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);
36 $VERSION = sprintf( "%d.%03d", q$Revision$ =~ /(\d+)\.(\d+)/ );
37 $BRANCH = sprintf( "%d.%03d", q$Revision$ =~ /\d+\.\d+\.(\d+)\.(\d+)/ || (0,0));
38 $main::build += $VERSION;
39 $main::branch += $BRANCH;
41 use vars qw($pi $d2r $r2d);
52 # reload the keps data
56 my $s = readfilestr("$main::root/local/Keps.pm");
71 $year=$year-1 if( $month <= 2 );
72 $month=$month+12 if( $month <= 2);
74 $julianday = int(365.25*($year+4716)+int(30.6001*($month+1)))+$day-13-1524.5;
77 sub Julian_Date_of_Epoch
80 my $year=int($epoch/1000);
81 my $day=$epoch-$year*1000;
88 my $Julian_Date_of_Epoch=Julian_Date_of_Year($year)+$day;
89 return $Julian_Date_of_Epoch;
92 sub Julian_Date_of_Year
98 my $Julian_Date_of_Year=int(365.25*$year)+int(30.6001*14)+
100 return $Julian_Date_of_Year;
105 my $omega_E=1.00273790934; # earth rotations per sidereal day
107 my $UT=($jd+0.5)-int($jd+0.5);
109 my $TU=($jd-2451545.0)/36525;
110 my $GMST=24110.54841+$TU*(8640184.812866+$TU*(0.093104-$TU*6.2e-6));
111 my $thetag_jd=mod2p(2*$pi*($GMST/$secday+$omega_E*$UT));
115 sub reduce_angle_to_360
119 $angle=$angle-int($angle/360)*360;
120 $angle=$angle+360 if( $angle < 0 );
128 $angle=$angle-int($angle/$twopi)*$twopi;
129 $angle=$angle+$twopi if( $angle < 0 );
134 my $angle_in_degrees = shift;
136 return sin($angle_in_degrees*$d2r);
140 my $angle_in_degrees = shift;
142 return cos($angle_in_degrees*$d2r);
146 my $angle_in_degrees = shift;
148 return tan($angle_in_degrees*$d2r);
156 my $az=$r2d * atan2( sindeg($H), cosdeg($H)*sindeg($lat)-tandeg($delta)*cosdeg($lat) );
157 my $h=$r2d * asin( sindeg($lat)*sindeg($delta)+cosdeg($lat)*cosdeg($delta)*cosdeg($H) );
169 my $sun0_moon1=shift; # 0 for sun, 1 for moon, 2 for venus...
173 my ($risehr,$risemin,$risetime,$sethr,$setmin,$settime);
175 my ($alpha1,$alpha2,$alpha3,$delta1,$delta2,$delta3);
176 my ($m0,$m1,$m2,$theta,$alpha,$delta,$H,$az,$h,$h0,$aznow,$hnow,$corr);
177 my ($i,$arg,$argtest,$H0,$alphanow,$deltanow,$distance,$distancenow);
178 my ($ifrac,$ifracnow);
180 my $julianday=Julian_Day($year,$month,$day);
181 my $tt1 = ($julianday-1-2451545)/36525.;
182 my $tt2 = ($julianday-2451545)/36525.;
183 my $tt3 = ($julianday+1-2451545)/36525.;
184 my $ttnow = ($julianday+$hr/24+$min/24/60-2451545)/36525.;
186 my $theta0=280.46061837+360.98564736629*($julianday-2451545.0)+
187 0.000387933*$tt2*$tt2-$tt2*$tt2*$tt2/38710000;
188 $theta0=reduce_angle_to_360($theta0);
190 my $thetanow=280.46061837+360.98564736629*($julianday+$hr/24+$min/24/60-2451545.0)+
191 0.000387933*$ttnow*$ttnow-$ttnow*$ttnow*$ttnow/38710000;
192 $thetanow=reduce_angle_to_360($thetanow);
194 if ( $sun0_moon1 == 0 ) {
195 ($alpha1, $delta1)=get_sun_alpha_delta($tt1);
196 ($alpha2, $delta2)=get_sun_alpha_delta($tt2);
197 ($alpha3, $delta3)=get_sun_alpha_delta($tt3);
198 ($alphanow, $deltanow)=get_sun_alpha_delta($ttnow);
200 $H=$thetanow-$lon-$alphanow;
201 $H=reduce_angle_to_360($H);
202 ($aznow,$hnow)=get_az_el($H,$deltanow,$lat);
204 1.02/(tandeg($hnow+10.3/($hnow+5.11)))/60;
207 if ( $sun0_moon1 == 1 ) {
208 ($alpha1, $delta1, $distance, $ifrac)=get_moon_alpha_delta($tt1);
209 ($alpha2, $delta2, $distance, $ifrac)=get_moon_alpha_delta($tt2);
210 ($alpha3, $delta3, $distance, $ifrac)=get_moon_alpha_delta($tt3);
211 ($alphanow, $deltanow, $distancenow, $ifracnow)=get_moon_alpha_delta($ttnow);
212 $h0=0.7275*$r2d*asin(6378.14/$distancenow)-34./60.;
213 $H=$thetanow-$lon-$alphanow;
214 $H=reduce_angle_to_360($H);
215 ($aznow,$hnow)=get_az_el($H,$deltanow,$lat);
216 $hnow=$hnow-$r2d*asin(sin(6378.14/$distancenow)*cosdeg($hnow))+
217 1.02/(tandeg($hnow+10.3/($hnow+5.11)))/60;
220 $arg = (sindeg($h0)-sindeg($lat)*sindeg($delta2))/(cosdeg($lat)*cosdeg($delta2));
221 if ( abs($arg) > 1. ) { # either up all day or down all day
222 $norise = 1; # leave it to the user to examine
223 $noset = 1; # the elevation angle (or look outside!)
