-10 b(V,)31 b(EQ,)f(D)m(A)-8 b(TE,)32 b(RA,)e(D)m(A\))472 2137 y(Mean)h(place)g(to)g(geo)s(cen)m(tric)g(apparen)m(t)g(place)236 2305 y(CALL)f(sla)p Fq(_)p FA(MAPP)-8 b(A)30 b(\(EQ,)h(D)m(A)-8 b(TE,)32 b(AMPRMS\))472 2418 y(Precompute)f(mean)f(to)i(apparen)m(t)e (parameters)236 2586 y(CALL)g(sla)p Fq(_)p FA(MAPQK)f(\(RM,)j(DM,)f (PR,)f(PD,)h(PX,)g(R)-10 b(V,)30 b(AMPRMS,)h(RA,)g(D)m(A\))472 2699 y(Mean)g(to)h(apparen)m(t)e(using)f(precomputed)h(parameters)236 2866 y(CALL)g(sla)p Fq(_)p 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(OPRMS\))472 4403 y(Precompute)h(apparen)m(t)g(to)g(observ)m(ed)f (parameters)236 4570 y(CALL)g(sla)p Fq(_)p FA(A)m(OPP)-8 b(A)g(T)30 b(\(UTC,)h(A)m(OPRMS\))472 4683 y(Up)s(date)g(sidereal)e (time)h(in)f(apparen)m(t)h(to)i(observ)m(ed)e(parameters)236 4851 y(CALL)g(sla)p Fq(_)p FA(A)m(OPQK)f(\(RAP)-8 b(,)32 b(D)m(AP)-8 b(,)31 b(A)m(OPRMS,)g(A)m(OB,)g(ZOB,)g(HOB,)f(DOB,)i(R)m (OB\))472 4964 y(Apparen)m(t)f(to)g(observ)m(ed)f(using)f(precomputed)h (parameters)236 5132 y(CALL)g(sla)p Fq(_)p FA(O)m(AP)g(\(TYPE,)g(OB1,)h (OB2,)h(UTC,)e(DUT,)g(ELONGM,)h(PHIM,)g(HM,)g(XP)-8 b(,)31 b(YP)-8 b(,)932 5245 y(TDK,)31 b(PMB,)g(RH,)f(WL,)h(TLR,)f(RAP)-8 b(,)31 b(D)m(AP\))472 5339 y(Observ)m(ed)f(to)h(apparen)m(t)236 5506 y(CALL)f(sla)p Fq(_)p FA(O)m(APQK)f(\(TYPE,)i(OB1,)g(OB2,)g(A)m (OPRMS,)f(RA,)h(D)m(A\))472 5619 y(Observ)m(ed)f(to)h(apparen)m(t)g (using)e(precomputed)g(parameters)p eop %%Page: 209 211 209 210 bop 0 52 a Ft(SUN/67.45)3206 b FA(209)0 351 y Fs(Azim)m(uth)35 b(and)k(Elev)-6 b(ation)236 628 y FA(CALL)30 b(sla)p Fq(_)p FA(AL)-8 b(T)g(AZ)30 b(\(HA,)h(DEC,)g(PHI,)1033 741 y(AZ,)f(AZD,)h(AZDD,)g(EL,)g(ELD,)f(ELDD,)h(P)-8 b(A,)31 b(P)-8 b(AD,)32 b(P)-8 b(ADD\))472 835 y(P)m(ositions,)30 b(v)m(elo)s(cities)g Fn(etc.)g FA(for)g(an)h(altazim)m(uth)f(moun)m(t) 236 1033 y(CALL)g(sla)p Fq(_)p FA(E2H)g(\(HA,)h(DEC,)g(PHI,)f(AZ,)h (EL\))236 1146 y(CALL)f(sla)p Fq(_)p FA(DE2H)h(\(HA,)g(DEC,)f(PHI,)h (AZ,)f(EL\))472 1259 y([)15 b Fi(h;)g(\016)21 b FA(])30 b(to)h([)15 b Fi(Az)t(;)g(E)5 b(l)34 b FA(])236 1458 y(CALL)c(sla)p Fq(_)p FA(H2E)g(\(AZ,)h(EL,)f(PHI,)g(HA,)h(DEC\))236 1571 y(CALL)f(sla)p Fq(_)p FA(DH2E)h(\(AZ,)f(EL,)g(PHI,)h(HA,)g(DEC\)) 