3 # This module was written by Steve Franke K9AN.
6 # The formulas used in this module
8 # Astronomical Algorithms, Second Edition
10 # Published by Willmann-Bell, Inc.
11 # P.O. Box 35025, Richmond, Virginia 23235
13 # Atmospheric refraction and parallax are taken into
14 # account when calculating positions of the sun and moon,
15 # and also when calculating the rise and set times.
17 # Copyright (c) 1999 - Steve Franke K9AN
21 # 2001/12/16 Fixed Julian_Date_of_Epoch and now I actually use it...
22 # 2001/09/15 some changes to take care of cases where the object
23 # doesn't rise or set on a given day...
31 @EXPORT = qw($pi $d2r $r2d );
35 use vars qw($VERSION $BRANCH);
37 main::mkver($VERSION = q$Revision$);
39 use vars qw($pi $d2r $r2d);
50 # reload the keps data
54 my $s = readfilestr("$main::root/local/Keps.pm");
69 $year=$year-1 if( $month <= 2 );
70 $month=$month+12 if( $month <= 2);
72 $julianday = int(365.25*($year+4716)+int(30.6001*($month+1)))+$day-13-1524.5;
75 sub Julian_Date_of_Epoch
78 my $year=int($epoch/1000);
79 my $day=$epoch-$year*1000;
86 my $Julian_Date_of_Epoch=Julian_Date_of_Year($year)+$day;
87 return $Julian_Date_of_Epoch;
90 sub Julian_Date_of_Year
96 my $Julian_Date_of_Year=int(365.25*$year)+int(30.6001*14)+
98 return $Julian_Date_of_Year;
103 my $omega_E=1.00273790934; # earth rotations per sidereal day
105 my $UT=($jd+0.5)-int($jd+0.5);
107 my $TU=($jd-2451545.0)/36525;
108 my $GMST=24110.54841+$TU*(8640184.812866+$TU*(0.093104-$TU*6.2e-6));
109 my $thetag_jd=mod2p(2*$pi*($GMST/$secday+$omega_E*$UT));
113 sub reduce_angle_to_360
117 $angle=$angle-int($angle/360)*360;
118 $angle=$angle+360 if( $angle < 0 );
126 $angle=$angle-int($angle/$twopi)*$twopi;
127 $angle=$angle+$twopi if( $angle < 0 );
132 my $angle_in_degrees = shift;
134 return sin($angle_in_degrees*$d2r);
138 my $angle_in_degrees = shift;
140 return cos($angle_in_degrees*$d2r);
144 my $angle_in_degrees = shift;
146 return tan($angle_in_degrees*$d2r);
154 my $az=$r2d * atan2( sindeg($H), cosdeg($H)*sindeg($lat)-tandeg($delta)*cosdeg($lat) );
155 my $h=$r2d * asin( sindeg($lat)*sindeg($delta)+cosdeg($lat)*cosdeg($delta)*cosdeg($H) );
167 my $sun0_moon1=shift; # 0 for sun, 1 for moon, 2 for venus...
168 my ($alpha1,$delta1,$alpha2,$delta2,$alpha3,$delta3);
169 my ($aznow,$hnow,$alphanow,$deltanow,$distance,$distancenow);
171 my ($risetime,$settime);
172 my ($dawntime,$dusktime);
174 my ($ifrac,$ifracnow);
176 my $julianday=Julian_Day($year,$month,$day);
177 my $tt1 = ($julianday-1-2451545)/36525.;
178 my $tt2 = ($julianday-2451545)/36525.;
179 my $tt3 = ($julianday+1-2451545)/36525.;
180 my $ttnow = ($julianday+$hr/24+$min/24/60-2451545)/36525.;
182 my $theta0=280.46061837+360.98564736629*($julianday-2451545.0)+
183 0.000387933*$tt2*$tt2-$tt2*$tt2*$tt2/38710000;
184 $theta0=reduce_angle_to_360($theta0);
186 my $thetanow=280.46061837+360.98564736629*($julianday+$hr/24+$min/24/60-2451545.0)+
187 0.000387933*$ttnow*$ttnow-$ttnow*$ttnow*$ttnow/38710000;
188 $thetanow=reduce_angle_to_360($thetanow);
190 if ( $sun0_moon1 == 0 ) {
191 ($alpha1, $delta1)=get_sun_alpha_delta($tt1);
192 ($alpha2, $delta2)=get_sun_alpha_delta($tt2);
193 ($alpha3, $delta3)=get_sun_alpha_delta($tt3);
194 ($alphanow, $deltanow)=get_sun_alpha_delta($ttnow);
195 $H=$thetanow-$lon-$alphanow;
196 $H=reduce_angle_to_360($H);
197 ($aznow,$hnow)=get_az_el($H,$deltanow,$lat);
199 1.02/(tandeg($hnow+10.3/($hnow+5.11)))/60;
200 $h0=-0.8333; # this is for sun rise and sun set
201 ($risetime,$settime)=
202 do_rise_set_calculations($h0,$theta0,$lat,$lon,$alpha1,$delta1,
203 $alpha2,$delta2,$alpha3,$delta3);
204 $h0=-6.0; # this is for civil dawn and dusk
205 ($dawntime,$dusktime)=
206 do_rise_set_calculations($h0,$theta0,$lat,$lon,$alpha1,$delta1,
207 $alpha2,$delta2,$alpha3,$delta3);
208 $dawntime = "------" if( $dawntime eq "NoRise" );