224 } # to figure out which.
226 $H0 = acos($arg)*$r2d;
227 my $aa=$alpha2-$alpha1;
228 my $ba=$alpha3-$alpha2;
229 $aa=$aa+360 if ($aa < -180);
230 $aa=$aa-360 if ($aa > 180);
231 $ba=$ba+360 if ($ba < -180);
232 $ba=$ba-360 if ($ba > 180);
235 my $ad=$delta2-$delta1;
236 my $bd=$delta3-$delta2;
237 $ad=$ad+360 if ($ad < -180);
238 $ad=$ad-360 if ($ad > 180);
239 $bd=$bd+360 if ($bd < -180);
240 $bd=$bd-360 if ($bd > 180);
243 $m0 = ($alpha2 + $lon - $theta0)/360.;
244 $m0=$m0+1 if( $m0 < 0 );
245 $m0=$m0-1 if( $m0 > 1 );
246 for ($i=1; $i<=2; $i++) {
247 $theta = $theta0+360.985647*$m0;
248 $alpha=$alpha2+$m0*($aa+$ba+$m0*$ca)/2;
249 $delta=$delta2+$m0*($ad+$bd+$m0*$cd)/2;
250 $H=$theta-$lon-$alpha;
251 $H=reduce_angle_to_360($H);
252 $H=$H-360 if ($H > 180);
253 ($az,$h)=get_az_el($H,$delta,$lat);
256 $m0=$m0+1 if( $m0 < 0 );
257 $m0=$m0-1 if( $m0 > 1 );
262 $m1 = $m0 - $H0/360.;
263 $m1=$m1+1 if( $m1 < 0 );
264 $m1=$m1-1 if( $m1 > 1 );
265 for ($i=1; $i<=2; $i++) {
266 $theta = $theta0+360.985647*$m1;
267 $alpha=$alpha2+$m1*($aa+$ba+$m1*$ca)/2;
268 $delta=$delta2+$m1*($ad+$bd+$m1*$cd)/2;
269 $H=$theta-$lon-$alpha;
270 $H=reduce_angle_to_360($H);
271 ($az,$h)=get_az_el($H,$delta,$lat);
272 $corr=($h-$h0)/(360*(cosdeg($delta)*cosdeg($lat)*sindeg($H)));
274 $norise=1 if( $m1 < 0 || $m1 > 1);
280 $risemin=($m1*24-int($m1*24))*60+0.5;
281 if ( $risemin >= 60 ) {
282 $risemin=$risemin-60;
285 $risetime=sprintf("%02d:%02dZ",$risehr,$risemin);
291 $m2 = $m0 + $H0/360.;
292 $m2=$m2+1 if( $m2 < 0 );
293 $m2=$m2-1 if( $m2 > 1 );
294 for ($i=1; $i<=2; $i++) {
295 $theta = $theta0+360.985647*$m2;
296 $alpha=$alpha2+$m2*($aa+$ba+$m2*$ca)/2;
297 $delta=$delta2+$m2*($ad+$bd+$m2*$cd)/2;
298 $H=$theta-$lon-$alpha;
299 $H=reduce_angle_to_360($H);
300 ($az,$h)=get_az_el($H,$delta,$lat);
301 $corr=($h-$h0)/(360*(cosdeg($delta)*cosdeg($lat)*sindeg($H)));
303 $noset=1 if( $m2 < 0 || $m2 > 1);
309 $setmin=($m2*24-int($m2*24))*60+0.5;
310 if ( $setmin >= 60 ) {
314 $settime=sprintf("%02d:%02dZ",$sethr,$setmin);
320 if ( $sun0_moon1 == 0 ) {
321 return (sprintf("%s", $risetime), sprintf("%s",$settime),$aznow+180,$hnow);
323 if ( $sun0_moon1 == 1 ) {
324 return (sprintf("%s", $risetime), sprintf("%s",$settime),
325 $aznow+180,$hnow, -40*log10($distance/385000), $ifracnow );
328 sub get_moon_alpha_delta
331 # Calculate the moon's right ascension and declination
333 # As of October 2001, also calculate the illuminated fraction of the
334 # moon's disk... (why not?)