472 1684 y([)15 b Fi(Az)t(;)g(E)5 b(l)34 b FA(])d(to)g([)15 b Fi(h;)g(\016)20 b FA(])236 1882 y(CALL)30 b(sla)p Fq(_)p FA(PD)m(A2H)h(\(P)-8 b(,)31 b(D,)g(A,)g(H1,)g(J1,)g(H2,)g(J2\))472 1995 y(Hour)f(Angle)h(corresp)s(onding)d(to)j(a)g(giv)m(en)f(azim)m (uth)236 2194 y(CALL)g(sla)p Fq(_)p FA(PDQ2H)g(\(P)-8 b(,)31 b(D,)g(Q,)g(H1,)g(J1,)g(H2,)g(J2\))472 2306 y(Hour)f(Angle)h (corresp)s(onding)d(to)j(a)g(giv)m(en)f(parallactic)g(angle)236 2505 y(D)h(=)f(sla)p Fq(_)p FA(P)-8 b(A)30 b(\(HA,)h(DEC,)g(PHI\))472 2618 y([)15 b Fi(h;)g(\016)21 b FA(])30 b(to)h(parallactic)f(angle)236 2817 y(D)h(=)f(sla)p Fq(_)p FA(ZD)g(\(HA,)h(DEC,)f(PHI\))472 2929 y([)15 b Fi(h;)g(\016)21 b FA(])30 b(to)h(zenith)f(distance)0 3337 y Fs(Refraction)36 b(and)j(Air)d(Mass)236 3613 y FA(CALL)30 b(sla)p Fq(_)p FA(REFR)m(O)g(\(ZOBS,)g(HM,)h(TDK,)f(PMB,)h (RH,)g(WL,)g(PHI,)f(TLR,)g(EPS,)g(REF\))472 3726 y(Change)h(in)e (zenith)h(distance)g(due)f(to)i(refraction)236 3925 y(CALL)f(sla)p Fq(_)p FA(REF)m(CO)g(\(HM,)h(TDK,)f(PMB,)i(RH,)e(WL,)h(PHI,)f(TLR,)g (EPS,)g(REF)-10 b(A,)31 b(REFB\))472 4038 y(Constan)m(ts)g(for)f (simple)f(refraction)h(mo)s(del)f(\(accurate\))236 4236 y(CALL)h(sla)p Fq(_)p FA(REF)m(COQ)f(\(TDK,)i(PMB,)g(RH,)g(WL,)g(REF) -10 b(A,)30 b(REFB\))472 4349 y(Constan)m(ts)h(for)f(simple)f (refraction)h(mo)s(del)f(\(fast\))236 4548 y(CALL)g(sla)p Fq(_)p FA(A)-8 b(TMDSP)30 b(\()g(TDK,)f(PMB,)i(RH,)f(WL1,)g(REF)-10 b(A1,)31 b(REFB1,)g(WL2,)g(REF)-10 b(A2,)31 b(REFB2)f(\))472 4660 y(Adjust)g(refraction)g(constan)m(ts)i(for)e(colour)236 4859 y(CALL)g(sla)p Fq(_)p FA(REFZ)f(\(ZU,)i(REF)-10 b(A,)31 b(REFB,)g(ZR\))472 4972 y(Unrefracted)g(to)g(refracted)g(ZD,)f (simple)f(mo)s(del)236 5171 y(CALL)h(sla)p Fq(_)p FA(REFV)g(\(VU,)h (REF)-10 b(A,)31 b(REFB,)g(VR\))472 5283 y(Unrefracted)g(to)g (refracted)g([)15 b Fi(Az)t(;)g(E)5 b(l)34 b FA(])c(v)m(ector,)i (simple)d(mo)s(del)236 5482 y(D)i(=)f(sla)p Fq(_)p FA(AIRMAS)g(\(ZD\)) 472 5595 y(Air)g(mass)p eop %%Page: 210 212 210 211 bop 0 52 a FA(210)0 351 y Fs(Ecliptic)34 b(Co)s(ordinates)236 592 y FA(CALL)c(sla)p Fq(_)p FA(ECMA)-8 b(T)30 b(\(D)m(A)-8 b(TE,)32 b(RMA)-8 b(T\))472 705 y(Equatorial)30 b(to)h(ecliptic)e (rotation)i(matrix)236 882 y(CALL)f(sla)p Fq(_)p FA(EQECL)f(\(DR,)i (DD,)g(D)m(A)-8 b(TE,)32 b(DL,)f(DB\))472 995 y(J2000.0)i(`FK5')e(to)g (ecliptic)f(co)s(ordinates)236 1172 y(CALL)g(sla)p Fq(_)p FA(ECLEQ)f(\(DL,)i(DB,)g(D)m(A)-8 b(TE,)32 b(DR,)f(DD\))472 1285 y(Ecliptic)e(co)s(ordinates)h(to)h(J2000.0)i(`FK5')0 1627 y Fs(Galactic)j(Co)s(ordinates)236 1868 y FA(CALL)30 b(sla)p Fq(_)p FA(EG50)h(\(DR,)g(DD,)g(DL,)g(DB\))472 1981 y(B1950.0)j(`FK4')d(to)g(galactic)236 2158 y(CALL)f(sla)p Fq(_)p FA(GE50)h(\(DL,)g(DB,)g(DR,)g(DD\))472 2271 y(Galactic)h(to)f (B1950.0)i(`FK4')236 2448 y(CALL)d(sla)p Fq(_)p FA(EQGAL)g(\(DR,)h(DD,) g(DL,)g(DB\))472 2561 y(J2000.0)i(`FK5')e(to)g(galactic)236 2738 y(CALL)f(sla)p Fq(_)p FA(GALEQ)g(\(DL,)h(DB,)g(DR,)g(DD\))472 2851 y(Galactic)h(to)f(J2000.0)h(`FK5')0 3193 y Fs(Sup)s(ergalactic)37 b(Co)s(ordinates)236 3434 y FA(CALL)30 b(sla)p Fq(_)p FA(GALSUP)f(\(DL,)j(DB,)f(DSL,)f(DSB\))472 3547 y(Galactic)i(to)f(sup)s (ergalactic)236 3724 y(CALL)f(sla)p Fq(_)p FA(SUPGAL)f(\(DSL,)i(DSB,)g (DL,)g(DB\))472 3837 y(Sup)s(ergalactic)f(to)h(galactic)0 4180 y Fs(Ephemerides)236 4420 y FA(CALL)f(sla)p Fq(_)p FA(DMOON)g(\(D)m(A)-8 b(TE,)32 b(PV\))472 4533 y(Appro)m(ximate)f(geo)s (cen)m(tric)g(p)s(osition)e(and)g(v)m(elo)s(cit)m(y)i(of)g(the)f(Mo)s (on)236 4710 y(CALL)g(sla)p Fq(_)p FA(EAR)-8 b(TH)30 b(\(IY,)h(ID,)g(FD,)g(PV\))472 4823 y(Appro)m(ximate)g(helio)s(cen)m (tric)e(p)s(osition)f(and)i(v)m(elo)s(cit)m(y)h(of)f(the)h(Earth)236 5000 y(CALL)f(sla)p Fq(_)p FA(EVP)g(\(D)m(A)-8 b(TE,)31 b(DEQX,)g(D)m(VB,)h(DPB,)g(D)m(VH,)f(DPH\))472 5113 y(Barycen)m(tric)h (and)d(helio)s(cen)m(tric)g(v)m(elo)s(cit)m(y)i(and)f(p)s(osition)f(of) h(the)h(Earth)236 5290 y(CALL)f(sla)p Fq(_)p FA(MOON)g(\(IY,)g(ID,)h (FD,)h(PV\))472 5403 y(Appro)m(ximate)f(geo)s(cen)m(tric)g(p)s(osition) e(and)g(v)m(elo)s(cit)m(y)i(of)g(the)f(Mo)s(on)236 5580 y(CALL)g(sla)p Fq(_)p FA(PLANET)f(\(D)m(A)-8 b(TE,)32 b(NP)-8 b(,)31 b(PV,)g(JST)-8 b(A)g(T\))472 5693 y(Appro)m(ximate)31 b(helio)s(cen)m(tric)e(p)s(osition)f(and)i(v)m(elo)s(cit)m(y)h(of)f(a)h (planet)p eop %%Page: 211 213 211 212 bop 0 52 a Ft(SUN/67.45)3206 b FA(211)236 351 y(CALL)30 b(sla)p Fq(_)p