209 $dusktime = "------" if( $dusktime eq "NoSet " );
212 sprintf("%s", $dawntime), sprintf("%s",$risetime),
213 sprintf("%s", $settime), sprintf("%s",$dusktime),
218 if ( $sun0_moon1 == 1 ) {
219 ($alpha1, $delta1, $distance, $ifrac)=get_moon_alpha_delta($tt1);
220 ($alpha2, $delta2, $distance, $ifrac)=get_moon_alpha_delta($tt2);
221 ($alpha3, $delta3, $distance, $ifrac)=get_moon_alpha_delta($tt3);
222 ($alphanow, $deltanow, $distancenow, $ifracnow)=get_moon_alpha_delta($ttnow);
223 $h0=0.7275*$r2d*asin(6378.14/$distancenow)-34.0/60.;
224 $H=$thetanow-$lon-$alphanow;
225 $H=reduce_angle_to_360($H);
226 ($aznow,$hnow)=get_az_el($H,$deltanow,$lat);
227 $hnow=$hnow-$r2d*asin(sin(6378.14/$distancenow)*cosdeg($hnow))+
228 1.02/(tandeg($hnow+10.3/($hnow+5.11)))/60;
229 ($risetime,$settime)=
230 do_rise_set_calculations($h0,$theta0,$lat,$lon,$alpha1,$delta1,
231 $alpha2,$delta2,$alpha3,$delta3);
232 return (sprintf("%s", $risetime), sprintf("%s",$settime),
233 $aznow+180,$hnow, -40*log10($distance/385000), $ifracnow );
239 sub do_rise_set_calculations
243 my ($risehr,$risemin,$risetime,$sethr,$setmin,$settime);
244 my ($m0,$m1,$m2,$theta,$alpha,$delta,$H,$az,$h,$corr);
245 my ($i,$arg,$argtest,$H0);
258 $arg = (sindeg($h0)-sindeg($lat)*sindeg($delta2))/(cosdeg($lat)*cosdeg($delta2));
259 if ( abs($arg) > 1. ) { # either up all day or down all day
260 $norise = 1; # leave it to the user to examine
261 $noset = 1; # the elevation angle (or look outside!)
262 } # to figure out which.
264 $H0 = acos($arg)*$r2d;
265 my $aa=$alpha2-$alpha1;
266 my $ba=$alpha3-$alpha2;
267 $aa=$aa+360 if ($aa < -180);
268 $aa=$aa-360 if ($aa > 180);
269 $ba=$ba+360 if ($ba < -180);
270 $ba=$ba-360 if ($ba > 180);
273 my $ad=$delta2-$delta1;
274 my $bd=$delta3-$delta2;
275 $ad=$ad+360 if ($ad < -180);
276 $ad=$ad-360 if ($ad > 180);
277 $bd=$bd+360 if ($bd < -180);
278 $bd=$bd-360 if ($bd > 180);
281 $m0 = ($alpha2 + $lon - $theta0)/360.;
282 $m0=$m0+1 if( $m0 < 0 );
283 $m0=$m0-1 if( $m0 > 1 );
284 for ($i=1; $i<=2; $i++) {
285 $theta = $theta0+360.985647*$m0;
286 $alpha=$alpha2+$m0*($aa+$ba+$m0*$ca)/2;
287 $delta=$delta2+$m0*($ad+$bd+$m0*$cd)/2;
288 $H=$theta-$lon-$alpha;
289 $H=reduce_angle_to_360($H);
290 $H=$H-360 if ($H > 180);
291 ($az,$h)=get_az_el($H,$delta,$lat);
294 $m0=$m0+1 if( $m0 < 0 );
295 $m0=$m0-1 if( $m0 >= 1 );
300 $m1 = $m0 - $H0/360.;
301 $m1=$m1+1 if( $m1 < 0 );
302 $m1=$m1-1 if( $m1 > 1 );
303 for ($i=1; $i<=2; $i++) {
304 $theta = $theta0+360.985647*$m1;
305 $alpha=$alpha2+$m1*($aa+$ba+$m1*$ca)/2;
306 $delta=$delta2+$m1*($ad+$bd+$m1*$cd)/2;
307 $H=$theta-$lon-$alpha;
308 $H=reduce_angle_to_360($H);
309 ($az,$h)=get_az_el($H,$delta,$lat);
310 $corr=($h-$h0)/(360*(cosdeg($delta)*cosdeg($lat)*sindeg($H)));
312 # $norise=1 if( $m1 < 0 || $m1 > 1);
313 $m1=$m1-1 if( $m1 >= 1);
314 $m1=$m1+1 if( $m1 < 0);
320 $risemin=($m1*24-int($m1*24))*60+0.5;
321 if ( $risemin >= 60 ) {
322 $risemin=$risemin-60;
325 $risehr=0 if($risehr==24);
326 $risetime=sprintf("%02d:%02dZ",$risehr,$risemin);
332 $m2 = $m0 + $H0/360.;
333 $m2=$m2+1 if( $m2 < 0 );
334 $m2=$m2-1 if( $m2 >= 1 );
335 for ($i=1; $i<=2; $i++) {
336 $theta = $theta0+360.985647*$m2;
337 $alpha=$alpha2+$m2*($aa+$ba+$m2*$ca)/2;
338 $delta=$delta2+$m2*($ad+$bd+$m2*$cd)/2;
339 $H=$theta-$lon-$alpha;
340 $H=reduce_angle_to_360($H);
341 ($az,$h)=get_az_el($H,$delta,$lat);
342 $corr=($h-$h0)/(360*(cosdeg($delta)*cosdeg($lat)*sindeg($H)));
344 # $noset=1 if( $m2 < 0 || $m2 > 1);
345 $m2=$m2-1 if( $m2 >= 1);
346 $m2=$m2+1 if( $m2 < 0);
352 $setmin=($m2*24-int($m2*24))*60+0.5;
353 if ( $setmin >= 60 ) {
357 $sethr=0 if($sethr==24);
358 $settime=sprintf("%02d:%02dZ",$sethr,$setmin);
362 return $risetime,$settime;
367 sub get_moon_alpha_delta
370 # Calculate the moon's right ascension and declination
372 # As of October 2001, also calculate the illuminated fraction of the
373 # moon's disk... (why not?)