338 my $Lp=218.3164477+481267.88123421*$tt-
339 0.0015786*$tt*$tt+$tt*$tt*$tt/538841-$tt*$tt*$tt*$tt/65194000;
340 $Lp=reduce_angle_to_360($Lp);
342 my $D = 297.8501921+445267.1114034*$tt-0.0018819*$tt*$tt+
343 $tt*$tt*$tt/545868.-$tt*$tt*$tt*$tt/113065000.;
344 $D=reduce_angle_to_360($D);
346 my $M = 357.5291092 + 35999.0502909*$tt-0.0001536*$tt*$tt+
347 $tt*$tt*$tt/24490000.;
348 $M=reduce_angle_to_360($M);
350 my $Mp = 134.9633964 + 477198.8675055*$tt+0.0087414*$tt*$tt+
351 $tt*$tt*$tt/69699-$tt*$tt*$tt*$tt/14712000;
352 $Mp=reduce_angle_to_360($Mp);
354 my $F = 93.2720950 + 483202.0175233*$tt - 0.0036539*$tt*$tt-
355 $tt*$tt*$tt/3526000 + $tt*$tt*$tt*$tt/863310000;
356 $F=reduce_angle_to_360($F);
358 my $A1 = 119.75 + 131.849 * $tt;
359 $A1=reduce_angle_to_360($A1);
361 my $A2 = 53.09 + 479264.290 * $tt;
362 $A2=reduce_angle_to_360($A2);
364 my $A3 = 313.45 + 481266.484 * $tt;
365 $A3=reduce_angle_to_360($A3);
367 my $E = 1 - 0.002516 * $tt - 0.0000074 * $tt * $tt;
369 my $Sl= 6288774*sindeg( 1 * $Mp ) +
370 1274027*sindeg(2 * $D + -1 * $Mp ) +
371 658314 *sindeg(2 * $D ) +
372 213618 *sindeg( 2 * $Mp ) +
373 -185116 *sindeg( 1 * $M )*$E +
374 -114332 *sindeg( 2 * $F ) +
375 58793 *sindeg(2 * $D + -2 * $Mp ) +
376 57066 *sindeg(2 * $D - 1 * $M -1 * $Mp )*$E +
377 53322 *sindeg(2 * $D + 1 * $Mp ) +
378 45758 *sindeg(2 * $D - 1 * $M )*$E +
379 -40923 *sindeg( + 1 * $M -1 * $Mp )*$E +
380 -34720 *sindeg(1 * $D ) +
381 -30383 *sindeg( + 1 * $M + 1 * $Mp )*$E +
382 15327 *sindeg(2 * $D + -2 * $F ) +
383 -12528 *sindeg( 1 * $Mp + 2 * $F ) +
384 10980 *sindeg( 1 * $Mp - 2 * $F ) +
385 10675 *sindeg(4 * $D + -1 * $Mp ) +
386 10034 *sindeg( 3 * $Mp ) +
387 8548 *sindeg(4 * $D + 0 * $M - 2 * $Mp + 0 * $F ) +
388 -7888 *sindeg(2 * $D + 1 * $M - 1 * $Mp + 0 * $F )*$E +
389 -6766 *sindeg(2 * $D + 1 * $M + 0 * $Mp + 0 * $F )*$E +
390 -5163 *sindeg(1 * $D + 0 * $M - 1 * $Mp + 0 * $F ) +
391 4987 *sindeg(1 * $D + 1 * $M + 0 * $Mp + 0 * $F )*$E +
392 4036 *sindeg(2 * $D - 1 * $M + 1 * $Mp + 0 * $F )*$E +
393 3994 *sindeg(2 * $D + 0 * $M + 2 * $Mp + 0 * $F ) +
394 3861 *sindeg(4 * $D + 0 * $M + 0 * $Mp + 0 * $F ) +
395 3665 *sindeg(2 * $D + 0 * $M - 3 * $Mp + 0 * $F ) +
396 -2689 *sindeg(0 * $D + 1 * $M - 2 * $Mp + 0 * $F )*$E +
397 -2602 *sindeg(2 * $D + 0 * $M - 1 * $Mp + 2 * $F ) +
398 2390 *sindeg(2 * $D - 1 * $M - 2 * $Mp + 0 * $F )*$E +
399 -2348 *sindeg(1 * $D + 0 * $M + 1 * $Mp + 0 * $F ) +
400 2236 *sindeg(2 * $D - 2 * $M + 0 * $Mp + 0 * $F )*$E*$E +
401 -2120 *sindeg(0 * $D + 1 * $M + 2 * $Mp + 0 * $F )*$E +
402 -2069 *sindeg(0 * $D + 2 * $M + 0 * $Mp + 0 * $F )*$E*$E +
403 2048 *sindeg(2 * $D - 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
404 -1773 *sindeg(2 * $D + 0 * $M + 1 * $Mp - 2 * $F ) +
405 -1595 *sindeg(2 * $D + 0 * $M + 0 * $Mp + 2 * $F ) +
406 1215 *sindeg(4 * $D - 1 * $M - 1 * $Mp + 0 * $F )*$E +
407 -1110 *sindeg(0 * $D + 0 * $M + 2 * $Mp + 2 * $F ) +
408 -892 *sindeg(3 * $D + 0 * $M - 1 * $Mp + 0 * $F ) +
409 -810 *sindeg(2 * $D + 1 * $M + 1 * $Mp + 0 * $F )*$E +
410 759 *sindeg(4 * $D - 1 * $M - 2 * $Mp + 0 * $F )*$E +
411 -713 *sindeg(0 * $D + 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