FA(RDPLAN)g(\(D)m(A)-8 b(TE,)32 b(NP)-8 b(,)31 b(ELONG,)f(PHI,)h(RA,)g(DEC,)f(DIAM\))472 464 y(Appro)m(ximate)h(top)s(o)s(cen)m(tric)f(apparen)m(t)h(place)f(of) h(a)f(planet)236 636 y(CALL)g(sla)p Fq(_)p FA(PLANEL)f(\(D)m(A)-8 b(TE,)32 b(JF)m(ORM,)f(EPOCH,)f(ORBINC,)g(ANODE,)h(PERIH,)1107 749 y(A)m(OR)m(Q,)h(E,)e(A)m(ORL,)h(DM,)g(PV,)g(JST)-8 b(A)g(T\))472 843 y(Helio)s(cen)m(tric)21 b(p)s(osition)f(and)h(v)m (elo)s(cit)m(y)h(of)g(a)g(planet,)h(asteroid)e(or)g(comet,)k(starting)d (from)f(orbital)472 956 y(elemen)m(ts)236 1128 y(CALL)30 b(sla)p Fq(_)p FA(PLANTE)f(\(D)m(A)-8 b(TE,)32 b(ELONG,)f(PHI,)f(JF)m (ORM,)h(EPOCH,)f(ORBINC,)g(ANODE,)1116 1241 y(PERIH,)h(A)m(OR)m(Q,)g (E,)f(A)m(ORL,)h(DM,)g(RA,)g(DEC,)f(R,)h(JST)-8 b(A)g(T\))472 1335 y(T)g(op)s(o)s(cen)m(tric)31 b(apparen)m(t)h(place)f(of)g(a)g (Solar-System)g(ob)5 b(ject)32 b(whose)f(helio)s(cen)m(tric)e(orbital)h (ele-)472 1448 y(men)m(ts)h(are)g(kno)m(wn)236 1620 y(CALL)f(sla)p Fq(_)p FA(PV2EL)g(\(PV,)h(D)m(A)-8 b(TE,)31 b(PMASS,)f(JF)m(ORMR,)h(JF) m(ORM,)g(EPOCH,)f(ORBINC,)1028 1733 y(ANODE,)h(PERIH,)f(A)m(OR)m(Q,)h (E,)g(A)m(ORL,)f(DM,)i(JST)-8 b(A)g(T\))472 1827 y(Orbital)29 b(elemen)m(ts)i(of)f(a)h(planet)f(from)g(instan)m(taneous)g(p)s (osition)e(and)i(v)m(elo)s(cit)m(y)236 1999 y(CALL)g(sla)p Fq(_)p FA(PER)-8 b(TEL)29 b(\(JF)m(ORM,)i(D)m(A)-8 b(TE0,)32 b(D)m(A)-8 b(TE1,)1101 2111 y(EPOCH0,)31 b(ORBI0,)g(ANODE0,)g(PERIH0,)g (A)m(OR)m(Q0,)g(E0,)g(AM0,)1101 2224 y(EPOCH1,)g(ORBI1,)g(ANODE1,)g (PERIH1,)g(A)m(OR)m(Q1,)g(E1,)g(AM1,)1101 2337 y(JST)-8 b(A)g(T\))472 2431 y(Up)s(date)31 b(elemen)m(ts)f(b)m(y)h(applying)d(p) s(erturbations)236 2603 y(CALL)i(sla)p Fq(_)p FA(EL2UE)g(\(D)m(A)-8 b(TE,)32 b(JF)m(ORM,)f(EPOCH,)f(ORBINC,)g(ANODE,)1028 2716 y(PERIH,)g(A)m(OR)m(Q,)h(E,)g(A)m(ORL,)f(DM,)1028 2829 y(U,)h(JST)-8 b(A)g(T\))472 2923 y(T)g(ransform)30 b(con)m(v)m(en)m(tional)h(elemen)m(ts)g(to)g(univ)m(ersal)e(elemen)m (ts)236 3095 y(CALL)h(sla)p Fq(_)p FA(UE2EL)g(\(U,)h(JF)m(ORMR,)1028 3208 y(JF)m(ORM,)g(EPOCH,)f(ORBINC,)g(ANODE,)h(PERIH,)1028 3321 y(A)m(OR)m(Q,)g(E,)g(A)m(ORL,)f(DM,)i(JST)-8 b(A)g(T\))472 3415 y(T)g(ransform)30 b(univ)m(ersal)e(elemen)m(ts)j(to)g(con)m(v)m (en)m(tional)h(elemen)m(ts)236 