377 my $Lp=218.3164477+481267.88123421*$tt-
378 0.0015786*$tt*$tt+$tt*$tt*$tt/538841-$tt*$tt*$tt*$tt/65194000;
379 $Lp=reduce_angle_to_360($Lp);
381 my $D = 297.8501921+445267.1114034*$tt-0.0018819*$tt*$tt+
382 $tt*$tt*$tt/545868.-$tt*$tt*$tt*$tt/113065000.;
383 $D=reduce_angle_to_360($D);
385 my $M = 357.5291092 + 35999.0502909*$tt-0.0001536*$tt*$tt+
386 $tt*$tt*$tt/24490000.;
387 $M=reduce_angle_to_360($M);
389 my $Mp = 134.9633964 + 477198.8675055*$tt+0.0087414*$tt*$tt+
390 $tt*$tt*$tt/69699-$tt*$tt*$tt*$tt/14712000;
391 $Mp=reduce_angle_to_360($Mp);
393 my $F = 93.2720950 + 483202.0175233*$tt - 0.0036539*$tt*$tt-
394 $tt*$tt*$tt/3526000 + $tt*$tt*$tt*$tt/863310000;
395 $F=reduce_angle_to_360($F);
397 my $A1 = 119.75 + 131.849 * $tt;
398 $A1=reduce_angle_to_360($A1);
400 my $A2 = 53.09 + 479264.290 * $tt;
401 $A2=reduce_angle_to_360($A2);
403 my $A3 = 313.45 + 481266.484 * $tt;
404 $A3=reduce_angle_to_360($A3);
406 my $E = 1 - 0.002516 * $tt - 0.0000074 * $tt * $tt;
408 my $Sl= 6288774*sindeg( 1 * $Mp ) +
409 1274027*sindeg(2 * $D + -1 * $Mp ) +
410 658314 *sindeg(2 * $D ) +
411 213618 *sindeg( 2 * $Mp ) +
412 -185116 *sindeg( 1 * $M )*$E +
413 -114332 *sindeg( 2 * $F ) +
414 58793 *sindeg(2 * $D + -2 * $Mp ) +
415 57066 *sindeg(2 * $D - 1 * $M -1 * $Mp )*$E +
416 53322 *sindeg(2 * $D + 1 * $Mp ) +
417 45758 *sindeg(2 * $D - 1 * $M )*$E +
418 -40923 *sindeg( + 1 * $M -1 * $Mp )*$E +
419 -34720 *sindeg(1 * $D ) +
420 -30383 *sindeg( + 1 * $M + 1 * $Mp )*$E +
421 15327 *sindeg(2 * $D + -2 * $F ) +
422 -12528 *sindeg( 1 * $Mp + 2 * $F ) +
423 10980 *sindeg( 1 * $Mp - 2 * $F ) +
424 10675 *sindeg(4 * $D + -1 * $Mp ) +
425 10034 *sindeg( 3 * $Mp ) +
426 8548 *sindeg(4 * $D + 0 * $M - 2 * $Mp + 0 * $F ) +
427 -7888 *sindeg(2 * $D + 1 * $M - 1 * $Mp + 0 * $F )*$E +
428 -6766 *sindeg(2 * $D + 1 * $M + 0 * $Mp + 0 * $F )*$E +
429 -5163 *sindeg(1 * $D + 0 * $M - 1 * $Mp + 0 * $F ) +
430 4987 *sindeg(1 * $D + 1 * $M + 0 * $Mp + 0 * $F )*$E +
431 4036 *sindeg(2 * $D - 1 * $M + 1 * $Mp + 0 * $F )*$E +
432 3994 *sindeg(2 * $D + 0 * $M + 2 * $Mp + 0 * $F ) +
433 3861 *sindeg(4 * $D + 0 * $M + 0 * $Mp + 0 * $F ) +
434 3665 *sindeg(2 * $D + 0 * $M - 3 * $Mp + 0 * $F ) +
435 -2689 *sindeg(0 * $D + 1 * $M - 2 * $Mp + 0 * $F )*$E +
436 -2602 *sindeg(2 * $D + 0 * $M - 1 * $Mp + 2 * $F ) +
437 2390 *sindeg(2 * $D - 1 * $M - 2 * $Mp + 0 * $F )*$E +
438 -2348 *sindeg(1 * $D + 0 * $M + 1 * $Mp + 0 * $F ) +
439 2236 *sindeg(2 * $D - 2 * $M + 0 * $Mp + 0 * $F )*$E*$E +
440 -2120 *sindeg(0 * $D + 1 * $M + 2 * $Mp + 0 * $F )*$E +
441 -2069 *sindeg(0 * $D + 2 * $M + 0 * $Mp + 0 * $F )*$E*$E +
442 2048 *sindeg(2 * $D - 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
443 -1773 *sindeg(2 * $D + 0 * $M + 1 * $Mp - 2 * $F ) +
444 -1595 *sindeg(2 * $D + 0 * $M + 0 * $Mp + 2 * $F ) +
445 1215 *sindeg(4 * $D - 1 * $M - 1 * $Mp + 0 * $F )*$E +
446 -1110 *sindeg(0 * $D + 0 * $M + 2 * $Mp + 2 * $F ) +
447 -892 *sindeg(3 * $D + 0 * $M - 1 * $Mp + 0 * $F ) +
448 -810 *sindeg(2 * $D + 1 * $M + 1 * $Mp + 0 * $F )*$E +
449 759 *sindeg(4 * $D - 1 * $M - 2 * $Mp + 0 * $F )*$E +
450 -713 *sindeg(0 * $D + 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
