#/usr/bin/perl -w # # This module was written by Steve Franke K9AN. # November, 1999. # # The formulas used in this module # are described in: # Astronomical Algorithms, Second Edition # by Jean Meeus, 1998 # Published by Willmann-Bell, Inc. # P.O. Box 35025, Richmond, Virginia 23235 # # Atmospheric refraction and parallax are taken into # account when calculating positions of the sun and moon, # and also when calculating the rise and set times. # # Copyright (c) 1999 - Steve Franke K9AN # # # # 2005/02/25 add calculation of civil dawn and dusk, defined to be times # when solar zenith angle is 96 degrees. # 2001/12/16 Fixed Julian_Date_of_Epoch and now I actually use it... # 2001/09/15 some changes to take care of cases where the object # doesn't rise or set on a given day... package Sun; require Exporter; @ISA = qw(Exporter); @EXPORT = qw($pi $d2r $r2d ); use strict; use vars qw($pi $d2r $r2d); $pi = 3.141592653589; $d2r = ($pi/180); $r2d = (180/$pi); use vars qw(%keps); use Keps; use DXVars; use DXUtil; use DXDebug; use POSIX qw(:math_h); # reload the keps data sub load { my @out; my $s = readfilestr("$main::root/local/Keps.pm"); if ($s) { eval $s; push @out, $@ if $@; } return @out; } sub Julian_Day { my $year = shift; my $month = shift; my $day = shift; my $julianday; $year=$year-1 if( $month <= 2 ); $month=$month+12 if( $month <= 2); $julianday = int(365.25*($year+4716)+int(30.6001*($month+1)))+$day-13-1524.5; return $julianday; } sub Julian_Date_of_Epoch { my $epoch=shift; my $year=int($epoch/1000); my $day=$epoch-$year*1000; if ($year < 57 ) { $year=$year+2000; } else { $year=$year+1900; } my $Julian_Date_of_Epoch=Julian_Date_of_Year($year)+$day; return $Julian_Date_of_Epoch; } sub Julian_Date_of_Year { my $year=shift; $year=$year-1; my $A=int($year/100); my $B=2-$A+int($A/4); my $Julian_Date_of_Year=int(365.25*$year)+int(30.6001*14)+ 1720994.5+$B; return $Julian_Date_of_Year; } sub ThetaG_JD { my $jd=shift; my $omega_E=1.00273790934; # earth rotations per sidereal day my $secday=86400; my $UT=($jd+0.5)-int($jd+0.5); $jd=$jd-$UT; my $TU=($jd-2451545.0)/36525; my $GMST=24110.54841+$TU*(8640184.812866+$TU*(0.093104-$TU*6.2e-6)); my $thetag_jd=mod2p(2*$pi*($GMST/$secday+$omega_E*$UT)); return $thetag_jd; } sub reduce_angle_to_360 { my $angle = shift; $angle=$angle-int($angle/360)*360; $angle=$angle+360 if( $angle < 0 ); return $angle; } sub mod2p { my $twopi=$pi*2; my $angle = shift; $angle=$angle-int($angle/$twopi)*$twopi; $angle=$angle+$twopi if( $angle < 0 ); return $angle; } sub sindeg { my $angle_in_degrees = shift; return sin($angle_in_degrees*$d2r); } sub cosdeg { my $angle_in_degrees = shift; return cos($angle_in_degrees*$d2r); } sub tandeg { my $angle_in_degrees = shift; return tan($angle_in_degrees*$d2r); } sub get_az_el { my $H=shift; my $delta=shift; my $lat=shift; my $az=$r2d * atan2( sindeg($H), cosdeg($H)*sindeg($lat)-tandeg($delta)*cosdeg($lat) ); my $h=$r2d * asin( sindeg($lat)*sindeg($delta)+cosdeg($lat)*cosdeg($delta)*cosdeg($H) ); return ($az,$h); } sub rise_set { my $year = shift; my $month = shift; my $day = shift; my $hr = shift; my $min = shift; my $lat = shift; my $lon = shift; my $sun0_moon1=shift; # 0 for sun, 1 for moon, 2 for venus... my ($alpha1,$delta1,$alpha2,$delta2,$alpha3,$delta3); my ($aznow,$hnow,$alphanow,$deltanow,$distance,$distancenow); my ($h0,$H); my ($risetime,$settime); my ($dawntime,$dusktime); my ($ifrac,$ifracnow); my $julianday=Julian_Day($year,$month,$day); my $tt1 = ($julianday-1-2451545)/36525.; my $tt2 = ($julianday-2451545)/36525.; my $tt3 = ($julianday+1-2451545)/36525.; my $ttnow = ($julianday+$hr/24+$min/24/60-2451545)/36525.; my $theta0=280.46061837+360.98564736629*($julianday-2451545.0)+ 0.000387933*$tt2*$tt2-$tt2*$tt2*$tt2/38710000; $theta0=reduce_angle_to_360($theta0); my $thetanow=280.46061837+360.98564736629*($julianday+$hr/24+$min/24/60-2451545.0)+ 0.000387933*$ttnow*$ttnow-$ttnow*$ttnow*$ttnow/38710000; $thetanow=reduce_angle_to_360($thetanow); if ( $sun0_moon1 == 0 ) { ($alpha1, $delta1)=get_sun_alpha_delta($tt1); ($alpha2, $delta2)=get_sun_alpha_delta($tt2); ($alpha3, $delta3)=get_sun_alpha_delta($tt3); ($alphanow, $deltanow)=get_sun_alpha_delta($ttnow); $H=$thetanow-$lon-$alphanow; $H=reduce_angle_to_360($H); ($aznow,$hnow)=get_az_el($H,$deltanow,$lat); $hnow=$hnow + 1.02/(tandeg($hnow+10.3/($hnow+5.11)))/60; $h0=-0.8333; # this is for sun rise and sun set ($risetime,$settime)= do_rise_set_calculations($h0,$theta0,$lat,$lon,$alpha1,$delta1, $alpha2,$delta2,$alpha3,$delta3); $h0=-6.0; # this is for civil dawn and dusk ($dawntime,$dusktime)= do_rise_set_calculations($h0,$theta0,$lat,$lon,$alpha1,$delta1, $alpha2,$delta2,$alpha3,$delta3); $dawntime = "------" if( $dawntime eq "NoRise" ); $dusktime = "------" if( $dusktime eq "NoSet " ); return ( sprintf("%s", $dawntime), sprintf("%s",$risetime), sprintf("%s", $settime), sprintf("%s",$dusktime), $aznow+180,$hnow ); } if ( $sun0_moon1 == 1 ) { ($alpha1, $delta1, $distance, $ifrac)=get_moon_alpha_delta($tt1); ($alpha2, $delta2, $distance, $ifrac)=get_moon_alpha_delta($tt2); ($alpha3, $delta3, $distance, $ifrac)=get_moon_alpha_delta($tt3); ($alphanow, $deltanow, $distancenow, $ifracnow)=get_moon_alpha_delta($ttnow); $h0=0.7275*$r2d*asin(6378.14/$distancenow)-34.0/60.; $H=$thetanow-$lon-$alphanow; $H=reduce_angle_to_360($H); ($aznow,$hnow)=get_az_el($H,$deltanow,$lat); $hnow=$hnow-$r2d*asin(sin(6378.14/$distancenow)*cosdeg($hnow))+ 1.02/(tandeg($hnow+10.3/($hnow+5.11)))/60; ($risetime,$settime)= do_rise_set_calculations($h0,$theta0,$lat,$lon,$alpha1,$delta1, $alpha2,$delta2,$alpha3,$delta3); return (sprintf("%s", $risetime), sprintf("%s",$settime), $aznow+180,$hnow, -40*log10($distance/385000), $ifracnow ); } } sub do_rise_set_calculations { my $norise = 0; my $noset = 0; my ($risehr,$risemin,$risetime,$sethr,$setmin,$settime); my ($m0,$m1,$m2,$theta,$alpha,$delta,$H,$az,$h,$corr); my ($i,$arg,$argtest,$H0); my $h0=shift; my $theta0=shift; my $lat=shift; my $lon=shift; my $alpha1=shift; my $delta1=shift; my $alpha2=shift; my $delta2=shift; my $alpha3=shift; my $delta3=shift; $arg = (sindeg($h0)-sindeg($lat)*sindeg($delta2))/(cosdeg($lat)*cosdeg($delta2)); if ( abs($arg) > 1. ) { # either up all day or down all day $norise = 1; # leave it to the user to examine $noset = 1; # the elevation angle (or look outside!) } # to figure out which. $H0 = acos($arg)*$r2d; my $aa=$alpha2-$alpha1; my $ba=$alpha3-$alpha2; $aa=$aa+360 if ($aa < -180); $aa=$aa-360 if ($aa > 180); $ba=$ba+360 if ($ba < -180); $ba=$ba-360 if ($ba > 180); my $ca=$ba-$aa; my $ad=$delta2-$delta1; my $bd=$delta3-$delta2; $ad=$ad+360 if ($ad < -180); $ad=$ad-360 if ($ad > 180); $bd=$bd+360 if ($bd < -180); $bd=$bd-360 if ($bd > 180); my $cd=$bd-$ad; $m0 = ($alpha2 + $lon - $theta0)/360.; $m0=$m0+1 if( $m0 < 0 ); $m0=$m0-1 if( $m0 > 1 ); for ($i=1; $i<=2; $i++) { $theta = $theta0+360.985647*$m0; $alpha=$alpha2+$m0*($aa+$ba+$m0*$ca)/2; $delta=$delta2+$m0*($ad+$bd+$m0*$cd)/2; $H=$theta-$lon-$alpha; $H=reduce_angle_to_360($H); $H=$H-360 if ($H > 180); ($az,$h)=get_az_el($H,$delta,$lat); $corr=-$H/360; $m0=$m0+$corr; $m0=$m0+1 if( $m0 < 0 ); $m0=$m0-1 if( $m0 >= 1 ); } if( !$norise ){ $m1 = $m0 - $H0/360.; $m1=$m1+1 if( $m1 < 0 ); $m1=$m1-1 if( $m1 > 1 ); for ($i=1; $i<=2; $i++) { $theta = $theta0+360.985647*$m1; $alpha=$alpha2+$m1*($aa+$ba+$m1*$ca)/2; $delta=$delta2+$m1*($ad+$bd+$m1*$cd)/2; $H=$theta-$lon-$alpha; $H=reduce_angle_to_360($H); ($az,$h)=get_az_el($H,$delta,$lat); $corr=($h-$h0)/(360*(cosdeg($delta)*cosdeg($lat)*sindeg($H))); $m1=$m1+$corr; # $norise=1 if( $m1 < 0 || $m1 > 1); $m1=$m1-1 if( $m1 >= 1); $m1=$m1+1 if( $m1 < 0); } } if( !$norise ) { $risehr=int($m1*24); $risemin=($m1*24-int($m1*24))*60+0.5; if ( $risemin >= 60 ) { $risemin=$risemin-60; $risehr=$risehr+1; } $risehr=0 if($risehr==24); $risetime=sprintf("%02d:%02dZ",$risehr,$risemin); } else { $risetime="NoRise"; } if( !$noset ){ $m2 = $m0 + $H0/360.; $m2=$m2+1 if( $m2 < 0 ); $m2=$m2-1 if( $m2 >= 1 ); for ($i=1; $i<=2; $i++) { $theta = $theta0+360.985647*$m2; $alpha=$alpha2+$m2*($aa+$ba+$m2*$ca)/2; $delta=$delta2+$m2*($ad+$bd+$m2*$cd)/2; $H=$theta-$lon-$alpha; $H=reduce_angle_to_360($H); ($az,$h)=get_az_el($H,$delta,$lat); $corr=($h-$h0)/(360*(cosdeg($delta)*cosdeg($lat)*sindeg($H))); $m2 = $m2 + $corr; # $noset=1 if( $m2 < 0 || $m2 > 1); $m2=$m2-1 if( $m2 >= 1); $m2=$m2+1 if( $m2 < 0); } } if( !$noset ) { $sethr=int($m2*24); $setmin=($m2*24-int($m2*24))*60+0.5; if ( $setmin >= 60 ) { $setmin=$setmin-60; $sethr=$sethr+1; } $sethr=0 if($sethr==24); $settime=sprintf("%02d:%02dZ",$sethr,$setmin); } else { $settime="NoSet "; } return $risetime,$settime; } sub get_moon_alpha_delta { # # Calculate the moon's right ascension and declination # # As of October 2001, also calculate the illuminated fraction of the # moon's disk... (why not?) # my $tt=shift; my $Lp=218.3164477+481267.88123421*$tt- 0.0015786*$tt*$tt+$tt*$tt*$tt/538841-$tt*$tt*$tt*$tt/65194000; $Lp=reduce_angle_to_360($Lp); my $D = 297.8501921+445267.1114034*$tt-0.0018819*$tt*$tt+ $tt*$tt*$tt/545868.-$tt*$tt*$tt*$tt/113065000.; $D=reduce_angle_to_360($D); my $M = 357.5291092 + 35999.0502909*$tt-0.0001536*$tt*$tt+ $tt*$tt*$tt/24490000.; $M=reduce_angle_to_360($M); my $Mp = 134.9633964 + 477198.8675055*$tt+0.0087414*$tt*$tt+ $tt*$tt*$tt/69699-$tt*$tt*$tt*$tt/14712000; $Mp=reduce_angle_to_360($Mp); my $F = 93.2720950 + 483202.0175233*$tt - 0.0036539*$tt*$tt- $tt*$tt*$tt/3526000 + $tt*$tt*$tt*$tt/863310000; $F=reduce_angle_to_360($F); my $A1 = 119.75 + 131.849 * $tt; $A1=reduce_angle_to_360($A1); my $A2 = 53.09 + 479264.290 * $tt; $A2=reduce_angle_to_360($A2); my $A3 = 313.45 + 481266.484 * $tt; $A3=reduce_angle_to_360($A3); my $E = 1 - 0.002516 * $tt - 0.0000074 * $tt * $tt; my $Sl= 6288774*sindeg( 1 * $Mp ) + 1274027*sindeg(2 * $D + -1 * $Mp ) + 658314 *sindeg(2 * $D ) + 213618 *sindeg( 2 * $Mp ) + -185116 *sindeg( 1 * $M )*$E + -114332 *sindeg( 2 * $F ) + 58793 *sindeg(2 * $D + -2 * $Mp ) + 57066 *sindeg(2 * $D - 1 * $M -1 * $Mp )*$E + 53322 *sindeg(2 * $D + 1 * $Mp ) + 45758 *sindeg(2 * $D - 1 * $M )*$E + -40923 *sindeg( + 1 * $M -1 * $Mp )*$E + -34720 *sindeg(1 * $D ) + -30383 *sindeg( + 1 * $M + 1 * $Mp )*$E + 15327 *sindeg(2 * $D + -2 * $F ) + -12528 *sindeg( 1 * $Mp + 2 * $F ) + 10980 *sindeg( 1 * $Mp - 2 * $F ) + 10675 *sindeg(4 * $D + -1 * $Mp ) + 10034 *sindeg( 3 * $Mp ) + 8548 *sindeg(4 * $D + 0 * $M - 2 * $Mp + 0 * $F ) + -7888 *sindeg(2 * $D + 1 * $M - 1 * $Mp + 0 * $F )*$E + -6766 *sindeg(2 * $D + 1 * $M + 0 * $Mp + 0 * $F )*$E + -5163 *sindeg(1 * $D + 0 * $M - 1 * $Mp + 0 * $F ) + 4987 *sindeg(1 * $D + 1 * $M + 0 * $Mp + 0 * $F )*$E + 4036 *sindeg(2 * $D - 1 * $M + 1 * $Mp + 0 * $F )*$E + 3994 *sindeg(2 * $D + 0 * $M + 2 * $Mp + 0 * $F ) + 3861 *sindeg(4 * $D + 0 * $M + 0 * $Mp + 0 * $F ) + 3665 *sindeg(2 * $D + 0 * $M - 3 * $Mp + 0 * $F ) + -2689 *sindeg(0 * $D + 1 * $M - 2 * $Mp + 0 * $F )*$E + -2602 *sindeg(2 * $D + 0 * $M - 1 * $Mp + 2 * $F ) + 2390 *sindeg(2 * $D - 1 * $M - 2 * $Mp + 0 * $F )*$E + -2348 *sindeg(1 * $D + 0 * $M + 1 * $Mp + 0 * $F ) + 2236 *sindeg(2 * $D - 2 * $M + 0 * $Mp + 0 * $F )*$E*$E + -2120 *sindeg(0 * $D + 1 * $M + 2 * $Mp + 0 * $F )*$E + -2069 *sindeg(0 * $D + 2 * $M + 0 * $Mp + 0 * $F )*$E*$E + 2048 *sindeg(2 * $D - 2 * $M - 1 * $Mp + 0 * $F )*$E*$E + -1773 *sindeg(2 * $D + 0 * $M + 1 * $Mp - 2 * $F ) + -1595 *sindeg(2 * $D + 0 * $M + 0 * $Mp + 2 * $F ) + 1215 *sindeg(4 * $D - 1 * $M - 1 * $Mp + 0 * $F )*$E + -1110 *sindeg(0 * $D + 0 * $M + 2 * $Mp + 2 * $F ) + -892 *sindeg(3 * $D + 0 * $M - 1 * $Mp + 0 * $F ) + -810 *sindeg(2 * $D + 1 * $M + 1 * $Mp + 0 * $F )*$E + 759 *sindeg(4 * $D - 1 * $M - 2 * $Mp + 0 * $F )*$E + -713 *sindeg(0 * $D + 2 * $M - 1 * $Mp + 0 * $F )*$E*$E + -700 *sindeg(2 * $D + 2 * $M - 1 * $Mp + 0 * $F )*$E*$E + 691 *sindeg(2 * $D + 1 * $M - 2 * $Mp + 0 * $F )*$E + 596 *sindeg(2 * $D - 1 * $M + 0 * $Mp - 2 * $F )*$E + 549 *sindeg(4 * $D + 0 * $M + 1 * $Mp + 0 * $F ) + 537 *sindeg(0 * $D + 0 * $M + 4 * $Mp + 0 * $F ) + 520 *sindeg(4 * $D - 1 * $M + 0 * $Mp + 0 * $F )*$E + -487 *sindeg(1 * $D + 0 * $M - 2 * $Mp + 0 * $F ) + -399 *sindeg(2 * $D + 1 * $M + 0 * $Mp - 2 * $F )*$E + -381 *sindeg(0 * $D + 0 * $M + 2 * $Mp - 2 * $F ) + 351 *sindeg(1 * $D + 1 * $M + 1 * $Mp + 0 * $F )*$E + -340 *sindeg(3 * $D + 0 * $M - 2 * $Mp + 0 * $F ) + 330 *sindeg(4 * $D + 0 * $M - 3 * $Mp + 0 * $F ) + 327 *sindeg(2 * $D - 1 * $M + 2 * $Mp + 0 * $F )*$E + -323 *sindeg(0 * $D + 2 * $M + 1 * $Mp + 0 * $F )*$E*$E + 299 *sindeg(1 * $D + 1 * $M - 1 * $Mp + 0 * $F )*$E + 294 *sindeg(2 * $D + 0 * $M + 3 * $Mp + 0 * $F ) + 3958 *sindeg($A1) + 1962*sindeg($Lp - $F) + 318*sindeg($A2); my $Sr=-20905355 *cosdeg( 1 * $Mp ) + -3699111 *cosdeg(2 * $D + -1 * $Mp ) + -2955968 *cosdeg(2 * $D ) + -569925 *cosdeg( 2 * $Mp ) + 48888 *cosdeg( 1 * $M )*$E + -3149 *cosdeg( 2 * $F ) + 246158 *cosdeg(2 * $D + -2 * $Mp ) + -152138 *cosdeg(2 * $D - 1 * $M -1 * $Mp )*$E + -170733 *cosdeg(2 * $D + 1 * $Mp ) + -204586 *cosdeg(2 * $D - 1 * $M )*$E + -129620 *cosdeg( + 1 * $M -1 * $Mp )*$E + 108743 *cosdeg(1 * $D ) + 104755 *cosdeg( + 1 * $M + 1 * $Mp )*$E + 10321 *cosdeg(2 * $D + -2 * $F ) + 79661 *cosdeg( 1 * $Mp - 2 * $F ) + -34782 *cosdeg(4 * $D + -1 * $Mp ) + -23210 *cosdeg( 3 * $Mp ) + -21636 *cosdeg(4 * $D + 0 * $M - 2 * $Mp + 0 * $F ) + 24208 *cosdeg(2 * $D + 1 * $M - 1 * $Mp + 0 * $F )*$E + 30824 *cosdeg(2 * $D + 1 * $M + 0 * $Mp + 0 * $F )*$E + -8379 *cosdeg(1 * $D + 0 * $M - 1 * $Mp + 0 * $F ) + -16675 *cosdeg(1 * $D + 1 * $M + 0 * $Mp + 0 * $F )*$E + -12831 *cosdeg(2 * $D - 1 * $M + 1 * $Mp + 0 * $F )*$E + -10445 *cosdeg(2 * $D + 0 * $M + 2 * $Mp + 0 * $F ) + -11650 *cosdeg(4 * $D + 0 * $M + 0 * $Mp + 0 * $F ) + 14403 *cosdeg(2 * $D + 0 * $M - 3 * $Mp + 0 * $F ) + -7003 *cosdeg(0 * $D + 1 * $M - 2 * $Mp + 0 * $F )*$E + 10056 *cosdeg(2 * $D - 1 * $M - 2 * $Mp + 0 * $F )*$E + 6322 *cosdeg(1 * $D + 0 * $M + 1 * $Mp + 0 * $F ) + -9884 *cosdeg(2 * $D - 2 * $M + 0 * $Mp + 0 * $F )*$E*$E + 5751 *cosdeg(0 * $D + 1 * $M + 2 * $Mp + 0 * $F )*$E + -4950 *cosdeg(2 * $D - 2 * $M - 1 * $Mp + 0 * $F )*$E*$E + 4130 *cosdeg(2 * $D + 0 * $M + 1 * $Mp - 2 * $F )+ -3958 *cosdeg(4 * $D - 1 * $M - 1 * $Mp + 0 * $F )*$E + 3258 *cosdeg(3 * $D + 0 * $M - 1 * $Mp + 0 * $F )+ 2616 *cosdeg(2 * $D + 1 * $M + 1 * $Mp + 0 * $F )*$E + -1897 *cosdeg(4 * $D - 1 * $M - 2 * $Mp + 0 * $F )*$E + -2117 *cosdeg(0 * $D + 2 * $M - 1 * $Mp + 0 * $F )*$E*$E + 2354 *cosdeg(2 * $D + 2 * $M - 1 * $Mp + 0 * $F )*$E*$E + -1423 *cosdeg(4 * $D + 0 * $M + 1 * $Mp + 0 * $F )+ -1117 *cosdeg(0 * $D + 0 * $M + 4 * $Mp + 0 * $F )+ -1571 *cosdeg(4 * $D - 1 * $M + 0 * $Mp + 0 * $F )*$E + -1739 *cosdeg(1 * $D + 0 * $M - 2 * $Mp + 0 * $F )+ -4421 *cosdeg(0 * $D + 0 * $M + 2 * $Mp - 2 * $F )+ 1165 *cosdeg(0 * $D + 2 * $M + 1 * $Mp + 0 * $F )*$E*$E + 8752 *cosdeg(2 * $D + 0 * $M - 1 * $Mp - 2 * $F ); my $Sb= 5128122 *sindeg( 1 * $F ) + 280602 *sindeg( 1 * $Mp + 1 * $F ) + 277693 *sindeg( 1 * $Mp - 1 * $F ) + 173237 *sindeg(2 * $D - 1 * $F ) + 55413 *sindeg(2 * $D -1 * $Mp + 1 * $F ) + 46271 *sindeg(2 * $D + -1 * $Mp - 1 * $F ) + 32573 *sindeg(2 * $D + 1 * $F ) + 17198 *sindeg( 2 * $Mp + 1 * $F )+ 9266 *sindeg(2 * $D + 0 * $M + 1 * $Mp - 1 * $F ) + 8822 *sindeg(0 * $D + 0 * $M + 2 * $Mp - 1 * $F ) + 8216 *sindeg(2 * $D - 1 * $M + 0 * $Mp - 1 * $F )*$E + 4324 *sindeg(2 * $D + 0 * $M - 2 * $Mp - 1 * $F ) + 4200 *sindeg(2 * $D + 0 * $M + 1 * $Mp + 1 * $F ) + -3359 *sindeg(2 * $D + 1 * $M + 0 * $Mp - 1 * $F )*$E + 2463 *sindeg(2 * $D - 1 * $M - 1 * $Mp + 1 * $F )*$E + 2211 *sindeg(2 * $D - 1 * $M + 0 * $Mp + 1 * $F )*$E + 2065 *sindeg(2 * $D - 1 * $M - 1 * $Mp - 1 * $F )*$E + -1870 *sindeg(0 * $D + 1 * $M - 1 * $Mp - 1 * $F )*$E + 1828 *sindeg(4 * $D + 0 * $M - 1 * $Mp - 1 * $F ) + -1794 *sindeg(0 * $D + 1 * $M + 0 * $Mp + 1 * $F )*$E + -1749 *sindeg(0 * $D + 0 * $M + 0 * $Mp + 3 * $F ) + -1565 *sindeg(0 * $D + 1 * $M - 1 * $Mp + 1 * $F )*$E + -1491 *sindeg(1 * $D + 0 * $M + 0 * $Mp + 1 * $F ) + -1475 *sindeg(0 * $D + 1 * $M + 1 * $Mp + 1 * $F )*$E + -1410 *sindeg(0 * $D + 1 * $M + 1 * $Mp - 1 * $F )*$E + -1344 *sindeg(0 * $D + 1 * $M + 0 * $Mp - 1 * $F )*$E + -1335 *sindeg(1 * $D + 0 * $M + 0 * $Mp - 1 * $F ) + 1107 *sindeg(0 * $D + 0 * $M + 3 * $Mp + 1 * $F ) + 1021 *sindeg(4 * $D + 0 * $M + 0 * $Mp - 1 * $F ) + 833 *sindeg(4 * $D + 0 * $M - 1 * $Mp + 1 * $F ) + 777 *sindeg(0 * $D + 0 * $M + 1 * $Mp - 3 * $F ) + 671 *sindeg(4 * $D + 0 * $M - 2 * $Mp + 1 * $F ) + 607 *sindeg(2 * $D + 0 * $M + 0 * $Mp - 3 * $F ) + 596 *sindeg(2 * $D + 0 * $M + 2 * $Mp - 1 * $F ) + 491 *sindeg(2 * $D - 1 * $M + 1 * $Mp - 1 * $F )*$E + -451 *sindeg(2 * $D + 0 * $M - 2 * $Mp + 1 * $F ) + 439 *sindeg(0 * $D + 0 * $M + 3 * $Mp - 1 * $F ) + 422 *sindeg(2 * $D + 0 * $M + 2 * $Mp + 1 * $F ) + 421 *sindeg(2 * $D + 0 * $M - 3 * $Mp - 1 * $F ) + -366 *sindeg(2 * $D + 1 * $M - 1 * $Mp + 1 * $F )*$E + -351 *sindeg(2 * $D + 1 * $M + 0 * $Mp + 1 * $F )*$E + 331 *sindeg(4 * $D + 0 * $M + 0 * $Mp + 1 * $F ) + 315 *sindeg(2 * $D - 1 * $M + 1 * $Mp + 1 * $F )*$E + 302 *sindeg(2 * $D - 2 * $M + 0 * $Mp - 1 * $F )*$E*$E + -283 *sindeg(0 * $D + 0 * $M + 1 * $Mp + 3 * $F ) + -229 *sindeg(2 * $D + 1 * $M + 1 * $Mp - 1 * $F )*$E + 223 *sindeg(1 * $D + 1 * $M + 0 * $Mp - 1 * $F )*$E + 223 *sindeg(1 * $D + 1 * $M + 0 * $Mp + 1 * $F )*$E + -220 *sindeg(0 * $D + 1 * $M - 2 * $Mp - 1 * $F )*$E + -220 *sindeg(2 * $D + 1 * $M - 1 * $Mp - 1 * $F )*$E + -185 *sindeg(1 * $D + 0 * $M + 1 * $Mp + 1 * $F ) + 181 *sindeg(2 * $D - 1 * $M - 2 * $Mp - 1 * $F )*$E + -177 *sindeg(0 * $D + 1 * $M + 2 * $Mp + 1 * $F )*$E + 176 *sindeg(4 * $D + 0 * $M - 2 * $Mp - 1 * $F ) + 166 *sindeg(4 * $D - 1 * $M - 1 * $Mp - 1 * $F )*$E + -164 *sindeg(1 * $D + 0 * $M + 1 * $Mp - 1 * $F ) + 132 *sindeg(4 * $D + 0 * $M + 1 * $Mp - 1 * $F ) + -119 *sindeg(1 * $D + 0 * $M - 1 * $Mp - 1 * $F ) + 115 *sindeg(4 * $D - 1 * $M + 0 * $Mp - 1 * $F )*$E + 107 *sindeg(2 * $D - 2 * $M + 0 * $Mp + 1 * $F )*$E*$E -2235 *sindeg($Lp) + 382*sindeg($A3) + 175 *sindeg($A1-$F) + 175*sindeg($A1+$F) + 127 *sindeg($Lp-$Mp) - 115*sindeg($Lp+$Mp); my $lambda=$Lp+$Sl/1000000.; my $beta=$Sb/1000000.; my $distance=385000.56 + $Sr/1000.; my $epsilon = 23+26./60.+21.448/(60.*60.); my $alpha=atan2(cosdeg($epsilon)*sindeg($lambda)-tandeg($beta)*sindeg($epsilon),cosdeg($lambda))*$r2d; $alpha = reduce_angle_to_360($alpha); my $delta=asin(cosdeg($beta)*sindeg($epsilon)*sindeg($lambda)+sindeg($beta)*cosdeg($epsilon))*$r2d; $delta = reduce_angle_to_360($delta); # $phase will be the "moon phase angle" from p. 346 of Meeus' book... my $phase=180.0 - $D - 6.289 *sindeg($Mp) + 2.100 *sindeg($M) - 1.274 *sindeg(2.*$D - $Mp) - 0.658 *sindeg(2.*$D) - 0.214 *sindeg(2.*$Mp) - 0.110 *sindeg($D); # $illum_frac is the fraction of the disk that is illuminated, and will be # zero at new moon and 1.0 at full moon. my $illum_frac = (1.0 + cosdeg( $phase ))/2.; return ($alpha,$delta,$distance,$illum_frac); } sub get_sun_alpha_delta { # # Calculate Sun's right ascension and declination # my $tt = shift; my $L0 = 280.46646+36000.76983*$tt+0.0003032*($tt^2); $L0=reduce_angle_to_360($L0); my $M = 357.52911 + 35999.05029*$tt-0.0001537*($tt^2); $M=reduce_angle_to_360($M); my $C = (1.914602 - 0.004817*$tt-0.000014*($tt^2))*sindeg($M) + (0.019993 - 0.000101*$tt)*sindeg(2*$M) + 0.000289*sindeg(3*$M); my $OMEGA = 125.04 - 1934.136*$tt; my $lambda=$L0+$C-0.00569-0.00478*sindeg($OMEGA); my $epsilon = 23+26./60.+21.448/(60.*60.); my $alpha=atan2(cosdeg($epsilon)*sindeg($lambda),cosdeg($lambda))*$r2d; $alpha = reduce_angle_to_360($alpha); my $delta=asin(sin($epsilon*$d2r)*sin($lambda*$d2r))*$r2d; $delta = reduce_angle_to_360($delta); return ($alpha,$delta); } sub get_satellite_pos { # # This code was translated more-or-less directly from the Pascal # routines contained in a report compiled by TS Kelso and based on: # Spacetrack Report No. 3 # "Models for Propagation of NORAD Element Sets" # Felix R. Hoots, Ronald L Roehrich # December 1980 # # See TS Kelso's web site for more details... # Only the SGP propagation model is implemented. # # Steve Franke, K9AN. 9 Dec 1999. # #NOAA 15 #1 25338U 98030A 99341.00000000 +.00000376 +00000-0 +18612-3 0 05978 #2 25338 098.6601 008.2003 0011401 112.4684 042.5140 14.23047277081382 #TDRS 5 #1 21639U 91054B 99341.34471854 .00000095 00000-0 10000-3 0 4928 #2 21639 1.5957 88.4884 0003028 161.6582 135.4323 1.00277774 30562 #OSCAR 16 (PACSAT) #1 20439U 90005D 99341.14501399 +.00000343 +00000-0 +14841-3 0 02859 #2 20439 098.4690 055.0032 0012163 066.4615 293.7842 14.30320285515297 # #Temporary keps database... # my $jtime = shift; my $lat = shift; my $lon = shift; my $alt = shift; my $satname = shift; my $sat_ref = $keps{$satname}; #printf("$jtime $lat $lon $alt Satellite name = $satname\n"); my $qo=120; my $so=78; my $xj2=1.082616e-3; my $xj3=-.253881e-5; my $xj4=-1.65597e-6; my $xke=.743669161e-1; my $xkmper=6378.135; my $xmnpda=1440.; my $ae=1.; my $ck2=.5*$xj2*$ae**2; my $ck4=-.375*$xj4*$ae**4; my $qoms2t=(($qo-$so)*$ae/$xkmper)**4; my $s=$ae*(1+$so/$xkmper); my $epoch = $sat_ref ->{epoch}; #printf("epoch = %10.2f\n",$epoch); my $jt_epoch=Julian_Date_of_Epoch($epoch); #printf("JT for epoch = %17.12f\n",$jt_epoch); my $tsince=($jtime-$jt_epoch)*24*60; #printf("tsince (min) = %17.12f\n",$tsince); my $mm1 = $sat_ref ->{mm1}; my $mm2 = $sat_ref ->{mm2}; my $bstar=$sat_ref ->{bstar}; # drag term for sgp4 model my $inclination=$sat_ref->{inclination}; # inclination in degrees my $raan=$sat_ref->{raan}; # right ascension of ascending node in degs my $eccentricity=$sat_ref ->{eccentricity}; # eccentricity - dimensionless my $omegao=$sat_ref ->{argperigee}; # argument of perigee in degs my $xmo=$sat_ref ->{meananomaly}; # mean anomaly in degrees my $xno=$sat_ref ->{meanmotion}; # mean motion in revs per day #printf("%10.6f %10.6f %10.6f %10.6f %10.6f %10.6f %10.6f %10.6f %10.6f\n", #$mm1,$mm2,$bstar,$inclination,$raan,$eccentricity,$omegao,$xmo,$xno); $raan=$raan*$d2r; $omegao=$omegao*$d2r; $xmo=$xmo*$d2r; $inclination=$inclination*$d2r; my $temp=2*$pi/$xmnpda/$xmnpda; $xno=$xno*$temp*$xmnpda; $mm1=$mm1*$temp; $mm2=$mm2*$temp/$xmnpda; my $c1=$ck2*1.5; my $c2=$ck2/4.0; my $c3=$ck2/2.0; my $c4=$xj3*$ae**3/(4*$ck2); my $cosio=cos($inclination); my $sinio=sin($inclination); my $a1=($xke/$xno)**(2./3.); my $d1=$c1/$a1/$a1*(3*$cosio*$cosio-1)/(1-$eccentricity*$eccentricity)**1.5; my $ao=$a1*(1-1./3.*$d1-$d1*$d1-134./81.*$d1*$d1*$d1); my $po=$ao*(1-$eccentricity*$eccentricity); $qo=$ao*(1-$eccentricity); my $xlo=$xmo+$omegao+$raan; my $d10=$c3*$sinio*$sinio; my $d20=$c2*(7.*$cosio*$cosio-1); my $d30=$c1*$cosio; my $d40=$d30*$sinio; my $po2no=$xno/($po*$po); my $omgdt=$c1*$po2no*(5.*$cosio*$cosio-1); my $xnodot=-2.*$d30*$po2no; my $c5=0.5*$c4*$sinio*(3+5*$cosio)/(1+$cosio); my $c6=$c4*$sinio; my $a=$xno+(2*$mm1+3*$mm2*$tsince)*$tsince; $a=$ao*($xno/$a)**(2./3.); my $e=1e-6; $e =1-$qo/$a if ($a > $qo); my $p=$a*(1-$e*$e); my $xnodes=$raan+$xnodot*$tsince; my $omgas=$omegao+$omgdt*$tsince; my $xls=mod2p($xlo+($xno+$omgdt+$xnodot+($mm1+$mm2*$tsince)*$tsince)*$tsince); my $axnsl=$e*cos($omgas); my $aynsl=$e*sin($omgas)-$c6/$p; my $xl=mod2p($xls-$c5/$p*$axnsl); my $u=mod2p($xl-$xnodes); my $item3; my $eo1=$u; my $tem5=1; my $coseo1=0; my $sineo1=0; for ($item3=0; abs($tem5) >= 1e-6 && $item3 < 10; $item3++ ) { $sineo1=sin($eo1); $coseo1=cos($eo1); $tem5=1-$coseo1*$axnsl-$sineo1*$aynsl; $tem5=($u-$aynsl*$coseo1+$axnsl*$sineo1-$eo1)/$tem5; my $tem2=abs($tem5); $tem5=$tem2/$tem5 if ($tem2 > 1); $eo1=$eo1+$tem5; } $sineo1=sin($eo1); $coseo1=cos($eo1); my $ecose=$axnsl*$coseo1+$aynsl*$sineo1; my $esine=$axnsl*$sineo1-$aynsl*$coseo1; my $el2=$axnsl*$axnsl+$aynsl*$aynsl; my $pl=$a*(1-$el2); my $pl2=$pl*$pl; my $r=$a*(1-$ecose); my $rdot=$xke*sqrt($a)/$r*$esine; my $rvdot=$xke*sqrt($pl)/$r; $temp=$esine/(1+sqrt(1-$el2)); my $sinu=$a/$r*($sineo1-$aynsl-$axnsl*$temp); my $cosu=$a/$r*($coseo1-$axnsl+$aynsl*$temp); my $su=atan2($sinu,$cosu); my $sin2u=($cosu+$cosu)*$sinu; my $cos2u=1-2*$sinu*$sinu; my $rk=$r+$d10/$pl*$cos2u; my $uk=$su-$d20/$pl2*$sin2u; my $xnodek=$xnodes+$d30*$sin2u/$pl2; my $xinck=$inclination+$d40/$pl2*$cos2u; my $sinuk=sin($uk); my $cosuk=cos($uk); my $sinnok=sin($xnodek); my $cosnok=cos($xnodek); my $sinik=sin($xinck); my $cosik=cos($xinck); my $xmx=-$sinnok*$cosik; my $xmy=$cosnok*$cosik; my $ux=$xmx*$sinuk+$cosnok*$cosuk; my $uy=$xmy*$sinuk+$sinnok*$cosuk; my $uz=$sinik*$sinuk; my $vx=$xmx*$cosuk-$cosnok*$sinuk; my $vy=$xmy*$cosuk-$sinnok*$sinuk; my $vz=$sinik*$cosuk; my $x=$rk*$ux*$xkmper/$ae; my $y=$rk*$uy*$xkmper/$ae; my $z=$rk*$uz*$xkmper/$ae; my $xdot=$rdot*$ux; my $ydot=$rdot*$uy; my $zdot=$rdot*$uz; $xdot=($rvdot*$vx+$xdot)*$xkmper/$ae*$xmnpda/86400; $ydot=($rvdot*$vy+$ydot)*$xkmper/$ae*$xmnpda/86400; $zdot=($rvdot*$vz+$zdot)*$xkmper/$ae*$xmnpda/86400; #printf("x=%17.6f y=%17.6f z=%17.6f \n",$x,$y,$z); #printf("xdot=%17.6f ydot=%17.6f zdot=%17.6f \n",$xdot,$ydot,$zdot); my ($sat_lat,$sat_lon,$sat_alt,$sat_theta)=Calculate_LatLonAlt($x,$y,$z,$jtime); my ($az, $el, $distance) = Calculate_Obs($x,$y,$z,$sat_theta,$xdot,$ydot,$zdot,$jtime,$lat,$lon,$alt); return ($sat_lat,$sat_lon,$sat_alt,$az,$el,$distance); } sub Calculate_LatLonAlt { # # convert from ECI coordinates to latitude, longitude and altitude. # my $x=shift; my $y=shift; my $z=shift; my $time=shift; my $theta=atan2($y,$x); my $lon=mod2p($theta-ThetaG_JD($time)); my $range=sqrt($x**2+$y**2); my $f=1/298.26; # earth flattening constant my $e2=$f*(2-$f); my $xkmper=6378.135; my $lat=atan2($z,$range); my ($phi,$c); do { $phi=$lat; $c=1/sqrt(1-$e2*sin($phi)**2); $lat=atan2($z+$xkmper*$c*$e2*sin($phi),$range); } until abs($lat-$phi) < 1e-10; my $alt=$range/cos($lat)-$xkmper*$c; return ($lat,$lon,$alt,$theta); # radians and kilometers } sub Calculate_User_PosVel { # change from lat/lon/alt/time coordinates to earth centered inertial (ECI) # position and local hour angle. my $lat=shift; my $lon=shift; my $alt=shift; my $time=shift; my $theta=mod2p(ThetaG_JD($time)+$lon); my $omega_E=1.00273790934; # earth rotations per sidereal day my $secday=86400; my $mfactor=2*$pi*$omega_E/$secday; my $f=1/298.26; # earth flattening constant my $xkmper=6378.135; my $c=1/sqrt(1+$f*($f-2)*sin($lat)**2); my $s=(1-$f)*(1-$f)*$c; my $achcp=($xkmper*$c+$alt)*cos($lat); my $x_user=$achcp*cos($theta); my $y_user=$achcp*sin($theta); my $z_user=($xkmper*$s+$alt)*sin($lat); my $xdot_user=-$mfactor*$y_user; my $ydot_user=$mfactor*$x_user; my $zdot_user=0; return ($x_user,$y_user,$z_user,$xdot_user,$ydot_user,$zdot_user,$theta); } sub Calculate_Obs { # calculate the azimuth/el of an object as viewed from observers position # with object position given in ECI coordinates and observer in lat/long/alt. # # inputs: object ECI position vector (km) # object velocity vector (km/s) # julian time # observer lat,lon,altitude (km) my $x=shift; my $y=shift; my $z=shift; my $theta_s=shift; my $xdot=shift; my $ydot=shift; my $zdot=shift; my $time=shift; my $lat=shift; my $lon=shift; my $alt=shift; my ($x_o,$y_o,$z_o,$xdot_o,$ydot_o,$zdot_o,$theta)= Calculate_User_PosVel($lat,$lon,$alt,$time); my $xx=$x-$x_o; my $yy=$y-$y_o; my $zz=$z-$z_o; my $xxdot=$xdot-$xdot_o; my $yydot=$ydot-$ydot_o; my $zzdot=$zdot-$zdot_o; my $sin_lat=sin($lat); my $cos_lat=cos($lat); my $sin_theta=sin($theta); my $cos_theta=cos($theta); my $top_s=$sin_lat*$cos_theta*$xx + $sin_lat*$sin_theta*$yy - $cos_lat*$zz; my $top_e=-$sin_theta*$xx + $cos_theta*$yy; my $top_z=$cos_lat*$cos_theta*$xx + $cos_lat*$sin_theta*$yy + $sin_lat*$zz; my $az=atan(-$top_e/$top_s); $az=$az+$pi if ( $top_s > 0 ); $az=$az+2*$pi if ( $az < 0 ); my $range=sqrt($xx*$xx+$yy*$yy+$zz*$zz); my $el=asin($top_z/$range); return ($az, $el, $range); } sub Calendar_date_and_time_from_JD { my ($jd,$z,$frac,$alpha,$a,$b,$c,$d,$e,$dom,$yr,$mon,$day,$hr,$min); $jd=shift; $jd=$jd+0.5; $z=int($jd); $frac=$jd-$z; $alpha = int( ($z-1867216.5)/36524.25 ); $a=$z + 1 + $alpha - int($alpha/4); $a=$z if( $z < 2299161 ); $b=$a+1524; $c=int(($b-122.1)/365.25); $d=int(365.25*$c); $e=int(($b-$d)/30.6001); $dom=$b-$d-int(30.6001*$e)+$frac; $day=int($dom); $mon=$e-1 if( $e < 14 ); $mon=$e-13 if( $e == 14 || $e == 15 ); $yr = $c-4716 if( $mon > 2 ); $yr = $c-4715 if( $mon == 1 || $mon == 2 ); $hr = int($frac*24); $min= int(($frac*24 - $hr)*60+0.5); if ($min == 60) { # this may well prove inadequate DJK $hr += 1; $min = 0; } return ($yr,$mon,$day,$hr,$min); }