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package Astro::Coords::Elements; |
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=head1 NAME |
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Astro::Coords::Elements - Specify astronomical coordinates using orbital elements |
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=head1 SYNOPSIS |
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$c = new Astro::Coords::Elements( elements => \%elements ); |
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12
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=head1 DESCRIPTION |
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This class is used by C<Astro::Coords> for handling coordinates |
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specified as orbital elements. |
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=cut |
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9138542
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use 5.006; |
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82
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use strict; |
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441
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21
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use warnings; |
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83
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579
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use Carp; |
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1869
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our $VERSION = '0.21'; |
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26
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# Need working palPlante |
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676
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use Astro::PAL 0.95 (); |
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4871
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534
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28
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614
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use Astro::Coords::Angle; |
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60
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580
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29
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7736
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use Time::Piece qw/ :override /; |
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141925
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1857
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use base qw/ Astro::Coords /; |
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2828
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32
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33
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126
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use overload '""' => "stringify"; |
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65
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158
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34
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35
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=head1 METHODS |
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36
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37
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38
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=head2 Constructor |
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40
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=over 4 |
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42
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=item B<new> |
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43
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44
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Instantiate a new object using the supplied options. |
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45
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46
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$c = new Astro::Coords::Elements( elements => \%elements ); |
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47
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$c = new Astro::Coords::Elements( elements => \@array ); |
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48
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49
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Returns undef on error. |
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50
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51
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The elements can be specified either by using a reference to an array |
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52
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returned by the C<array()> method of another elements object or in a |
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53
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reference to a hash containing the following keys: |
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54
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55
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suitable for the major planets: |
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56
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57
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EPOCH = epoch of elements t0 (TT MJD) |
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58
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ORBINC = inclination i (radians) |
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59
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ANODE = longitude of the ascending node [$\Omega$] (radians) |
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60
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PERIH = longitude of perihelion [$\varpi$] (radians) |
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61
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AORQ = mean distance a (AU) |
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62
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E = eccentricity e |
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63
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AORL = mean longitude L (radians) |
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64
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DM = daily motion n (radians) |
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65
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66
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suitable for minor planets: |
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67
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68
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69