451 -700 *sindeg(2 * $D + 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
452 691 *sindeg(2 * $D + 1 * $M - 2 * $Mp + 0 * $F )*$E +
453 596 *sindeg(2 * $D - 1 * $M + 0 * $Mp - 2 * $F )*$E +
454 549 *sindeg(4 * $D + 0 * $M + 1 * $Mp + 0 * $F ) +
455 537 *sindeg(0 * $D + 0 * $M + 4 * $Mp + 0 * $F ) +
456 520 *sindeg(4 * $D - 1 * $M + 0 * $Mp + 0 * $F )*$E +
457 -487 *sindeg(1 * $D + 0 * $M - 2 * $Mp + 0 * $F ) +
458 -399 *sindeg(2 * $D + 1 * $M + 0 * $Mp - 2 * $F )*$E +
459 -381 *sindeg(0 * $D + 0 * $M + 2 * $Mp - 2 * $F ) +
460 351 *sindeg(1 * $D + 1 * $M + 1 * $Mp + 0 * $F )*$E +
461 -340 *sindeg(3 * $D + 0 * $M - 2 * $Mp + 0 * $F ) +
462 330 *sindeg(4 * $D + 0 * $M - 3 * $Mp + 0 * $F ) +
463 327 *sindeg(2 * $D - 1 * $M + 2 * $Mp + 0 * $F )*$E +
464 -323 *sindeg(0 * $D + 2 * $M + 1 * $Mp + 0 * $F )*$E*$E +
465 299 *sindeg(1 * $D + 1 * $M - 1 * $Mp + 0 * $F )*$E +
466 294 *sindeg(2 * $D + 0 * $M + 3 * $Mp + 0 * $F ) +
467 3958 *sindeg($A1) + 1962*sindeg($Lp - $F) + 318*sindeg($A2);
469 my $Sr=-20905355 *cosdeg( 1 * $Mp ) +
470 -3699111 *cosdeg(2 * $D + -1 * $Mp ) +
471 -2955968 *cosdeg(2 * $D ) +
472 -569925 *cosdeg( 2 * $Mp ) +
473 48888 *cosdeg( 1 * $M )*$E +
474 -3149 *cosdeg( 2 * $F ) +
475 246158 *cosdeg(2 * $D + -2 * $Mp ) +
476 -152138 *cosdeg(2 * $D - 1 * $M -1 * $Mp )*$E +
477 -170733 *cosdeg(2 * $D + 1 * $Mp ) +
478 -204586 *cosdeg(2 * $D - 1 * $M )*$E +
479 -129620 *cosdeg( + 1 * $M -1 * $Mp )*$E +
480 108743 *cosdeg(1 * $D ) +
481 104755 *cosdeg( + 1 * $M + 1 * $Mp )*$E +
482 10321 *cosdeg(2 * $D + -2 * $F ) +
483 79661 *cosdeg( 1 * $Mp - 2 * $F ) +
484 -34782 *cosdeg(4 * $D + -1 * $Mp ) +
485 -23210 *cosdeg( 3 * $Mp ) +
486 -21636 *cosdeg(4 * $D + 0 * $M - 2 * $Mp + 0 * $F ) +
487 24208 *cosdeg(2 * $D + 1 * $M - 1 * $Mp + 0 * $F )*$E +
488 30824 *cosdeg(2 * $D + 1 * $M + 0 * $Mp + 0 * $F )*$E +
489 -8379 *cosdeg(1 * $D + 0 * $M - 1 * $Mp + 0 * $F ) +
490 -16675 *cosdeg(1 * $D + 1 * $M + 0 * $Mp + 0 * $F )*$E +
491 -12831 *cosdeg(2 * $D - 1 * $M + 1 * $Mp + 0 * $F )*$E +
492 -10445 *cosdeg(2 * $D + 0 * $M + 2 * $Mp + 0 * $F ) +
493 -11650 *cosdeg(4 * $D + 0 * $M + 0 * $Mp + 0 * $F ) +
494 14403 *cosdeg(2 * $D + 0 * $M - 3 * $Mp + 0 * $F ) +
495 -7003 *cosdeg(0 * $D + 1 * $M - 2 * $Mp + 0 * $F )*$E +
496 10056 *cosdeg(2 * $D - 1 * $M - 2 * $Mp + 0 * $F )*$E +
497 6322 *cosdeg(1 * $D + 0 * $M + 1 * $Mp + 0 * $F ) +
498 -9884 *cosdeg(2 * $D - 2 * $M + 0 * $Mp + 0 * $F )*$E*$E +
499 5751 *cosdeg(0 * $D + 1 * $M + 2 * $Mp + 0 * $F )*$E +
500 -4950 *cosdeg(2 * $D - 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
501 4130 *cosdeg(2 * $D + 0 * $M + 1 * $Mp - 2 * $F )+
502 -3958 *cosdeg(4 * $D - 1 * $M - 1 * $Mp + 0 * $F )*$E +
503 3258 *cosdeg(3 * $D + 0 * $M - 1 * $Mp + 0 * $F )+
504 2616 *cosdeg(2 * $D + 1 * $M + 1 * $Mp + 0 * $F )*$E +
505 -1897 *cosdeg(4 * $D - 1 * $M - 2 * $Mp + 0 * $F )*$E +
506 -2117 *cosdeg(0 * $D + 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
507 2354 *cosdeg(2 * $D + 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
508 -1423 *cosdeg(4 * $D + 0 * $M + 1 * $Mp + 0 * $F )+
509 -1117 *cosdeg(0 * $D + 0 * $M + 4 * $Mp + 0 * $F )+
