1 | #include "slalib.h"
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2 | #include "slamac.h"
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3 | void slaUe2el ( double u[], int jformr,
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4 | int *jform, double *epoch, double *orbinc,
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5 | double *anode, double *perih, double *aorq, double *e,
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6 | double *aorl, double *dm, int *jstat )
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7 | /*
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8 | ** - - - - - - - - -
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9 | ** s l a U e 2 e l
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10 | ** - - - - - - - - -
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11 | **
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12 | ** Transform universal elements into conventional heliocentric
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13 | ** osculating elements.
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14 | **
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15 | ** Given:
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16 | **
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17 | ** u double[13] universal orbital elements (Note 1)
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18 | **
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19 | ** [0] combined mass (M+m)
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20 | ** [1] total energy of the orbit (alpha)
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21 | ** [2] reference (osculating) epoch (t0)
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22 | ** [3-5] position at reference epoch (r0)
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23 | ** [6-8] velocity at reference epoch (v0)
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24 | ** [9] heliocentric distance at reference epoch
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25 | ** [10] r0.v0
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26 | ** [11] date (t)
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27 | ** [12] universal eccentric anomaly (psi) of date, approx
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28 | **
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29 | ** jformr int requested element set (1-3; Note 3)
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30 | **
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31 | ** Returned:
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32 | ** jform double* element set actually returned (1-3; Note 4)
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33 | ** epoch double* epoch of elements (TT MJD)
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34 | ** orbinc double* inclination (radians)
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35 | ** anode double* longitude of the ascending node (radians)
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36 | ** perih double* longitude or argument of perihelion (radians)
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37 | ** aorq double* mean distance or perihelion distance (AU)
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38 | ** e double* eccentricity
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39 | ** aorl double* mean anomaly or longitude (radians, jform=1,2 only)
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40 | ** dm double* daily motion (radians, jform=1 only)
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41 | ** jstat int* status: 0 = OK
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42 | ** -1 = illegal combined mass
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43 | ** -2 = illegal jformr
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44 | ** -3 = position/velocity out of range
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45 | **
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46 | ** Notes
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47 | **
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48 | ** 1 The "universal" elements are those which define the orbit for the
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49 | ** purposes of the method of universal variables (see reference 2).
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50 | ** They consist of the combined mass of the two bodies, an epoch,
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51 | ** and the position and velocity vectors (arbitrary reference frame)
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52 | ** at that epoch. The parameter set used here includes also various
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53 | ** quantities that can, in fact, be derived from the other
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54 | ** information. This approach is taken to avoiding unnecessary
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55 | ** computation and loss of accuracy. The supplementary quantities
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56 | ** are (i) alpha, which is proportional to the total energy of the
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57 | ** orbit, (ii) the heliocentric distance at epoch, (iii) the
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58 | ** outwards component of the velocity at the given epoch, (iv) an
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59 | ** estimate of psi, the "universal eccentric anomaly" at a given
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60 | ** date and (v) that date.
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61 | **
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62 | ** 2 The universal elements are with respect to the mean equator and
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63 | ** equinox of epoch J2000. The orbital elements produced are with
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64 | ** respect to the J2000 ecliptic and mean equinox.