3587 y(CALL)e(sla)p Fq(_)p FA(PV2UE)g(\(PV,)h(D)m(A)-8 b(TE,)32 b(PMASS,)e(U,)g(JST)-8 b(A)g(T\))472 3700 y(P)m(ac)m(k)j(age)34 b(a)c(p)s(osition)f(and)h(v)m (elo)s(cit)m(y)h(for)f(use)g(as)g(univ)m(ersal)f(elemen)m(ts)236 3872 y(CALL)h(sla)p Fq(_)p FA(UE2PV)g(\(D)m(A)-8 b(TE,)32 b(U,)f(PV,)f(JST)-8 b(A)g(T\))472 3985 y(Extract)32 b(the)e(p)s (osition)f(and)h(v)m(elo)s(cit)m(y)g(from)g(univ)m(ersal)f(elemen)m(ts) 236 4156 y(CALL)h(sla)p Fq(_)p FA(PER)-8 b(TUE)29 b(\(D)m(A)-8 b(TE,)32 b(U,)f(JST)-8 b(A)g(T\))472 4269 y(Up)s(date)31 b(univ)m(ersal)d(elemen)m(ts)j(b)m(y)f(applying)e(p)s(erturbations)236 4441 y(R)i(=)g(sla)p Fq(_)p FA(R)-10 b(VER)m(OT)30 b(\(PHI,)g(RA,)h(D)m (A,)h(ST\))472 4554 y(V)-8 b(elo)s(cit)m(y)31 b(comp)s(onen)m(t)g(due)f (to)h(rotation)g(of)f(the)h(Earth)236 4726 y(CALL)f(sla)p Fq(_)p FA(ECOR)f(\(RM,)i(DM,)g(IY,)g(ID,)g(FD,)g(R)-10 b(V,)31 b(TL\))472 4839 y(Comp)s(onen)m(ts)f(of)h(v)m(elo)s(cit)m(y)g (and)e(ligh)m(t)h(time)g(due)g(to)h(Earth)f(orbital)f(motion)236 5011 y(R)h(=)g(sla)p Fq(_)p FA(R)-10 b(VLSRD)30 b(\(R2000,)i(D2000\)) 472 5124 y(V)-8 b(elo)s(cit)m(y)31 b(comp)s(onen)m(t)g(due)f(to)h (solar)f(motion)g(wrt)g(dynamical)f(LSR)236 5295 y(R)h(=)g(sla)p Fq(_)p FA(R)-10 b(VLSRK)29 b(\(R2000,)k(D2000\))472 5408 y(V)-8 b(elo)s(cit)m(y)31 b(comp)s(onen)m(t)g(due)f(to)h(solar)f (motion)g(wrt)g(kinematical)f(LSR)236 5580 y(R)h(=)g(sla)p Fq(_)p FA(R)-10 b(V)m(GALC)31 b(\(R2000,)h(D2000\))472 5693 y(V)-8 b(elo)s(cit)m(y)31 b(comp)s(onen)m(t)g(due)f(to)h(rotation) g(of)f(the)h(Galaxy)p eop %%Page: 212 214 212 213 bop 0 52 a FA(212)236 351 y(R)30 b(=)g(sla)p Fq(_)p FA(R)-10 b(VLG)30 b(\(R2000,)j(D2000\))472 464 y(V)-8 b(elo)s(cit)m(y)37 b(comp)s(onen)m(t)g(due)e(to)i(rotation)f (and)g(translation)f(of)h(the)h(Galaxy)-8 b(,)38 b(relativ)m(e)e(to)h (the)472 577 y(mean)31 b(motion)f(of)g(the)h(lo)s(cal)f(group)0 948 y Fs(Astrometry)236 1205 y FA(CALL)g(sla)p Fq(_)p FA(S2TP)f(\(RA,)i(DEC,)g(RAZ,)f(DECZ,)g(XI,)g(ET)-8 b(A,)31 b(J\))236 1318 y(CALL)f(sla)p Fq(_)p FA(DS2TP)g(\(RA,)h(DEC,)f(RAZ,)g (DECZ,)g(XI,)h(ET)-8 b(A,)31 b(J\))472 1431 y(T)-8 b(ransform)30 b(spherical)e(co)s(ordinates)i(in)m(to)h(tangen)m(t)h(plane)236 1617 