510 -1571 *cosdeg(4 * $D - 1 * $M + 0 * $Mp + 0 * $F )*$E +
511 -1739 *cosdeg(1 * $D + 0 * $M - 2 * $Mp + 0 * $F )+
512 -4421 *cosdeg(0 * $D + 0 * $M + 2 * $Mp - 2 * $F )+
513 1165 *cosdeg(0 * $D + 2 * $M + 1 * $Mp + 0 * $F )*$E*$E +
514 8752 *cosdeg(2 * $D + 0 * $M - 1 * $Mp - 2 * $F );
516 my $Sb= 5128122 *sindeg( 1 * $F ) +
517 280602 *sindeg( 1 * $Mp + 1 * $F ) +
518 277693 *sindeg( 1 * $Mp - 1 * $F ) +
519 173237 *sindeg(2 * $D - 1 * $F ) +
520 55413 *sindeg(2 * $D -1 * $Mp + 1 * $F ) +
521 46271 *sindeg(2 * $D + -1 * $Mp - 1 * $F ) +
522 32573 *sindeg(2 * $D + 1 * $F ) +
523 17198 *sindeg( 2 * $Mp + 1 * $F )+
524 9266 *sindeg(2 * $D + 0 * $M + 1 * $Mp - 1 * $F ) +
525 8822 *sindeg(0 * $D + 0 * $M + 2 * $Mp - 1 * $F ) +
526 8216 *sindeg(2 * $D - 1 * $M + 0 * $Mp - 1 * $F )*$E +
527 4324 *sindeg(2 * $D + 0 * $M - 2 * $Mp - 1 * $F ) +
528 4200 *sindeg(2 * $D + 0 * $M + 1 * $Mp + 1 * $F ) +
529 -3359 *sindeg(2 * $D + 1 * $M + 0 * $Mp - 1 * $F )*$E +
530 2463 *sindeg(2 * $D - 1 * $M - 1 * $Mp + 1 * $F )*$E +
531 2211 *sindeg(2 * $D - 1 * $M + 0 * $Mp + 1 * $F )*$E +
532 2065 *sindeg(2 * $D - 1 * $M - 1 * $Mp - 1 * $F )*$E +
533 -1870 *sindeg(0 * $D + 1 * $M - 1 * $Mp - 1 * $F )*$E +
534 1828 *sindeg(4 * $D + 0 * $M - 1 * $Mp - 1 * $F ) +
535 -1794 *sindeg(0 * $D + 1 * $M + 0 * $Mp + 1 * $F )*$E +
536 -1749 *sindeg(0 * $D + 0 * $M + 0 * $Mp + 3 * $F ) +
537 -1565 *sindeg(0 * $D + 1 * $M - 1 * $Mp + 1 * $F )*$E +
538 -1491 *sindeg(1 * $D + 0 * $M + 0 * $Mp + 1 * $F ) +
539 -1475 *sindeg(0 * $D + 1 * $M + 1 * $Mp + 1 * $F )*$E +
540 -1410 *sindeg(0 * $D + 1 * $M + 1 * $Mp - 1 * $F )*$E +
541 -1344 *sindeg(0 * $D + 1 * $M + 0 * $Mp - 1 * $F )*$E +
542 -1335 *sindeg(1 * $D + 0 * $M + 0 * $Mp - 1 * $F ) +
543 1107 *sindeg(0 * $D + 0 * $M + 3 * $Mp + 1 * $F ) +
544 1021 *sindeg(4 * $D + 0 * $M + 0 * $Mp - 1 * $F ) +
545 833 *sindeg(4 * $D + 0 * $M - 1 * $Mp + 1 * $F ) +
546 777 *sindeg(0 * $D + 0 * $M + 1 * $Mp - 3 * $F ) +
547 671 *sindeg(4 * $D + 0 * $M - 2 * $Mp + 1 * $F ) +
548 607 *sindeg(2 * $D + 0 * $M + 0 * $Mp - 3 * $F ) +
549 596 *sindeg(2 * $D + 0 * $M + 2 * $Mp - 1 * $F ) +
550 491 *sindeg(2 * $D - 1 * $M + 1 * $Mp - 1 * $F )*$E +
551 -451 *sindeg(2 * $D + 0 * $M - 2 * $Mp + 1 * $F ) +
552 439 *sindeg(0 * $D + 0 * $M + 3 * $Mp - 1 * $F ) +
553 422 *sindeg(2 * $D + 0 * $M + 2 * $Mp + 1 * $F ) +
554 421 *sindeg(2 * $D + 0 * $M - 3 * $Mp - 1 * $F ) +
555 -366 *sindeg(2 * $D + 1 * $M - 1 * $Mp + 1 * $F )*$E +
556 -351 *sindeg(2 * $D + 1 * $M + 0 * $Mp + 1 * $F )*$E +
557 331 *sindeg(4 * $D + 0 * $M + 0 * $Mp + 1 * $F ) +
558 315 *sindeg(2 * $D - 1 * $M + 1 * $Mp + 1 * $F )*$E +
559 302 *sindeg(2 * $D - 2 * $M + 0 * $Mp - 1 * $F )*$E*$E +
560 -283 *sindeg(0 * $D + 0 * $M + 1 * $Mp + 3 * $F ) +
561 -229 *sindeg(2 * $D + 1 * $M + 1 * $Mp - 1 * $F )*$E +
562 223 *sindeg(1 * $D + 1 * $M + 0 * $Mp - 1 * $F )*$E +
563 223 *sindeg(1 * $D + 1 * $M + 0 * $Mp + 1 * $F )*$E +
564 -220 *sindeg(0 * $D + 1 * $M - 2 * $Mp - 1 * $F )*$E +
565 -220 *sindeg(2 * $D + 1 * $M - 1 * $Mp - 1 * $F )*$E +
566 -185 *sindeg(1 * $D + 0 * $M + 1 * $Mp + 1 * $F ) +
567 181 *sindeg(2 * $D - 1 * $M - 2 * $Mp - 1 * $F )*$E +