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EPOCH = epoch of elements t0 (TT MJD) |
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70
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ORBINC = inclination i (radians) |
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71
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ANODE = longitude of the ascending node [$\Omega$] (radians) |
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72
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PERIH = argument of perihelion [$\omega$] (radians) |
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73
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AORQ = mean distance a (AU) |
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74
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E = eccentricity e |
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75
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AORL = mean anomaly M (radians) |
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76
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77
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suitable for comets: |
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78
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79
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80
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EPOCH = epoch of elements t0 (TT MJD) |
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81
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ORBINC = inclination i (radians) |
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82
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ANODE = longitude of the ascending node [$\Omega$] (radians) |
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83
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PERIH = argument of perihelion [$\omega$] (radians) |
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84
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AORQ = perihelion distance q (AU) |
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85
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E = eccentricity e |
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86
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EPOCHPERIH = epoch of perihelion T (TT MJD) |
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87
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88
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See the documentation to palPlante() and palPertel() for more information. |
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89
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Keys must be upper case. |
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90
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91
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For comets if the only one epoch is specified it is assumed that the |
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92
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epochs are identical. This may cause problems if the epochs are not |
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93
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really close to each other. |
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94
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95
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In order to better match normal usage, EPOCH can also be specified |
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96
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as a string of the form 'YYYY mmm D.frac' (e.g. '1997 Apr 1.567'). |
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97
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(no decimal place after the month). This is the format used by JPL. |
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98
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99
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=cut |
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100
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101
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sub new { |
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102
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5
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5
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1
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13
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my $proto = shift; |
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103
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5
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33
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22
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my $class = ref($proto) || $proto; |
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104
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105
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5
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20
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my %opts = @_; |
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106
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107
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# "elements" key must be defined and point to a reference |
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108
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5
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50
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33
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31
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return undef unless (exists $opts{elements} && ref($opts{elements})); |
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109
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110
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# We allow use of an array reference or a hash |
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111
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# The array ref is converted to a hash |
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112
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5
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14
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my %elements; |
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113
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5
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100
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33
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39
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if (ref($opts{elements}) eq 'HASH') { |
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50
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114
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4
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11
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%elements = %{ $opts{elements} }; |