y(CALL)e(sla)p Fq(_)p FA(V2TP)g(\(V,)h(V0,)g(XI,)g(ET)-8 b(A,)30 b(J\))236 1730 y(CALL)g(sla)p Fq(_)p FA(D)m(V2TP)h(\(V,)g(V0,)g (XI,)g(ET)-8 b(A,)30 b(J\))472 1843 y(T)-8 b(ransform)30 b([)15 b Fi(x;)g(y)s(;)g(z)20 b FA(])31 b(in)m(to)f(tangen)m(t)i(plane) d(co)s(ordinates)236 2030 y(CALL)h(sla)p Fq(_)p FA(DTP2S)g(\(XI,)g(ET) -8 b(A,)31 b(RAZ,)f(DECZ,)g(RA,)h(DEC\))236 2143 y(CALL)f(sla)p Fq(_)p FA(TP2S)f(\(XI,)i(ET)-8 b(A,)31 b(RAZ,)f(DECZ,)g(RA,)h(DEC\))472 2255 y(T)-8 b(ransform)30 b(tangen)m(t)i(plane)d(co)s(ordinates)h(in)m (to)h(spherical)d(co)s(ordinates)236 2442 y(CALL)i(sla)p Fq(_)p FA(DTP2V)g(\(XI,)h(ET)-8 b(A,)31 b(V0,)g(V\))236 2555 y(CALL)f(sla)p Fq(_)p FA(TP2V)g(\(XI,)h(ET)-8 b(A,)30 b(V0,)i(V\))472 2668 y(T)-8 b(ransform)30 b(tangen)m(t)i(plane)d(co)s (ordinates)h(in)m(to)h([)15 b Fi(x;)g(y)s(;)g(z)20 b FA(])236 2854 y(CALL)30 b(sla)p Fq(_)p FA(DTPS2C)f(\(XI,)i(ET)-8 b(A,)31 b(RA,)f(DEC,)h(RAZ1,)g(DECZ1,)f(RAZ2,)h(DECZ2,)f(N\))236 2967 y(CALL)g(sla)p Fq(_)p FA(TPS2C)f(\(XI,)i(ET)-8 b(A,)30 b(RA,)h(DEC,)g(RAZ1,)f(DECZ1,)h(RAZ2,)f(DECZ2,)h(N\))472 3080 y(Get)h(plate)e(cen)m(tre)i(from)d(star)i([)15 b Fi(\013;)g(\016)20 b FA(])31 b(and)f(tangen)m(t)h(plane)f(co)s (ordinates)236 3267 y(CALL)g(sla)p Fq(_)p FA(DTPV2C)g(\(XI,)h(ET)-8 b(A,)30 b(V,)h(V01,)h(V02,)f(N\))236 3380 y(CALL)f(sla)p Fq(_)p FA(TPV2C)f(\(XI,)i(ET)-8 b(A,)31 b(V,)g(V01,)g(V02,)h(N\))472 3493 y(Get)g(plate)e(cen)m(tre)i(from)d(star)i([)15 b Fi(x;)g(y)s(;)g(z)20 b FA(])31 b(and)f(tangen)m(t)i(plane)d(co)s (ordinates)236 3679 y(CALL)h(sla)p Fq(_)p FA(PCD)g(\(DISCO,)g(X,)g(Y\)) 472 3792 y(Apply)f(pincushion/barrel)e(distortion)236 3979 y(CALL)j(sla)p Fq(_)p FA(UNPCD)g(\(DISCO,)g(X,)h(Y\))472 4092 y(Remo)m(v)m(e)i(pincushion/barrel)26 b(distortion)236 4278 y(CALL)k(sla)p Fq(_)p FA(FITXY)g(\(ITYPE,)g(NP)-8 b(,)31 b(XYE,)g(XYM,)g(COEFFS,)f(J\))472 4391 y(Fit)h(a)f(linear)f(mo)s (del)g(to)j(relate)e(t)m(w)m(o)i(sets)f(of)f([)15 b Fi(x;)g(y)k FA(])31 b(co)s(ordinates)236 4578 y(CALL)f(sla)p Fq(_)p FA(PXY)g(\(NP)-8 b(,)31 b(XYE,)g(XYM,)g(COEFFS,)f(XYP)-8 b(,)31 b(XRMS,)g(YRMS,)f(RRMS\))472 4691 y(Compute)g(predicted)g(co)s (ordinates)g(and)f(residuals)236 4877 y(CALL)h(sla)p