568 -177 *sindeg(0 * $D + 1 * $M + 2 * $Mp + 1 * $F )*$E +
569 176 *sindeg(4 * $D + 0 * $M - 2 * $Mp - 1 * $F ) +
570 166 *sindeg(4 * $D - 1 * $M - 1 * $Mp - 1 * $F )*$E +
571 -164 *sindeg(1 * $D + 0 * $M + 1 * $Mp - 1 * $F ) +
572 132 *sindeg(4 * $D + 0 * $M + 1 * $Mp - 1 * $F ) +
573 -119 *sindeg(1 * $D + 0 * $M - 1 * $Mp - 1 * $F ) +
574 115 *sindeg(4 * $D - 1 * $M + 0 * $Mp - 1 * $F )*$E +
575 107 *sindeg(2 * $D - 2 * $M + 0 * $Mp + 1 * $F )*$E*$E
576 -2235 *sindeg($Lp) + 382*sindeg($A3) +
577 175 *sindeg($A1-$F) + 175*sindeg($A1+$F) +
578 127 *sindeg($Lp-$Mp) - 115*sindeg($Lp+$Mp);
580 my $lambda=$Lp+$Sl/1000000.;
582 my $beta=$Sb/1000000.;
584 my $distance=385000.56 + $Sr/1000.;
586 my $epsilon = 23+26./60.+21.448/(60.*60.);
588 my $alpha=atan2(cosdeg($epsilon)*sindeg($lambda)-tandeg($beta)*sindeg($epsilon),cosdeg($lambda))*$r2d;
589 $alpha = reduce_angle_to_360($alpha);
591 my $delta=asin(cosdeg($beta)*sindeg($epsilon)*sindeg($lambda)+sindeg($beta)*cosdeg($epsilon))*$r2d;
592 $delta = reduce_angle_to_360($delta);
594 # $phase will be the "moon phase angle" from p. 346 of Meeus' book...
595 my $phase=180.0 - $D - 6.289 *sindeg($Mp)
597 - 1.274 *sindeg(2.*$D - $Mp)
598 - 0.658 *sindeg(2.*$D)
599 - 0.214 *sindeg(2.*$Mp)
602 # $illum_frac is the fraction of the disk that is illuminated, and will be
603 # zero at new moon and 1.0 at full moon.
605 my $illum_frac = (1.0 + cosdeg( $phase ))/2.;
607 return ($alpha,$delta,$distance,$illum_frac);
610 sub get_sun_alpha_delta
613 # Calculate Sun's right ascension and declination
617 my $L0 = 280.46646+36000.76983*$tt+0.0003032*($tt^2);
618 $L0=reduce_angle_to_360($L0);
620 my $M = 357.52911 + 35999.05029*$tt-0.0001537*($tt^2);
621 $M=reduce_angle_to_360($M);
623 my $C = (1.914602 - 0.004817*$tt-0.000014*($tt^2))*sindeg($M) +
624 (0.019993 - 0.000101*$tt)*sindeg(2*$M) +
625 0.000289*sindeg(3*$M);
627 my $OMEGA = 125.04 - 1934.136*$tt;
629 my $lambda=$L0+$C-0.00569-0.00478*sindeg($OMEGA);
631 my $epsilon = 23+26./60.+21.448/(60.*60.);
633 my $alpha=atan2(cosdeg($epsilon)*sindeg($lambda),cosdeg($lambda))*$r2d;
634 $alpha = reduce_angle_to_360($alpha);
636 my $delta=asin(sin($epsilon*$d2r)*sin($lambda*$d2r))*$r2d;
637 $delta = reduce_angle_to_360($delta);
639 return ($alpha,$delta);
641 sub get_satellite_pos
644 # This code was translated more-or-less directly from the Pascal
645 # routines contained in a report compiled by TS Kelso and based on:
646 # Spacetrack Report No. 3
647 # "Models for Propagation of NORAD Element Sets"
648 # Felix R. Hoots, Ronald L Roehrich
651 # See TS Kelso's web site for more details...
652 # Only the SGP propagation model is implemented.
654 # Steve Franke, K9AN. 9 Dec 1999.
658 #1 25338U 98030A 99341.00000000 +.00000376 +00000-0 +18612-3 0 05978
659 #2 25338 098.6601 008.2003 0011401 112.4684 042.5140 14.23047277081382
661 #1 21639U 91054B 99341.34471854 .00000095 00000-0 10000-3 0 4928
662 #2 21639 1.5957 88.4884 0003028 161.6582 135.4323 1.00277774 30562
664 #1 20439U 90005D 99341.14501399 +.00000343 +00000-0 +14841-3 0 02859
665 #2 20439 098.4690 055.0032 0012163 066.4615 293.7842 14.30320285515297
667 #Temporary keps database...
674 my $sat_ref = $keps{$satname};
675 #printf("$jtime $lat $lon $alt Satellite name = $satname\n");
682 my $xke=.743669161e-1;
686 my $ck2=.5*$xj2*$ae**2;
687 my $ck4=-.375*$xj4*$ae**4;
688 my $qoms2t=(($qo-$so)*$ae/$xkmper)**4;
689 my $s=$ae*(1+$so/$xkmper);
691 my $epoch = $sat_ref ->{epoch};
692 #printf("epoch = %10.2f\n",$epoch);
693 my $jt_epoch=Julian_Date_of_Epoch($epoch);
694 #printf("JT for epoch = %17.12f\n",$jt_epoch);
695 my $tsince=($jtime-$jt_epoch)*24*60;
696 #printf("tsince (min) = %17.12f\n",$tsince);
698 my $mm1 = $sat_ref ->{mm1};
699 my $mm2 = $sat_ref ->{mm2};
700 my $bstar=$sat_ref ->{bstar}; # drag term for sgp4 model
701 my $inclination=$sat_ref->{inclination}; # inclination in degrees
702 my $raan=$sat_ref->{raan}; # right ascension of ascending node in degs
703 my $eccentricity=$sat_ref ->{eccentricity}; # eccentricity - dimensionless
704 my $omegao=$sat_ref ->{argperigee}; # argument of perigee in degs
705 my $xmo=$sat_ref ->{meananomaly}; # mean anomaly in degrees
706 my $xno=$sat_ref ->{meanmotion}; # mean motion in revs per day
708 #printf("%10.6f %10.6f %10.6f %10.6f %10.6f %10.6f %10.6f %10.6f %10.6f\n",
709 #$mm1,$mm2,$bstar,$inclination,$raan,$eccentricity,$omegao,$xmo,$xno);
711 $omegao=$omegao*$d2r;
713 $inclination=$inclination*$d2r;
714 my $temp=2*$pi/$xmnpda/$xmnpda;
715 $xno=$xno*$temp*$xmnpda;
717 $mm2=$mm2*$temp/$xmnpda;
722 my $c4=$xj3*$ae**3/(4*$ck2);
723 my $cosio=cos($inclination);
724 my $sinio=sin($inclination);
725 my $a1=($xke/$xno)**(2./3.);
726 my $d1=$c1/$a1/$a1*(3*$cosio*$cosio-1)/(1-$eccentricity*$eccentricity)**1.5;
727 my $ao=$a1*(1-1./3.*$d1-$d1*$d1-134./81.*$d1*$d1*$d1);
728 my $po=$ao*(1-$eccentricity*$eccentricity);
729 $qo=$ao*(1-$eccentricity);
730 my $xlo=$xmo+$omegao+$raan;
731 my $d10=$c3*$sinio*$sinio;
732 my $d20=$c2*(7.*$cosio*$cosio-1);
735 my $po2no=$xno/($po*$po);
736 my $omgdt=$c1*$po2no*(5.*$cosio*$cosio-1);
737 my $xnodot=-2.*$d30*$po2no;
738 my $c5=0.5*$c4*$sinio*(3+5*$cosio)/(1+$cosio);
741 my $a=$xno+(2*$mm1+3*$mm2*$tsince)*$tsince;
742 $a=$ao*($xno/$a)**(2./3.);
744 $e =1-$qo/$a if ($a > $qo);
746 my $xnodes=$raan+$xnodot*$tsince;
747 my $omgas=$omegao+$omgdt*$tsince;
748 my $xls=mod2p($xlo+($xno+$omgdt+$xnodot+($mm1+$mm2*$tsince)*$tsince)*$tsince);
750 my $axnsl=$e*cos($omgas);
751 my $aynsl=$e*sin($omgas)-$c6/$p;
752 my $xl=mod2p($xls-$c5/$p*$axnsl);
754 my $u=mod2p($xl-$xnodes);
760 for ($item3=0; abs($tem5) >= 1e-6 && $item3 < 10; $item3++ )
764 $tem5=1-$coseo1*$axnsl-$sineo1*$aynsl;
765 $tem5=($u-$aynsl*$coseo1+$axnsl*$sineo1-$eo1)/$tem5;
767 $tem5=$tem2/$tem5 if ($tem2 > 1);
773 my $ecose=$axnsl*$coseo1+$aynsl*$sineo1;
774 my $esine=$axnsl*$sineo1-$aynsl*$coseo1;
775 my $el2=$axnsl*$axnsl+$aynsl*$aynsl;
779 my $rdot=$xke*sqrt($a)/$r*$esine;
780 my $rvdot=$xke*sqrt($pl)/$r;
781 $temp=$esine/(1+sqrt(1-$el2));
782 my $sinu=$a/$r*($sineo1-$aynsl-$axnsl*$temp);
783 my $cosu=$a/$r*($coseo1-$axnsl+$aynsl*$temp);
784 my $su=atan2($sinu,$cosu);
786 my $sin2u=($cosu+$cosu)*$sinu;
787 my $cos2u=1-2*$sinu*$sinu;
788 my $rk=$r+$d10/$pl*$cos2u;
789 my $uk=$su-$d20/$pl2*$sin2u;
790 my $xnodek=$xnodes+$d30*$sin2u/$pl2;
791 my $xinck=$inclination+$d40/$pl2*$cos2u;
795 my $sinnok=sin($xnodek);
796 my $cosnok=cos($xnodek);
797 my $sinik=sin($xinck);
798 my $cosik=cos($xinck);
799 my $xmx=-$sinnok*$cosik;
800 my $xmy=$cosnok*$cosik;
801 my $ux=$xmx*$sinuk+$cosnok*$cosuk;
802 my $uy=$xmy*$sinuk+$sinnok*$cosuk;
803 my $uz=$sinik*$sinuk;
804 my $vx=$xmx*$cosuk-$cosnok*$sinuk;
805 my $vy=$xmy*$cosuk-$sinnok*$sinuk;
806 my $vz=$sinik*$cosuk;
808 my $x=$rk*$ux*$xkmper/$ae;
809 my $y=$rk*$uy*$xkmper/$ae;
810 my $z=$rk*$uz*$xkmper/$ae;
814 $xdot=($rvdot*$vx+$xdot)*$xkmper/$ae*$xmnpda/86400;
815 $ydot=($rvdot*$vy+$ydot)*$xkmper/$ae*$xmnpda/86400;
816 $zdot=($rvdot*$vz+$zdot)*$xkmper/$ae*$xmnpda/86400;
817 #printf("x=%17.6f y=%17.6f z=%17.6f \n",$x,$y,$z);
818 #printf("xdot=%17.6f ydot=%17.6f zdot=%17.6f \n",$xdot,$ydot,$zdot);
819 my ($sat_lat,$sat_lon,$sat_alt,$sat_theta)=Calculate_LatLonAlt($x,$y,$z,$jtime);
820 my ($az, $el, $distance) = Calculate_Obs($x,$y,$z,$sat_theta,$xdot,$ydot,$zdot,$jtime,$lat,$lon,$alt);
821 return ($sat_lat,$sat_lon,$sat_alt,$az,$el,$distance);
824 sub Calculate_LatLonAlt
827 # convert from ECI coordinates to latitude, longitude and altitude.