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4
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23
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115
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} elsif (ref($opts{elements}) eq 'ARRAY' && |
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116
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$opts{elements}->[0] eq 'ELEMENTS') { |
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117
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118
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1
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4
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my $i = 3; |
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119
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1
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4
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for my $key (qw/ EPOCH ORBINC ANODE PERIH AORQ E AORL /) { |
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120
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7
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14
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$elements{$key} = $opts{elements}->[$i]; |
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121
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7
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11
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$i++; |
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122
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} |
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123
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# assign EPOCHPERIH |
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124
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1
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50
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33
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30
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if (!defined $elements{AORL} && defined $opts{elements}->[$i]) { |
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125
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1
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6
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$elements{EPOCHPERIH} = $opts{elements}->[$i]; |
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126
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} else { |
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127
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0
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0
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$elements{DM} = $opts{elements}->[$i]; |
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128
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} |
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129
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130
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} else { |
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131
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0
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0
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return undef; |
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132
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} |
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133
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134
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# Sanity check |
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135
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5
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22
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for (qw/ ORBINC ANODE PERIH AORQ E/) { |
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136
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#return undef unless exists $elements{$_}; |
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137
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croak "Must supply element $_ to constructor" |
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138
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25
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50
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56
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unless exists $elements{$_}; |
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139
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} |
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140
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141
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# Fix up EPOCHs if it has been specified as a string |
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142
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5
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19
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for my $key (qw/ EPOCH EPOCHPERIH / ) { |
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143
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10
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50
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27
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next unless exists $elements{$key}; |
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144
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10
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21
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my $epoch = $elements{$key}; |
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145
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146
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# if we are missing one of the EPOCHs that is okay |
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147
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# so just skip |
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148
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10
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50
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38
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if (! defined $epoch) { |
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149
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# and delete it from the hash as if it was never supplied |
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150
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# this avoids complications later |
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151
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0
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0
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delete $elements{$key}; |
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152
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0
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0