Fq(_)p FA(INVF)g(\(FWDS,)i(BKWDS,)f(J\))472 4990 y(In)m(v)m(ert)g(a)g (linear)e(mo)s(del)236 5177 y(CALL)h(sla)p Fq(_)p FA(XY2XY)h(\(X1,)g (Y1,)h(COEFFS,)d(X2,)j(Y2\))472 5290 y(T)-8 b(ransform)30 b(one)h([)15 b Fi(x;)g(y)j FA(])236 5476 y(CALL)30 b(sla)p Fq(_)p FA(DCMPF)g(\(COEFFS,)h(XZ,)f(YZ,)g(XS,)g(YS,)h(PERP)-8 b(,)30 b(ORIENT\))472 5589 y(Decomp)s(ose)i(a)f(linear)d(\014t)j(in)m (to)f(scales)h Fn(etc.)p eop %%Page: 213 215 213 214 bop 0 52 a Ft(SUN/67.45)3206 b FA(213)0 351 y Fs(Numerical)35 b(Metho)s(ds)236 589 y FA(CALL)30 b(sla)p Fq(_)p FA(COMBN)g(\(NSEL,)g(NCAND,)h(LIST,)f(J\))472 702 y(Next)i(com)m(bination)d(\(subset)h(from)g(a)h(sp)s(eci\014ed)e(n) m(um)m(b)s(er)g(of)h(items\))236 877 y(CALL)g(sla)p Fq(_)p FA(PERMUT)f(\(N,)j(IST)-8 b(A)g(TE,)30 b(IORDER,)g(J\))472 990 y(Next)i(p)s(erm)m(utation)d(of)i(a)f(sp)s(eci\014ed)f(n)m(um)m(b)s (er)g(of)i(items)236 1165 y(CALL)f(sla)p Fq(_)p FA(SMA)-8 b(T)30 b(\(N,)h(A,)g(Y,)f(D,)h(JF,)g(IW\))236 1278 y(CALL)f(sla)p Fq(_)p FA(DMA)-8 b(T)31 b(\(N,)g(A,)f(Y,)h(D,)g(JF,)g(IW\))472 1391 y(Matrix)g(in)m(v)m(ersion)e(and)h(solution)f(of)h(sim)m (ultaneous)f(equations)236 1566 y(CALL)h(sla)p Fq(_)p FA(SVD)g(\(M,)h(N,)g(MP)-8 b(,)31 b(NP)-8 b(,)31 b(A,)g(W,)g(V,)f(W)m (ORK,)h(JST)-8 b(A)g(T\))472 1679 y(Singular)28 b(v)-5 b(alue)30 b(decomp)s(osition)f(of)i(a)f(matrix)236 1854 y(CALL)g(sla)p Fq(_)p FA(SVDSOL)f(\(M,)i(N,)g(MP)-8 b(,)31 b(NP)-8 b(,)31 b(B,)g(U,)g(W,)g(V,)f(W)m(ORK,)h(X\))472 1967 y(Solution)e(from)h(giv)m(en)g(v)m(ector)i(plus)d(SVD)236 2142 y(CALL)h(sla)p Fq(_)p FA(SVDCO)m(V)g(\(N,)h(NP)-8 b(,)31 b(NC,)f(W,)h(V,)g(W)m(ORK,)g(CVM\))472 2255 y(Co)m(v)-5 b(ariance)31 b(matrix)f(from)g(SVD)236 2430 y(R)g(=)g(sla)p Fq(_)p FA(RANDOM)h(\(SEED\))472 2543 y(Generate)h(pseudo-random)d(real) h(n)m(um)m(b)s(er)f(in)g(the)i(range)g(0)25 b Fl(\024)g Fi(x)h(<)f FA(1)236 2718 y(R)30 b(=)g(sla)p Fq(_)p FA(GRESID)g(\(S\)) 472 2831 y(Generate)i(pseudo-random)d(normal)h(deviate)g(\()p Fl(\021)h FA(`Gaussian)e(residual'\))0 3168 y Fs(Real-time)236 3406 y FA(CALL)h(sla)p Fq(_)p FA(W)-10 b(AIT)30 b(\(DELA)-8 b(Y\))472 3519 y(In)m(terv)j(al)31 b(w)m(ait)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF