X-Git-Url: http://dxcluster.org/gitweb/gitweb.cgi?a=blobdiff_plain;f=perl%2FSun.pm;h=aaf85a33eeb18e569f00bdf2309afa28c717ef70;hb=refs%2Fheads%2Fip_address;hp=10a7f77cb6288c668523fd1ee01e7357facea60b;hpb=0e84728de35d2dadbb9d624614a471b68ae9eef6;p=spider.git diff --git a/perl/Sun.pm b/perl/Sun.pm index 10a7f77c..aaf85a33 100644 --- a/perl/Sun.pm +++ b/perl/Sun.pm @@ -1,115 +1,963 @@ -#!/usr/bin/perl -w +#/usr/bin/perl -w # -# The subroutines "julian_day" and "riseset" written by -# Steve Franke, November 1999. +# This module was written by Steve Franke K9AN. +# November, 1999. # -# The formulas used to calculate sunrise and sunset times -# are described in Chapters 7, 12, 15, and 25 of +# 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; -use POSIX; require Exporter; @ISA = qw(Exporter); @EXPORT = qw($pi $d2r $r2d ); use strict; -use vars qw($pi $d2r $r2d ); +use vars qw($pi $d2r $r2d); + $pi = 3.141592653589; $d2r = ($pi/180); $r2d = (180/$pi); -sub julian_day +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; -sub riseset + $angle=$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 $julianday; - - $julianday=julian_day($year,$month,$day); - - my $tt = ($julianday-2451545)/36525.; + 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*($tt^2)-($tt^3)/38710000; - $theta0=$theta0-int($theta0/360)*360; - $theta0=$theta0+360 if( $theta0 < 0 ); - + 0.000387933*$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); - $L0=$L0-int($L0/360)*360; - $L0=$L0+360 if( $L0 < 0 ); - + $L0=reduce_angle_to_360($L0); + my $M = 357.52911 + 35999.05029*$tt-0.0001537*($tt^2); - $M=$M-int($M/360)*360; - $M=$M+360 if( $M < 0 ); - - my $C = (1.914602 - 0.004817*$tt-0.000014*($tt^2))*sin($M*$d2r) + - (0.019993 - 0.000101*$tt)*sin(2*$M*$d2r) + - 0.000289*sin(3*$M*$d2r); - + $M=reduce_angle_to_360($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+$C-0.00569-0.00478*sin($OMEGA*$d2r); - + my $lambda=$L0+$C-0.00569-0.00478*sindeg($OMEGA); + my $epsilon = 23+26./60.+21.448/(60.*60.); - - my $alpha=atan2(cos($epsilon*$d2r)*sin($lambda*$d2r),cos($lambda*$d2r))*$r2d; - $alpha = $alpha-int($alpha/360)*360; - $alpha=$alpha+360 if ( $alpha < 0 ); - + + 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 = $delta-int($delta/360)*360; - $delta = $delta+360 if ( $delta < 0 ); - - my $arg = (sin(-.8333*$d2r)-sin($lat)*sin($delta*$d2r))/(cos($lat)*cos($delta*$d2r)); - my $argtest = tan($lat)*tan($delta*$d2r); + $delta = reduce_angle_to_360($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; - if ( $argtest < -1. ) { - return sprintf("Sun doesn't rise."); - } - if ( $argtest > 1. ) { - return sprintf("Sun doesn't set."); + 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 - my $H0 = acos($arg)*$r2d; - - my $transit = ($alpha + $lon*$r2d - $theta0)/360.; - $transit=$transit+1 if( $transit < 0 ); - $transit=$transit-1 if( $transit > 1 ); - - my $rise = $transit - $H0/360.; - $rise=$rise+1 if( $rise < 0 ); - $rise=$rise-1 if( $rise > 1 ); - - my $set = $transit + $H0/360.; - $set=$set+1 if( $set < 0 ); - $set=$set-1 if( $set > 1 ); +} + +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); - return sprintf("Sunrise: %2.2d%2.2dZ Sunset: %2.2d%2.2dZ",int($rise*24), - ($rise*24-int($rise*24))*60., - int($set*24),($set*24-int($set*24))*60.); + 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); } + + -1;