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next; |
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153
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} |
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154
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155
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10
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100
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100
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117
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if ($epoch =~ /^\d+\.\d+$/ || $epoch =~ /^\d+$/) { |
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50
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156
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# an MJD so do not modify |
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157
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} elsif ($epoch =~ /\d\d\d\d \w\w\w \d+\.\d+/) { |
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158
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# has letters in it so try to parse |
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159
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# Split on decimal point |
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160
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2
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9
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my ($date, $frac) = split(/\./,$epoch,2); |
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161
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2
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6
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$frac = "0.". $frac; # preserve as decimal fraction |
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162
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2
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5
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my $format = '%Y %b %d'; |
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163
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#print "EPOCH : $epoch and $date and $frac\n"; |
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164
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2
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11
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my $obj = Time::Piece->strptime($date, $format); |
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165
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2
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167
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my $tzoffset = $obj->tzoffset; |
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166
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2
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50
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42
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$tzoffset = $tzoffset->seconds if defined $tzoffset; |
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167
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2
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51
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$obj = gmtime($obj->epoch() + $tzoffset); |
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168
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169
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# get the MJD and add on the fraction |
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170
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2
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120
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my $mjd = $obj->mjd() + $frac; |
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171
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2
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83
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$elements{$key} = $mjd; |
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172
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#print "MJD: $mjd\n"; |
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173
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174
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} else { |
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175
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# do not understand the format so return undef |
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176
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0
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0
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warn "Unable to recognize format for elements $key [$epoch]"; |
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177
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0
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0
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return undef; |
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178
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} |
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179
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180
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# Convert JD to MJD |
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181
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10
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50
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39
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if ($elements{$key} > 2400000.5) { |
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182
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0
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0
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$elements{$key} -= 2400000.5; |
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183
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} |
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184
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185
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} |
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186
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187
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# but complain if we do not have one of them |
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188
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croak "Must supply one of EPOCH or EPOCHPERIH - both were undefined" |
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189
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if (!exists $elements{EPOCH} && |
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190
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5
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0
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33
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37
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!exists $elements{EPOCHPERIH}); |
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192
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# create the object |
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5
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42
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bless { elements => \%elements, name => $opts{name} }, $class; |
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195
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} |
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196
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197
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198
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199
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=back |
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201
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=head2 Accessor Methods |
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203
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=over 4 |
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204
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205
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=item B<elements> |
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206
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207
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Returns the hash containing the elements. |
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209
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%el = $c->elements; |
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210
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211
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=cut |
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212
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213
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sub elements { |
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214
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26
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26
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1
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262
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my $self = shift; |
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215
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26
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43
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return %{ $self->{elements}}; |
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26
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242
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216
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} |
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217
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218
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=back |
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219
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220
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=head1 General Methods |
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222
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=over 4 |
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224
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=item B<array> |
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225
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226
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Return back 11 element array with first element containing the |
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227
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string "ELEMENTS", the next two elements as undef and up to 8 |
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228
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following elements containing the orbital elements in the order |
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229
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presented in the documentation of the constructor. |
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230
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231
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This method returns a standardised set of elements across all |
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232
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types of coordinates. |
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233
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234
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Note that for JFORM=3 (Comet) case the epoch of perihelion |
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235
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is stored as the 8th element (the epoch of the elements is still |
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236
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returned as the first element) [corresponding to array index 10]. |
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237
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This usage of the final element can be determined by noting that |
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238
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the element before it (AORL) will be undefined in the case of JFORM=3. |
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239
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If AORL is defined then the Epoch of perihelion will not be written |
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240
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even if it is defined. |
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241
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242
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=cut |
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243
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244
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sub array { |
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245
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1
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1
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1
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117
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my $self = shift; |
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246
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1
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4
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my %el = $self->elements; |
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247
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248
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# use EPOCHPERIH if EPOCH is not defined |
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249
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1
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3
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my $epoch = $el{EPOCH}; |
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250
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1
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50
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4
|
$epoch = $el{EPOCHPERIH} unless $epoch; |
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251
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252
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# the 8th element can be the EPOCHPERIH or DM field |
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253
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# dependent on the element type. |
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254
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1
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2
|
my $lastel; |
|
255
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1
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50
|
33
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|
11
|
if (defined $el{EPOCHPERIH} && !defined $el{DM} |
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33
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256
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&& !defined $el{AORL}) { |
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257
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1
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3
|
$lastel = $el{EPOCHPERIH}; |
|
258
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} else { |
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259
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0
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0
|
$lastel = $el{DM}; |
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260
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} |
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261
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262
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return ( $self->type, undef, undef, |
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263
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|
$epoch, $el{ORBINC}, $el{ANODE}, $el{PERIH}, |
|
264
|
1
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4
|
$el{AORQ}, $el{E}, $el{AORL}, $lastel); |
|
265
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|
} |
|
266
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|
267
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|
=item B<type> |
|
268
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|
269
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|
|
Returns the generic type associated with the coordinate system. |
|
270
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|
|
For this class the answer is always "ELEMENTS". |
|
271
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|
272
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|
|
This is used to aid construction of summary tables when using |
|
273
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mixed coordinates. |
|
274
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|
275
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|
|
It could be done using isa relationships. |
|
276
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277
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|
=cut |
|
278
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|
279
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|
|
sub type { |
|
280
|
3
|
|
|
3
|
1
|
30
|
return "ELEMENTS"; |
|
281
|
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|
|
} |
|
282
|
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|
283
|
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|
|
=item B<stringify> |
|
284
|
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|
285
|
|
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|
|
Stringify overload. Returns comma-separated list of |
|
286
|
|
|
|
|
|
|
the elements. |
|
287
|
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|
288
|
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|
|
=cut |
|
289
|
|
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|
290
|
|
|
|
|
|
|
sub stringify { |
|
291
|
4
|
|
|
4
|
1
|
439
|
my $self = shift; |
|
292
|
4
|
|
|
|
|
14
|
my %el = $self->elements; |
|
293
|
4
|
100
|
|
|
|
18
|
my $str = join(",", map { (defined $_ ? $_ : 'UNDEF' ) } values %el); |
|
|
29
|
|
|
|
|
117
|
|
|
294
|
4
|
|
|
|
|
18
|
return $str; |
|
295
|
|
|
|
|
|
|
} |
|
296
|
|
|
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|
297
|
|
|
|
|
|
|
=item B<summary> |
|
298
|
|
|
|
|
|
|
|
|
299
|
|
|
|
|
|
|
Return a one line summary of the coordinates. |
|
300
|
|
|
|
|
|
|
In the future will accept arguments to control output. |
|
301
|
|
|
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|
|
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|
|
302
|
|
|
|
|
|
|
$summary = $c->summary(); |
|
303
|
|
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|
304
|
|
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|
|
=cut |
|
305
|
|
|
|
|
|
|
|
|
306
|
|
|
|
|
|
|
sub summary { |
|
307
|
0
|
|
|
0
|
1
|
0
|
my $self = shift; |
|
308
|
0
|
|
|
|
|
0
|
my $name = $self->name; |
|
309
|
0
|
0
|
|
|
|
0
|
$name = '' unless defined $name; |
|
310
|
0
|
|
|
|
|
0
|
return sprintf("%-16s %-12s %-11s ELEMENTS",$name,'',''); |
|
311
|
|
|
|
|
|
|
} |
|
312
|
|
|
|
|
|
|
|
|
313
|
|
|
|
|
|
|
=item B<apparent> |
|
314
|
|
|
|
|
|
|
|
|
315
|
|
|
|
|
|
|
Return the apparent RA and Dec (as two C<Astro::Coords::Angle> |
|
316
|
|
|
|
|
|
|
objects) for the current coordinates and time. Includes perterbation |
|
317
|
|
|
|
|
|
|
corrections to convert the elements to the required epoch. |
|
318
|
|
|
|
|
|
|
|
|
319
|
|
|
|
|
|
|
Returns empty list on error. |
|
320
|
|
|
|
|
|
|
|
|
321
|
|
|
|
|
|
|
=cut |
|
322
|
|
|
|
|
|
|
|
|
323
|
|
|
|
|
|
|
sub apparent { |
|
324
|
23
|
|
|
23
|
1
|
38
|
my $self = shift; |
|
325
|
|
|
|
|
|
|
|
|
326
|
23
|
|
|
|
|
91
|
my ($ra_app,$dec_app) = $self->_cache_read( "RA_APP", "DEC_APP" ); |
|
327
|
|
|
|
|
|
|
|
|
328
|
|
|
|
|
|
|
# not in cache so must calculate it |
|
329
|
23
|
100
|
66
|
|
|
100
|
if (!defined $ra_app || !defined $dec_app) { |
|
330
|
|
|
|
|
|
|
|
|
331
|
20
|
|
|
|
|
56
|
my $tel = $self->telescope; |
|
332
|
20
|
100
|
|
|
|
95
|
my $long = (defined $tel ? $tel->long : 0.0 ); |
|
333
|
20
|
100
|
|
|
|
177
|
my $lat = (defined $tel ? $tel->lat : 0.0 ); |
|
334
|
20
|
|
|
|
|
157
|
my %el = $self->elements; |
|
335
|
20
|
|
|
|
|
50
|
my $jform; |
|
336
|
20
|
50
|
33
|
|
|
96
|
if (exists $el{DM} and defined $el{DM}) { |
|
|
|
50
|
66
|
|
|
|
|
|
337
|
|
|
|
|
|
|
# major planets |
|
338
|
0
|
|
|
|
|
0
|
$jform = 1; |
|
339
|
|
|
|
|
|
|
} elsif (exists $el{AORL} and defined $el{AORL}) { |
|
340
|
|
|
|
|
|
|
# minor planets |
|
341
|
0
|
|
|
|
|
0
|
$jform = 2; |
|
342
|
0
|
|
|
|
|
0
|
$el{DM} = 0; |
|
343
|
|
|
|
|
|
|
} else { |
|
344
|
|
|
|
|
|
|
# comets |
|
345
|
20
|
|
|
|
|
34
|
$jform = 3; |
|
346
|
20
|
|
|
|
|
41
|
$el{DM} = 0; |
|
347
|
20
|
|
|
|
|
36
|
$el{AORL} = 0; |
|
348
|
|
|
|
|
|
|
} |
|
349
|
|
|
|
|
|
|
|
|
350
|
|
|
|
|
|
|
# synch epoch if need be |
|
351
|
20
|
50
|
33
|
|
|
110
|
if (!exists $el{EPOCH} || !exists $el{EPOCHPERIH}) { |
|
352
|
0
|
0
|
|
|
|
0
|
if (exists $el{EPOCH}) { |
|
353
|
0
|
|
|
|
|
0
|
$el{EPOCHPERIH} = $el{EPOCH}; |
|
354
|
|
|
|
|
|
|
} else { |
|
355
|
0
|
|
|
|
|
0
|
$el{EPOCH} = $el{EPOCHPERIH}; |
|
356
|
|
|
|
|
|
|
} |
|
357
|
|
|
|
|
|
|
} |
|
358
|
|
|
|
|
|
|
|
|
359
|
|
|
|
|
|
|
# First have to perturb the elements to the current epoch |
|
360
|
|
|
|
|
|
|
# if we have a minor planet or comet |
|
361
|
20
|
50
|
33
|
|
|
86
|
if ( $jform == 2 || $jform == 3) { |
|
362
|
|
|
|
|
|
|
# for now we do not have enough information for jform=3 |
|
363
|
|
|
|
|
|
|
# so just assume the EPOCH is the same |
|
364
|
|
|
|
|
|
|
# use Data::Dumper; |
|
365
|
|
|
|
|
|
|
# print "Before perturbing: ". Dumper(\%el); |
|
366
|
|
|
|
|
|
|
# print "MJD ref : " . $self->_mjd_tt . " and jform = $jform\n"; |
|
367
|
|
|
|
|
|
|
($el{EPOCH},$el{ORBINC}, $el{ANODE}, |
|
368
|
|
|
|
|
|
|
$el{PERIH},$el{AORQ},$el{E},$el{AORL}, |
|
369
|
|
|
|
|
|
|
my $jstat) = Astro::PAL::palPertel($jform,$el{EPOCH},$self->_mjd_tt, |
|
370
|
|
|
|
|
|
|
$el{EPOCHPERIH},$el{ORBINC},$el{ANODE}, |
|
371
|
20
|
|
|
|
|
78
|
$el{PERIH},$el{AORQ},$el{E},$el{AORL} ); |
|
372
|
|
|
|
|
|
|
|
|
373
|
|
|
|
|
|
|
# print "After perturbing: " .Dumper(\%el); |
|
374
|
20
|
0
|
|
|
|
119
|
croak "Error perturbing elements for target ". |
|
|
|
50
|
|
|
|
|
|
|
375
|
|
|
|
|
|
|
(defined $self->name ? $self->name : '' ) |
|
376
|
|
|
|
|
|
|
." [status=$jstat]" |
|
377
|
|
|
|
|
|
|
if $jstat != 0; |
|
378
|
|
|
|
|
|
|
} |
|
379
|
|
|
|
|
|
|
|
|
380
|
|
|
|
|
|
|
|
|
381
|
|
|
|
|
|
|
# Print out the values |
|
382
|
|
|
|
|
|
|
#print "EPOCH: $el{EPOCH}\n"; |
|
383
|
|
|
|
|
|
|
#print "ORBINC: ". ($el{ORBINC}*Astro::PAL::DR2D) . "\n"; |
|
384
|
|
|
|
|
|
|
#print "ANODE: ". ($el{ANODE}*Astro::PAL::DR2D) . "\n"; |
|
385
|
|
|
|
|
|
|
#print "PERIH : ". ($el{PERIH}*Astro::PAL::DR2D) . "\n"; |
|
386
|
|
|
|
|
|
|
#print "AORQ: $el{AORQ}\n"; |
|
387
|
|
|
|
|
|
|
#print "E: $el{E}\n"; |
|
388
|
|
|
|
|
|
|
|
|
389
|
|
|
|
|
|
|
my ($ra, $dec, $dist, $j) = Astro::PAL::palPlante($self->_mjd_tt, $long, $lat, $jform, |
|
390
|
|
|
|
|
|
|
$el{EPOCH}, $el{ORBINC}, $el{ANODE}, $el{PERIH}, |
|
391
|
20
|
|
|
|
|
73
|
$el{AORQ}, $el{E}, $el{AORL}, $el{DM} ); |
|
392
|
|
|
|
|
|
|
|
|
393
|
20
|
0
|
|
|
|
97
|
croak "Error determining apparent RA/Dec for target ". |
|
|
|
50
|
|
|
|
|
|
|
394
|
|
|
|
|
|
|
(defined $self->name ? $self->name : '' ) |
|
395
|
|
|
|
|
|
|
."[status=$j]" if $j != 0; |
|
396
|
|
|
|
|
|
|
|
|
397
|
|
|
|
|
|
|
# Convert to angle object |
|
398
|
20
|
|
|
|
|
85
|
$ra_app = new Astro::Coords::Angle::Hour($ra, units => 'rad', range => '2PI'); |
|
399
|
20
|
|
|
|
|
77
|
$dec_app = new Astro::Coords::Angle($dec, units => 'rad'); |
|
400
|
|
|
|
|
|
|
|
|
401
|
|
|
|
|
|
|
# Store in cache |
|
402
|
20
|
|
|
|
|
75
|
$self->_cache_write( "RA_APP" => $ra_app, "DEC_APP" => $dec_app ); |
|
403
|
|
|
|
|
|
|
} |
|
404
|
|
|
|
|
|
|
|
|
405
|
23
|
|
|
|
|
65
|
return( $ra_app, $dec_app ); |
|
406
|
|
|
|
|
|
|
} |
|
407
|
|
|
|
|
|
|
|
|
408
|
|
|
|
|
|
|
=item B<rv> |
|
409
|
|
|
|
|
|
|
|
|
410
|
|
|
|
|
|
|
Radial velocity of the planet relative to the Earth geocentre. |
|
411
|
|
|
|
|
|
|
|
|
412
|
|
|
|
|
|
|
=cut |
|
413
|
|
|
|
|
|
|
|
|
414
|
|
|
|
|
|
|
sub rv { |
|
415
|
0
|
|
|
0
|
1
|
0
|
croak "Not yet implemented element radial velocities"; |
|
416
|
|
|
|
|
|
|
} |
|
417
|
|
|
|
|
|
|
|
|
418
|
|
|
|
|
|
|
=item B<vdefn> |
|
419
|
|
|
|
|
|
|
|
|
420
|
|
|
|
|
|
|
Velocity definition. Always 'RADIO'. |
|
421
|
|
|
|
|
|
|
|
|
422
|
|
|
|
|
|
|
=cut |
|
423
|
|
|
|
|
|
|
|
|
424
|
|
|
|
|
|
|
sub vdefn { |
|
425
|
0
|
|
|
0
|
1
|
0
|
return 'RADIO'; |
|
426
|
|
|
|
|
|
|
} |
|
427
|
|
|
|
|
|
|
|
|
428
|
|
|
|
|
|
|
=item B<vframe> |
|
429
|
|
|
|
|
|
|
|
|
430
|
|
|
|
|
|
|
Velocity reference frame. Always 'GEO'. |
|
431
|
|
|
|
|
|
|
|
|
432
|
|
|
|
|
|
|
=cut |
|
433
|
|
|
|
|
|
|
|
|
434
|
|
|
|
|
|
|
sub vframe { |
|
435
|
0
|
|
|
0
|
1
|
0
|
return 'GEO'; |
|
436
|
|
|
|
|
|
|
} |
|
437
|
|
|
|
|
|
|
|
|
438
|
|
|
|
|
|
|
=item B<apply_offset> |
|
439
|
|
|
|
|
|
|
|
|
440
|
|
|
|
|
|
|
Overrided method to warn if C<Astro::Coords::apply_offset> is |
|
441
|
|
|
|
|
|
|
called on this subclass. |
|
442
|
|
|
|
|
|
|
|
|
443
|
|
|
|
|
|
|
=cut |
|
444
|
|
|
|
|
|
|
|
|
445
|
|
|
|
|
|
|
sub apply_offset { |
|
446
|
1
|
|
|
1
|
1
|
34
|
my $self = shift; |
|
447
|
1
|
|
|
|
|
11
|
warn "apply_offset: applying offset to orbital elements position for a specific time.\n"; |
|
448
|
1
|
|
|
|
|
26
|
return $self->SUPER::apply_offset(@_); |
|
449
|
|
|
|
|
|
|
} |
|
450
|
|
|
|
|
|
|
|
|
451
|
|
|
|
|
|
|
=back |
|
452
|
|
|
|
|
|
|
|
|
453
|
|
|
|
|
|
|
=head1 NOTES |
|
454
|
|
|
|
|
|
|
|
|
455
|
|
|
|
|
|
|
Usually called via C<Astro::Coords>. |
|
456
|
|
|
|
|
|
|
|
|
457
|
|
|
|
|
|
|
=head1 LINKS |
|
458
|
|
|
|
|
|
|
|
|
459
|
|
|
|
|
|
|
Useful sources of orbital elements can be found at |
|
460
|
|
|
|
|
|
|
http://ssd.jpl.nasa.gov and http://cfa-www.harvard.edu/iau/Ephemerides/ |
|
461
|
|
|
|
|
|
|
|
|
462
|
|
|
|
|
|
|
=head1 REQUIREMENTS |
|
463
|
|
|
|
|
|
|
|
|
464
|
|
|
|
|
|
|
C<Astro::PAL> is used for all internal astrometric calculations. |
|
465
|
|
|
|
|
|
|
|
|
466
|
|
|
|
|
|
|
=head1 AUTHOR |
|
467
|
|
|
|
|
|
|
|
|
468
|
|
|
|
|
|
|
Tim Jenness E<lt>tjenness@cpan.orgE<gt> |
|
469
|
|
|
|
|
|
|
|
|
470
|
|
|
|
|
|
|
=head1 COPYRIGHT |
|
471
|
|
|
|
|
|
|
|
|
472
|
|
|
|
|
|
|
Copyright (C) 2001-2005 Particle Physics and Astronomy Research Council. |
|
473
|
|
|
|
|
|
|
All Rights Reserved. |
|
474
|
|
|
|
|
|
|
|
|
475
|
|
|
|
|
|
|
This program is free software; you can redistribute it and/or modify it under |
|
476
|
|
|
|
|
|
|
the terms of the GNU General Public License as published by the Free Software |
|
477
|
|
|
|
|
|
|
Foundation; either version 3 of the License, or (at your option) any later |
|
478
|
|
|
|
|
|
|
version. |
|
479
|
|
|
|
|
|
|
|
|
480
|
|
|
|
|
|
|
This program is distributed in the hope that it will be useful,but WITHOUT ANY |
|
481
|
|
|
|
|
|
|
WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A |
|
482
|
|
|
|
|
|
|
PARTICULAR PURPOSE. See the GNU General Public License for more details. |
|
483
|
|
|
|
|
|
|
|
|
484
|
|
|
|
|
|
|
You should have received a copy of the GNU General Public License along with |
|
485
|
|
|
|
|
|
|
this program; if not, write to the Free Software Foundation, Inc., 59 Temple |
|
486
|
|
|
|
|
|
|
Place,Suite 330, Boston, MA 02111-1307, USA |
|
487
|
|
|
|
|
|
|
|
|
488
|
|
|
|
|
|
|
=cut |
|
489
|
|
|
|
|
|
|
|
|
490
|
|
|
|
|
|
|
1; |