412 -700 *sindeg(2 * $D + 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
413 691 *sindeg(2 * $D + 1 * $M - 2 * $Mp + 0 * $F )*$E +
414 596 *sindeg(2 * $D - 1 * $M + 0 * $Mp - 2 * $F )*$E +
415 549 *sindeg(4 * $D + 0 * $M + 1 * $Mp + 0 * $F ) +
416 537 *sindeg(0 * $D + 0 * $M + 4 * $Mp + 0 * $F ) +
417 520 *sindeg(4 * $D - 1 * $M + 0 * $Mp + 0 * $F )*$E +
418 -487 *sindeg(1 * $D + 0 * $M - 2 * $Mp + 0 * $F ) +
419 -399 *sindeg(2 * $D + 1 * $M + 0 * $Mp - 2 * $F )*$E +
420 -381 *sindeg(0 * $D + 0 * $M + 2 * $Mp - 2 * $F ) +
421 351 *sindeg(1 * $D + 1 * $M + 1 * $Mp + 0 * $F )*$E +
422 -340 *sindeg(3 * $D + 0 * $M - 2 * $Mp + 0 * $F ) +
423 330 *sindeg(4 * $D + 0 * $M - 3 * $Mp + 0 * $F ) +
424 327 *sindeg(2 * $D - 1 * $M + 2 * $Mp + 0 * $F )*$E +
425 -323 *sindeg(0 * $D + 2 * $M + 1 * $Mp + 0 * $F )*$E*$E +
426 299 *sindeg(1 * $D + 1 * $M - 1 * $Mp + 0 * $F )*$E +
427 294 *sindeg(2 * $D + 0 * $M + 3 * $Mp + 0 * $F ) +
428 3958 *sindeg($A1) + 1962*sindeg($Lp - $F) + 318*sindeg($A2);
430 my $Sr=-20905355 *cosdeg( 1 * $Mp ) +
431 -3699111 *cosdeg(2 * $D + -1 * $Mp ) +
432 -2955968 *cosdeg(2 * $D ) +
433 -569925 *cosdeg( 2 * $Mp ) +
434 48888 *cosdeg( 1 * $M )*$E +
435 -3149 *cosdeg( 2 * $F ) +
436 246158 *cosdeg(2 * $D + -2 * $Mp ) +
437 -152138 *cosdeg(2 * $D - 1 * $M -1 * $Mp )*$E +
438 -170733 *cosdeg(2 * $D + 1 * $Mp ) +
439 -204586 *cosdeg(2 * $D - 1 * $M )*$E +
440 -129620 *cosdeg( + 1 * $M -1 * $Mp )*$E +
441 108743 *cosdeg(1 * $D ) +
442 104755 *cosdeg( + 1 * $M + 1 * $Mp )*$E +
443 10321 *cosdeg(2 * $D + -2 * $F ) +
444 79661 *cosdeg( 1 * $Mp - 2 * $F ) +
445 -34782 *cosdeg(4 * $D + -1 * $Mp ) +
446 -23210 *cosdeg( 3 * $Mp ) +
447 -21636 *cosdeg(4 * $D + 0 * $M - 2 * $Mp + 0 * $F ) +
448 24208 *cosdeg(2 * $D + 1 * $M - 1 * $Mp + 0 * $F )*$E +
449 30824 *cosdeg(2 * $D + 1 * $M + 0 * $Mp + 0 * $F )*$E +
450 -8379 *cosdeg(1 * $D + 0 * $M - 1 * $Mp + 0 * $F ) +
451 -16675 *cosdeg(1 * $D + 1 * $M + 0 * $Mp + 0 * $F )*$E +
452 -12831 *cosdeg(2 * $D - 1 * $M + 1 * $Mp + 0 * $F )*$E +
453 -10445 *cosdeg(2 * $D + 0 * $M + 2 * $Mp + 0 * $F ) +
454 -11650 *cosdeg(4 * $D + 0 * $M + 0 * $Mp + 0 * $F ) +
455 14403 *cosdeg(2 * $D + 0 * $M - 3 * $Mp + 0 * $F ) +
456 -7003 *cosdeg(0 * $D + 1 * $M - 2 * $Mp + 0 * $F )*$E +
457 10056 *cosdeg(2 * $D - 1 * $M - 2 * $Mp + 0 * $F )*$E +
458 6322 *cosdeg(1 * $D + 0 * $M + 1 * $Mp + 0 * $F ) +
459 -9884 *cosdeg(2 * $D - 2 * $M + 0 * $Mp + 0 * $F )*$E*$E +
460 5751 *cosdeg(0 * $D + 1 * $M + 2 * $Mp + 0 * $F )*$E +
461 -4950 *cosdeg(2 * $D - 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
462 4130 *cosdeg(2 * $D + 0 * $M + 1 * $Mp - 2 * $F )+
463 -3958 *cosdeg(4 * $D - 1 * $M - 1 * $Mp + 0 * $F )*$E +
464 3258 *cosdeg(3 * $D + 0 * $M - 1 * $Mp + 0 * $F )+
465 2616 *cosdeg(2 * $D + 1 * $M + 1 * $Mp + 0 * $F )*$E +
466 -1897 *cosdeg(4 * $D - 1 * $M - 2 * $Mp + 0 * $F )*$E +
467 -2117 *cosdeg(0 * $D + 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
468 2354 *cosdeg(2 * $D + 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
469 -1423 *cosdeg(4 * $D + 0 * $M + 1 * $Mp + 0 * $F )+
470 -1117 *cosdeg(0 * $D + 0 * $M + 4 * $Mp + 0 * $F )+