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65 | **
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66 | ** 3 Three different element-format options are supported:
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67 | **
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68 | ** Option jform=1, suitable for the major planets:
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69 | **
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70 | ** epoch = epoch of elements (TT MJD)
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71 | ** orbinc = inclination i (radians)
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72 | ** anode = longitude of the ascending node, big omega (radians)
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73 | ** perih = longitude of perihelion, curly pi (radians)
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74 | ** aorq = mean distance, a (AU)
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75 | ** e = eccentricity, e
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76 | ** aorl = mean longitude L (radians)
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77 | ** dm = daily motion (radians)
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78 | **
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79 | ** Option jform=2, suitable for minor planets:
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80 | **
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81 | ** epoch = epoch of elements (TT MJD)
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82 | ** orbinc = inclination i (radians)
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83 | ** anode = longitude of the ascending node, big omega (radians)
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84 | ** perih = argument of perihelion, little omega (radians)
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85 | ** aorq = mean distance, a (AU)
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86 | ** e = eccentricity, e
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87 | ** aorl = mean anomaly M (radians)
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88 | **
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89 | ** Option jform=3, suitable for comets:
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90 | **
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91 | ** epoch = epoch of perihelion (TT MJD)
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92 | ** orbinc = inclination i (radians)
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93 | ** anode = longitude of the ascending node, big omega (radians)
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94 | ** perih = argument of perihelion, little omega (radians)
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95 | ** aorq = perihelion distance, q (AU)
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96 | ** e = eccentricity, e
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97 | **
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98 | ** 4 It may not be possible to generate elements in the form
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99 | ** requested through jformr. The caller is notified of the form
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100 | ** of elements actually returned by means of the jform argument:
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101 | **
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102 | ** jformr jform meaning
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103 | **
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104 | ** 1 1 OK - elements are in the requested format
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105 | ** 1 2 never happens
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106 | ** 1 3 orbit not elliptical
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107 | **
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108 | ** 2 1 never happens
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109 | ** 2 2 OK - elements are in the requested format
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110 | ** 2 3 orbit not elliptical
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111 | **
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112 | ** 3 1 never happens
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113 | ** 3 2 never happens
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114 | ** 3 3 OK - elements are in the requested format
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115 | **
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116 | ** 5 The arguments returned for each value of jform (cf Note 6: jform
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117 | ** may not be the same as jformr) are as follows:
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118 | **
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119 | ** jform 1 2 3
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120 | ** epoch t0 t0 T
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121 | ** orbinc i i i
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122 | ** anode Omega Omega Omega
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123 | ** perih curly pi omega omega
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124 | ** aorq a a q
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125 | ** e e e e
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126 | ** aorl L M -
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127 | ** dm n - -
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128 | **
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129 | ** where:
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130 | **
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131 | ** t0 is the epoch of the elements (MJD, TT)
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132 | ** T " epoch of perihelion (MJD, TT)
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133 | ** i " inclination (radians)
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134 | ** Omega " longitude of the ascending node (radians)
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135 | ** curly pi " longitude of perihelion (radians)
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136 | ** omega " argument of perihelion (radians)
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137 | ** a " mean distance (AU)
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138 | ** q " perihelion distance (AU)
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139 | ** e " eccentricity
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140 | ** L " longitude (radians, 0-2pi)
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141 | ** M " mean anomaly (radians, 0-2pi)
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142 | ** n " daily motion (radians)
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143 | ** - means no value is set
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144 | **
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145 | ** 6 At very small inclinations, the longitude of the ascending node
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146 | ** anode becomes indeterminate and under some circumstances may be
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147 | ** set arbitrarily to zero. Similarly, if the orbit is close to
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148 | ** circular, the true anomaly becomes indeterminate and under some
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149 | ** circumstances may be set arbitrarily to zero. In such cases,
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150 | ** the other elements are automatically adjusted to compensate,
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151 | ** and so the elements remain a valid description of the orbit.
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152 | **
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153 | ** References:
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154 | **
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155 | ** 1 Sterne, Theodore E., "An Introduction to Celestial Mechanics",
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156 | ** Interscience Publishers Inc., 1960. Section 6.7, p199.
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157 | **
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158 | ** 2 Everhart, E. & Pitkin, E.T., Am.J.Phys. 51, 712, 1983.
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159 | **
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160 | ** Called: slaPv2el
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161 | **
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162 | ** Last revision: 18 March 1999
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163 | **
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164 | ** Copyright P.T.Wallace. All rights reserved.
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165 | */
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166 |
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167 | /* Gaussian gravitational constant (exact) */
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168 | #define GCON 0.01720209895
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169 |
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170 | /* Canonical days to seconds */
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171 | #define CD2S ( GCON / 86400.0 )
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172 |
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173 | {
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174 | int i;
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175 | double pmass, date, pv[6];
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176 |
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177 |
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178 | /* Unpack the universal elements. */
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179 | pmass = u[0] - 1.0;
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180 | date = u[2];
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181 | for ( i = 0; i < 3; i++ ) {
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182 | pv[i] = u[i+3];
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183 | pv[i+3] = u[i+6] * CD2S;
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184 | }
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185 |
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186 | /* Convert the position and velocity etc into conventional elements. */
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187 | slaPv2el ( pv, date, pmass, jformr, jform, epoch, orbinc, anode,
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188 | perih, aorq, e, aorl, dm, jstat );
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189 |
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190 | }
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