834 my $theta=atan2($y,$x);
835 my $lon=mod2p($theta-ThetaG_JD($time));
836 my $range=sqrt($x**2+$y**2);
837 my $f=1/298.26; # earth flattening constant
840 my $lat=atan2($z,$range);
845 $c=1/sqrt(1-$e2*sin($phi)**2);
846 $lat=atan2($z+$xkmper*$c*$e2*sin($phi),$range);
847 } until abs($lat-$phi) < 1e-10;
848 my $alt=$range/cos($lat)-$xkmper*$c;
849 return ($lat,$lon,$alt,$theta); # radians and kilometers
853 sub Calculate_User_PosVel
855 # change from lat/lon/alt/time coordinates to earth centered inertial (ECI)
856 # position and local hour angle.
861 my $theta=mod2p(ThetaG_JD($time)+$lon);
862 my $omega_E=1.00273790934; # earth rotations per sidereal day
864 my $mfactor=2*$pi*$omega_E/$secday;
865 my $f=1/298.26; # earth flattening constant
867 my $c=1/sqrt(1+$f*($f-2)*sin($lat)**2);
868 my $s=(1-$f)*(1-$f)*$c;
869 my $achcp=($xkmper*$c+$alt)*cos($lat);
870 my $x_user=$achcp*cos($theta);
871 my $y_user=$achcp*sin($theta);
872 my $z_user=($xkmper*$s+$alt)*sin($lat);
873 my $xdot_user=-$mfactor*$y_user;
874 my $ydot_user=$mfactor*$x_user;
876 return ($x_user,$y_user,$z_user,$xdot_user,$ydot_user,$zdot_user,$theta);
880 # calculate the azimuth/el of an object as viewed from observers position
881 # with object position given in ECI coordinates and observer in lat/long/alt.
883 # inputs: object ECI position vector (km)
884 # object velocity vector (km/s)
886 # observer lat,lon,altitude (km)
899 my ($x_o,$y_o,$z_o,$xdot_o,$ydot_o,$zdot_o,$theta)=
900 Calculate_User_PosVel($lat,$lon,$alt,$time);
904 my $xxdot=$xdot-$xdot_o;
905 my $yydot=$ydot-$ydot_o;
906 my $zzdot=$zdot-$zdot_o;
908 my $sin_lat=sin($lat);
909 my $cos_lat=cos($lat);
910 my $sin_theta=sin($theta);
911 my $cos_theta=cos($theta);
913 my $top_s=$sin_lat*$cos_theta*$xx
914 + $sin_lat*$sin_theta*$yy
917 my $top_e=-$sin_theta*$xx
920 my $top_z=$cos_lat*$cos_theta*$xx
921 + $cos_lat*$sin_theta*$yy
924 my $az=atan(-$top_e/$top_s);
925 $az=$az+$pi if ( $top_s > 0 );
926 $az=$az+2*$pi if ( $az < 0 );
928 my $range=sqrt($xx*$xx+$yy*$yy+$zz*$zz);
929 my $el=asin($top_z/$range);
930 return ($az, $el, $range);
933 sub Calendar_date_and_time_from_JD
935 my ($jd,$z,$frac,$alpha,$a,$b,$c,$d,$e,$dom,$yr,$mon,$day,$hr,$min);
940 $alpha = int( ($z-1867216.5)/36524.25 );
941 $a=$z + 1 + $alpha - int($alpha/4);
942 $a=$z if( $z < 2299161 );
944 $c=int(($b-122.1)/365.25);
946 $e=int(($b-$d)/30.6001);
947 $dom=$b-$d-int(30.6001*$e)+$frac;
949 $mon=$e-1 if( $e < 14 );
950 $mon=$e-13 if( $e == 14 || $e == 15 );
951 $yr = $c-4716 if( $mon > 2 );
952 $yr = $c-4715 if( $mon == 1 || $mon == 2 );
954 $min= int(($frac*24 - $hr)*60+0.5);
955 if ($min == 60) { # this may well prove inadequate DJK
959 return ($yr,$mon,$day,$hr,$min);