471 -1571 *cosdeg(4 * $D - 1 * $M + 0 * $Mp + 0 * $F )*$E +
472 -1739 *cosdeg(1 * $D + 0 * $M - 2 * $Mp + 0 * $F )+
473 -4421 *cosdeg(0 * $D + 0 * $M + 2 * $Mp - 2 * $F )+
474 1165 *cosdeg(0 * $D + 2 * $M + 1 * $Mp + 0 * $F )*$E*$E +
475 8752 *cosdeg(2 * $D + 0 * $M - 1 * $Mp - 2 * $F );
477 my $Sb= 5128122 *sindeg( 1 * $F ) +
478 280602 *sindeg( 1 * $Mp + 1 * $F ) +
479 277693 *sindeg( 1 * $Mp - 1 * $F ) +
480 173237 *sindeg(2 * $D - 1 * $F ) +
481 55413 *sindeg(2 * $D -1 * $Mp + 1 * $F ) +
482 46271 *sindeg(2 * $D + -1 * $Mp - 1 * $F ) +
483 32573 *sindeg(2 * $D + 1 * $F ) +
484 17198 *sindeg( 2 * $Mp + 1 * $F )+
485 9266 *sindeg(2 * $D + 0 * $M + 1 * $Mp - 1 * $F ) +
486 8822 *sindeg(0 * $D + 0 * $M + 2 * $Mp - 1 * $F ) +
487 8216 *sindeg(2 * $D - 1 * $M + 0 * $Mp - 1 * $F )*$E +
488 4324 *sindeg(2 * $D + 0 * $M - 2 * $Mp - 1 * $F ) +
489 4200 *sindeg(2 * $D + 0 * $M + 1 * $Mp + 1 * $F ) +
490 -3359 *sindeg(2 * $D + 1 * $M + 0 * $Mp - 1 * $F )*$E +
491 2463 *sindeg(2 * $D - 1 * $M - 1 * $Mp + 1 * $F )*$E +
492 2211 *sindeg(2 * $D - 1 * $M + 0 * $Mp + 1 * $F )*$E +
493 2065 *sindeg(2 * $D - 1 * $M - 1 * $Mp - 1 * $F )*$E +
494 -1870 *sindeg(0 * $D + 1 * $M - 1 * $Mp - 1 * $F )*$E +
495 1828 *sindeg(4 * $D + 0 * $M - 1 * $Mp - 1 * $F ) +
496 -1794 *sindeg(0 * $D + 1 * $M + 0 * $Mp + 1 * $F )*$E +
497 -1749 *sindeg(0 * $D + 0 * $M + 0 * $Mp + 3 * $F ) +
498 -1565 *sindeg(0 * $D + 1 * $M - 1 * $Mp + 1 * $F )*$E +
499 -1491 *sindeg(1 * $D + 0 * $M + 0 * $Mp + 1 * $F ) +
500 -1475 *sindeg(0 * $D + 1 * $M + 1 * $Mp + 1 * $F )*$E +
501 -1410 *sindeg(0 * $D + 1 * $M + 1 * $Mp - 1 * $F )*$E +
502 -1344 *sindeg(0 * $D + 1 * $M + 0 * $Mp - 1 * $F )*$E +
503 -1335 *sindeg(1 * $D + 0 * $M + 0 * $Mp - 1 * $F ) +
504 1107 *sindeg(0 * $D + 0 * $M + 3 * $Mp + 1 * $F ) +
505 1021 *sindeg(4 * $D + 0 * $M + 0 * $Mp - 1 * $F ) +
506 833 *sindeg(4 * $D + 0 * $M - 1 * $Mp + 1 * $F ) +
507 777 *sindeg(0 * $D + 0 * $M + 1 * $Mp - 3 * $F ) +
508 671 *sindeg(4 * $D + 0 * $M - 2 * $Mp + 1 * $F ) +
509 607 *sindeg(2 * $D + 0 * $M + 0 * $Mp - 3 * $F ) +
510 596 *sindeg(2 * $D + 0 * $M + 2 * $Mp - 1 * $F ) +
511 491 *sindeg(2 * $D - 1 * $M + 1 * $Mp - 1 * $F )*$E +
512 -451 *sindeg(2 * $D + 0 * $M - 2 * $Mp + 1 * $F ) +
513 439 *sindeg(0 * $D + 0 * $M + 3 * $Mp - 1 * $F ) +
514 422 *sindeg(2 * $D + 0 * $M + 2 * $Mp + 1 * $F ) +
515 421 *sindeg(2 * $D + 0 * $M - 3 * $Mp - 1 * $F ) +
516 -366 *sindeg(2 * $D + 1 * $M - 1 * $Mp + 1 * $F )*$E +
517 -351 *sindeg(2 * $D + 1 * $M + 0 * $Mp + 1 * $F )*$E +
518 331 *sindeg(4 * $D + 0 * $M + 0 * $Mp + 1 * $F ) +
519 315 *sindeg(2 * $D - 1 * $M + 1 * $Mp + 1 * $F )*$E +
520 302 *sindeg(2 * $D - 2 * $M + 0 * $Mp - 1 * $F )*$E*$E +
521 -283 *sindeg(0 * $D + 0 * $M + 1 * $Mp + 3 * $F ) +
522 -229 *sindeg(2 * $D + 1 * $M + 1 * $Mp - 1 * $F )*$E +
523 223 *sindeg(1 * $D + 1 * $M + 0 * $Mp - 1 * $F )*$E +
524 223 *sindeg(1 * $D + 1 * $M + 0 * $Mp + 1 * $F )*$E +
525 -220 *sindeg(0 * $D + 1 * $M - 2 * $Mp - 1 * $F )*$E +
526 -220 *sindeg(2 * $D + 1 * $M - 1 * $Mp - 1 * $F )*$E +
527 -185 *sindeg(1 * $D + 0 * $M + 1 * $Mp + 1 * $F ) +
528 181 *sindeg(2 * $D - 1 * $M - 2 * $Mp - 1 * $F )*$E +
529 -177 *sindeg(0 * $D + 1 * $M + 2 * $Mp + 1 * $F )*$E +
530 176 *sindeg(4 * $D + 0 * $M - 2 * $Mp - 1 * $F ) +
531 166 *sindeg(4 * $D - 1 * $M - 1 * $Mp - 1 * $F )*$E +
532 -164 *sindeg(1 * $D + 0 * $M + 1 * $Mp - 1 * $F ) +
533 132 *sindeg(4 * $D + 0 * $M + 1 * $Mp - 1 * $F ) +
534 -119 *sindeg(1 * $D + 0 * $M - 1 * $Mp - 1 * $F ) +
535 115 *sindeg(4 * $D - 1 * $M + 0 * $Mp - 1 * $F )*$E +
536 107 *sindeg(2 * $D - 2 * $M + 0 * $Mp + 1 * $F )*$E*$E
537 -2235 *sindeg($Lp) + 382*sindeg($A3) +
538 175 *sindeg($A1-$F) + 175*sindeg($A1+$F) +
539 127 *sindeg($Lp-$Mp) - 115*sindeg($Lp+$Mp);
541 my $lambda=$Lp+$Sl/1000000.;
543 my $beta=$Sb/1000000.;
545 my $distance=385000.56 + $Sr/1000.;
547 my $epsilon = 23+26./60.+21.448/(60.*60.);
549 my $alpha=atan2(cosdeg($epsilon)*sindeg($lambda)-tandeg($beta)*sindeg($epsilon),cosdeg($lambda))*$r2d;
550 $alpha = reduce_angle_to_360($alpha);
552 my $delta=asin(cosdeg($beta)*sindeg($epsilon)*sindeg($lambda)+sindeg($beta)*cosdeg($epsilon))*$r2d;
553 $delta = reduce_angle_to_360($delta);
555 # $phase will be the "moon phase angle" from p. 346 of Meeus' book...
556 my $phase=180.0 - $D - 6.289 *sindeg($Mp)
558 - 1.274 *sindeg(2.*$D - $Mp)
559 - 0.658 *sindeg(2.*$D)
560 - 0.214 *sindeg(2.*$Mp)
563 # $illum_frac is the fraction of the disk that is illuminated, and will be
564 # zero at new moon and 1.0 at full moon.
566 my $illum_frac = (1.0 + cosdeg( $phase ))/2.;
568 return ($alpha,$delta,$distance,$illum_frac);
571 sub get_sun_alpha_delta
574 # Calculate Sun's right ascension and declination
578 my $L0 = 280.46646+36000.76983*$tt+0.0003032*($tt^2);
579 $L0=reduce_angle_to_360($L0);
581 my $M = 357.52911 + 35999.05029*$tt-0.0001537*($tt^2);
582 $M=reduce_angle_to_360($M);
584 my $C = (1.914602 - 0.004817*$tt-0.000014*($tt^2))*sindeg($M) +
585 (0.019993 - 0.000101*$tt)*sindeg(2*$M) +
586 0.000289*sindeg(3*$M);
588 my $OMEGA = 125.04 - 1934.136*$tt;
590 my $lambda=$L0+$C-0.00569-0.00478*sindeg($OMEGA);
592 my $epsilon = 23+26./60.+21.448/(60.*60.);
594 my $alpha=atan2(cosdeg($epsilon)*sindeg($lambda),cosdeg($lambda))*$r2d;
595 $alpha = reduce_angle_to_360($alpha);
597 my $delta=asin(sin($epsilon*$d2r)*sin($lambda*$d2r))*$r2d;
598 $delta = reduce_angle_to_360($delta);
600 return ($alpha,$delta);
602 sub get_satellite_pos
605 # This code was translated more-or-less directly from the Pascal
606 # routines contained in a report compiled by TS Kelso and based on:
607 # Spacetrack Report No. 3
608 # "Models for Propagation of NORAD Element Sets"
609 # Felix R. Hoots, Ronald L Roehrich
612 # See TS Kelso's web site for more details...
613 # Only the SGP propagation model is implemented.
615 # Steve Franke, K9AN. 9 Dec 1999.
619 #1 25338U 98030A 99341.00000000 +.00000376 +00000-0 +18612-3 0 05978
620 #2 25338 098.6601 008.2003 0011401 112.4684 042.5140 14.23047277081382
622 #1 21639U 91054B 99341.34471854 .00000095 00000-0 10000-3 0 4928
623 #2 21639 1.5957 88.4884 0003028 161.6582 135.4323 1.00277774 30562
625 #1 20439U 90005D 99341.14501399 +.00000343 +00000-0 +14841-3 0 02859
626 #2 20439 098.4690 055.0032 0012163 066.4615 293.7842 14.30320285515297
628 #Temporary keps database...
635 my $sat_ref = $keps{$satname};
636 #printf("$jtime $lat $lon $alt Satellite name = $satname\n");
643 my $xke=.743669161e-1;
647 my $ck2=.5*$xj2*$ae**2;
648 my $ck4=-.375*$xj4*$ae**4;
649 my $qoms2t=(($qo-$so)*$ae/$xkmper)**4;
650 my $s=$ae*(1+$so/$xkmper);
652 my $epoch = $sat_ref ->{epoch};
653 #printf("epoch = %10.2f\n",$epoch);
654 my $jt_epoch=Julian_Date_of_Epoch($epoch);
655 #printf("JT for epoch = %17.12f\n",$jt_epoch);
656 my $tsince=($jtime-$jt_epoch)*24*60;
657 #printf("tsince (min) = %17.12f\n",$tsince);
659 my $mm1 = $sat_ref ->{mm1};
660 my $mm2 = $sat_ref ->{mm2};
661 my $bstar=$sat_ref ->{bstar}; # drag term for sgp4 model
662 my $inclination=$sat_ref->{inclination}; # inclination in degrees
663 my $raan=$sat_ref->{raan}; # right ascension of ascending node in degs
664 my $eccentricity=$sat_ref ->{eccentricity}; # eccentricity - dimensionless
665 my $omegao=$sat_ref ->{argperigee}; # argument of perigee in degs
666 my $xmo=$sat_ref ->{meananomaly}; # mean anomaly in degrees
667 my $xno=$sat_ref ->{meanmotion}; # mean motion in revs per day
669 #printf("%10.6f %10.6f %10.6f %10.6f %10.6f %10.6f %10.6f %10.6f %10.6f\n",
670 #$mm1,$mm2,$bstar,$inclination,$raan,$eccentricity,$omegao,$xmo,$xno);
672 $omegao=$omegao*$d2r;
674 $inclination=$inclination*$d2r;
675 my $temp=2*$pi/$xmnpda/$xmnpda;
676 $xno=$xno*$temp*$xmnpda;
678 $mm2=$mm2*$temp/$xmnpda;
683 my $c4=$xj3*$ae**3/(4*$ck2);
684 my $cosio=cos($inclination);
685 my $sinio=sin($inclination);
686 my $a1=($xke/$xno)**(2./3.);
687 my $d1=$c1/$a1/$a1*(3*$cosio*$cosio-1)/(1-$eccentricity*$eccentricity)**1.5;
688 my $ao=$a1*(1-1./3.*$d1-$d1*$d1-134./81.*$d1*$d1*$d1);
689 my $po=$ao*(1-$eccentricity*$eccentricity);
690 $qo=$ao*(1-$eccentricity);
691 my $xlo=$xmo+$omegao+$raan;
692 my $d10=$c3*$sinio*$sinio;
693 my $d20=$c2*(7.*$cosio*$cosio-1);
696 my $po2no=$xno/($po*$po);
697 my $omgdt=$c1*$po2no*(5.*$cosio*$cosio-1);
698 my $xnodot=-2.*$d30*$po2no;
699 my $c5=0.5*$c4*$sinio*(3+5*$cosio)/(1+$cosio);
702 my $a=$xno+(2*$mm1+3*$mm2*$tsince)*$tsince;
703 $a=$ao*($xno/$a)**(2./3.);
705 $e =1-$qo/$a if ($a > $qo);
707 my $xnodes=$raan+$xnodot*$tsince;
708 my $omgas=$omegao+$omgdt*$tsince;
709 my $xls=mod2p($xlo+($xno+$omgdt+$xnodot+($mm1+$mm2*$tsince)*$tsince)*$tsince);
711 my $axnsl=$e*cos($omgas);
712 my $aynsl=$e*sin($omgas)-$c6/$p;
713 my $xl=mod2p($xls-$c5/$p*$axnsl);
715 my $u=mod2p($xl-$xnodes);
721 for ($item3=0; abs($tem5) >= 1e-6 && $item3 < 10; $item3++ )
725 $tem5=1-$coseo1*$axnsl-$sineo1*$aynsl;
726 $tem5=($u-$aynsl*$coseo1+$axnsl*$sineo1-$eo1)/$tem5;
728 $tem5=$tem2/$tem5 if ($tem2 > 1);
734 my $ecose=$axnsl*$coseo1+$aynsl*$sineo1;
735 my $esine=$axnsl*$sineo1-$aynsl*$coseo1;
736 my $el2=$axnsl*$axnsl+$aynsl*$aynsl;
740 my $rdot=$xke*sqrt($a)/$r*$esine;
741 my $rvdot=$xke*sqrt($pl)/$r;
742 $temp=$esine/(1+sqrt(1-$el2));
743 my $sinu=$a/$r*($sineo1-$aynsl-$axnsl*$temp);
744 my $cosu=$a/$r*($coseo1-$axnsl+$aynsl*$temp);
745 my $su=atan2($sinu,$cosu);
747 my $sin2u=($cosu+$cosu)*$sinu;
748 my $cos2u=1-2*$sinu*$sinu;
749 my $rk=$r+$d10/$pl*$cos2u;
750 my $uk=$su-$d20/$pl2*$sin2u;
751 my $xnodek=$xnodes+$d30*$sin2u/$pl2;
752 my $xinck=$inclination+$d40/$pl2*$cos2u;
756 my $sinnok=sin($xnodek);
757 my $cosnok=cos($xnodek);
758 my $sinik=sin($xinck);
759 my $cosik=cos($xinck);
760 my $xmx=-$sinnok*$cosik;
761 my $xmy=$cosnok*$cosik;
762 my $ux=$xmx*$sinuk+$cosnok*$cosuk;
763 my $uy=$xmy*$sinuk+$sinnok*$cosuk;
764 my $uz=$sinik*$sinuk;
765 my $vx=$xmx*$cosuk-$cosnok*$sinuk;
766 my $vy=$xmy*$cosuk-$sinnok*$sinuk;
767 my $vz=$sinik*$cosuk;
769 my $x=$rk*$ux*$xkmper/$ae;
770 my $y=$rk*$uy*$xkmper/$ae;
771 my $z=$rk*$uz*$xkmper/$ae;
775 $xdot=($rvdot*$vx+$xdot)*$xkmper/$ae*$xmnpda/86400;
776 $ydot=($rvdot*$vy+$ydot)*$xkmper/$ae*$xmnpda/86400;
777 $zdot=($rvdot*$vz+$zdot)*$xkmper/$ae*$xmnpda/86400;
778 #printf("x=%17.6f y=%17.6f z=%17.6f \n",$x,$y,$z);
779 #printf("xdot=%17.6f ydot=%17.6f zdot=%17.6f \n",$xdot,$ydot,$zdot);
780 my ($sat_lat,$sat_lon,$sat_alt,$sat_theta)=Calculate_LatLonAlt($x,$y,$z,$jtime);
781 my ($az, $el, $distance) = Calculate_Obs($x,$y,$z,$sat_theta,$xdot,$ydot,$zdot,$jtime,$lat,$lon,$alt);
782 return ($sat_lat,$sat_lon,$sat_alt,$az,$el,$distance);
785 sub Calculate_LatLonAlt
788 # convert from ECI coordinates to latitude, longitude and altitude.
795 my $theta=atan2($y,$x);
796 my $lon=mod2p($theta-ThetaG_JD($time));
797 my $range=sqrt($x**2+$y**2);
798 my $f=1/298.26; # earth flattening constant
801 my $lat=atan2($z,$range);
806 $c=1/sqrt(1-$e2*sin($phi)**2);
807 $lat=atan2($z+$xkmper*$c*$e2*sin($phi),$range);
808 } until abs($lat-$phi) < 1e-10;
809 my $alt=$range/cos($lat)-$xkmper*$c;
810 return ($lat,$lon,$alt,$theta); # radians and kilometers
814 sub Calculate_User_PosVel
816 # change from lat/lon/alt/time coordinates to earth centered inertial (ECI)
817 # position and local hour angle.
822 my $theta=mod2p(ThetaG_JD($time)+$lon);
823 my $omega_E=1.00273790934; # earth rotations per sidereal day
825 my $mfactor=2*$pi*$omega_E/$secday;
826 my $f=1/298.26; # earth flattening constant
828 my $c=1/sqrt(1+$f*($f-2)*sin($lat)**2);
829 my $s=(1-$f)*(1-$f)*$c;
830 my $achcp=($xkmper*$c+$alt)*cos($lat);
831 my $x_user=$achcp*cos($theta);
832 my $y_user=$achcp*sin($theta);
833 my $z_user=($xkmper*$s+$alt)*sin($lat);
834 my $xdot_user=-$mfactor*$y_user;
835 my $ydot_user=$mfactor*$x_user;
837 return ($x_user,$y_user,$z_user,$xdot_user,$ydot_user,$zdot_user,$theta);
841 # calculate the azimuth/el of an object as viewed from observers position
842 # with object position given in ECI coordinates and observer in lat/long/alt.
844 # inputs: object ECI position vector (km)
845 # object velocity vector (km/s)
847 # observer lat,lon,altitude (km)
860 my ($x_o,$y_o,$z_o,$xdot_o,$ydot_o,$zdot_o,$theta)=
861 Calculate_User_PosVel($lat,$lon,$alt,$time);
865 my $xxdot=$xdot-$xdot_o;
866 my $yydot=$ydot-$ydot_o;
867 my $zzdot=$zdot-$zdot_o;
869 my $sin_lat=sin($lat);
870 my $cos_lat=cos($lat);
871 my $sin_theta=sin($theta);
872 my $cos_theta=cos($theta);
874 my $top_s=$sin_lat*$cos_theta*$xx
875 + $sin_lat*$sin_theta*$yy
878 my $top_e=-$sin_theta*$xx
881 my $top_z=$cos_lat*$cos_theta*$xx
882 + $cos_lat*$sin_theta*$yy
885 my $az=atan(-$top_e/$top_s);
886 $az=$az+$pi if ( $top_s > 0 );
887 $az=$az+2*$pi if ( $az < 0 );
889 my $range=sqrt($xx*$xx+$yy*$yy+$zz*$zz);
890 my $el=asin($top_z/$range);
891 return ($az, $el, $range);
894 sub Calendar_date_and_time_from_JD
896 my ($jd,$z,$frac,$alpha,$a,$b,$c,$d,$e,$dom,$yr,$mon,$day,$hr,$min);
901 $alpha = int( ($z-1867216.5)/36524.25 );
902 $a=$z + 1 + $alpha - int($alpha/4);
903 $a=$z if( $z < 2299161 );
905 $c=int(($b-122.1)/365.25);
907 $e=int(($b-$d)/30.6001);
908 $dom=$b-$d-int(30.6001*$e)+$frac;
910 $mon=$e-1 if( $e < 14 );
911 $mon=$e-13 if( $e == 14 || $e == 15 );
912 $yr = $c-4716 if( $mon > 2 );
913 $yr = $c-4715 if( $mon == 1 || $mon == 2 );
915 $min= int(($frac*24 - $hr)*60+0.5);
916 if ($min == 60) { # this may well prove inadequate DJK
920 return ($yr,$mon,$day,$hr,$min);