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 # 2005/02/25 add calculation of civil dawn and dusk, defined to be times
22 # when solar zenith angle is 96 degrees.
23 # 2001/12/16 Fixed Julian_Date_of_Epoch and now I actually use it...
24 # 2001/09/15 some changes to take care of cases where the object
25 # doesn't rise or set on a given day...
32 @EXPORT = qw($pi $d2r $r2d );
42 use POSIX qw(:math_h);
44 # reload the keps data
48 my $s = readfilestr("$main::root/local/Keps.pm");
63 $year=$year-1 if( $month <= 2 );
64 $month=$month+12 if( $month <= 2);
66 $julianday = int(365.25*($year+4716)+int(30.6001*($month+1)))+$day-13-1524.5;
69 sub Julian_Date_of_Epoch
72 my $year=int($epoch/1000);
73 my $day=$epoch-$year*1000;
80 my $Julian_Date_of_Epoch=Julian_Date_of_Year($year)+$day;
81 return $Julian_Date_of_Epoch;
84 sub Julian_Date_of_Year
90 my $Julian_Date_of_Year=int(365.25*$year)+int(30.6001*14)+
92 return $Julian_Date_of_Year;
97 my $omega_E=1.00273790934; # earth rotations per sidereal day
99 my $UT=($jd+0.5)-int($jd+0.5);
101 my $TU=($jd-2451545.0)/36525;
102 my $GMST=24110.54841+$TU*(8640184.812866+$TU*(0.093104-$TU*6.2e-6));
103 my $thetag_jd=mod2p(2*$pi*($GMST/$secday+$omega_E*$UT));
107 sub reduce_angle_to_360
111 $angle=$angle-int($angle/360)*360;
112 $angle=$angle+360 if( $angle < 0 );
120 $angle=$angle-int($angle/$twopi)*$twopi;
121 $angle=$angle+$twopi if( $angle < 0 );
126 my $angle_in_degrees = shift;
128 return sin($angle_in_degrees*$d2r);
132 my $angle_in_degrees = shift;
134 return cos($angle_in_degrees*$d2r);
138 my $angle_in_degrees = shift;
140 return tan($angle_in_degrees*$d2r);
148 my $az=$r2d * atan2( sindeg($H), cosdeg($H)*sindeg($lat)-tandeg($delta)*cosdeg($lat) );
149 my $h=$r2d * asin( sindeg($lat)*sindeg($delta)+cosdeg($lat)*cosdeg($delta)*cosdeg($H) );
161 my $sun0_moon1=shift; # 0 for sun, 1 for moon, 2 for venus...
162 my ($alpha1,$delta1,$alpha2,$delta2,$alpha3,$delta3);
163 my ($aznow,$hnow,$alphanow,$deltanow,$distance,$distancenow);
165 my ($risetime,$settime);
166 my ($dawntime,$dusktime);
168 my ($ifrac,$ifracnow);
170 my $julianday=Julian_Day($year,$month,$day);
171 my $tt1 = ($julianday-1-2451545)/36525.;
172 my $tt2 = ($julianday-2451545)/36525.;
173 my $tt3 = ($julianday+1-2451545)/36525.;
174 my $ttnow = ($julianday+$hr/24+$min/24/60-2451545)/36525.;
176 my $theta0=280.46061837+360.98564736629*($julianday-2451545.0)+
177 0.000387933*$tt2*$tt2-$tt2*$tt2*$tt2/38710000;
178 $theta0=reduce_angle_to_360($theta0);
180 my $thetanow=280.46061837+360.98564736629*($julianday+$hr/24+$min/24/60-2451545.0)+
181 0.000387933*$ttnow*$ttnow-$ttnow*$ttnow*$ttnow/38710000;
182 $thetanow=reduce_angle_to_360($thetanow);
184 if ( $sun0_moon1 == 0 ) {
185 ($alpha1, $delta1)=get_sun_alpha_delta($tt1);
186 ($alpha2, $delta2)=get_sun_alpha_delta($tt2);
187 ($alpha3, $delta3)=get_sun_alpha_delta($tt3);
188 ($alphanow, $deltanow)=get_sun_alpha_delta($ttnow);
189 $H=$thetanow-$lon-$alphanow;
190 $H=reduce_angle_to_360($H);
191 ($aznow,$hnow)=get_az_el($H,$deltanow,$lat);
193 1.02/(tandeg($hnow+10.3/($hnow+5.11)))/60;
194 $h0=-0.8333; # this is for sun rise and sun set
195 ($risetime,$settime)=
196 do_rise_set_calculations($h0,$theta0,$lat,$lon,$alpha1,$delta1,
197 $alpha2,$delta2,$alpha3,$delta3);
198 $h0=-6.0; # this is for civil dawn and dusk
199 ($dawntime,$dusktime)=
200 do_rise_set_calculations($h0,$theta0,$lat,$lon,$alpha1,$delta1,
201 $alpha2,$delta2,$alpha3,$delta3);
202 $dawntime = "------" if( $dawntime eq "NoRise" );
203 $dusktime = "------" if( $dusktime eq "NoSet " );
206 sprintf("%s", $dawntime), sprintf("%s",$risetime),
207 sprintf("%s", $settime), sprintf("%s",$dusktime),
212 if ( $sun0_moon1 == 1 ) {
213 ($alpha1, $delta1, $distance, $ifrac)=get_moon_alpha_delta($tt1);
214 ($alpha2, $delta2, $distance, $ifrac)=get_moon_alpha_delta($tt2);
215 ($alpha3, $delta3, $distance, $ifrac)=get_moon_alpha_delta($tt3);
216 ($alphanow, $deltanow, $distancenow, $ifracnow)=get_moon_alpha_delta($ttnow);
217 $h0=0.7275*$r2d*asin(6378.14/$distancenow)-34.0/60.;
218 $H=$thetanow-$lon-$alphanow;
219 $H=reduce_angle_to_360($H);
220 ($aznow,$hnow)=get_az_el($H,$deltanow,$lat);
221 $hnow=$hnow-$r2d*asin(sin(6378.14/$distancenow)*cosdeg($hnow))+
222 1.02/(tandeg($hnow+10.3/($hnow+5.11)))/60;
223 ($risetime,$settime)=
224 do_rise_set_calculations($h0,$theta0,$lat,$lon,$alpha1,$delta1,
225 $alpha2,$delta2,$alpha3,$delta3);
226 return (sprintf("%s", $risetime), sprintf("%s",$settime),
227 $aznow+180,$hnow, -40*log10($distance/385000), $ifracnow );
233 sub do_rise_set_calculations
237 my ($risehr,$risemin,$risetime,$sethr,$setmin,$settime);
238 my ($m0,$m1,$m2,$theta,$alpha,$delta,$H,$az,$h,$corr);
239 my ($i,$arg,$argtest,$H0);
252 $arg = (sindeg($h0)-sindeg($lat)*sindeg($delta2))/(cosdeg($lat)*cosdeg($delta2));
253 if ( abs($arg) > 1. ) { # either up all day or down all day
254 $norise = 1; # leave it to the user to examine
255 $noset = 1; # the elevation angle (or look outside!)
256 } # to figure out which.
258 $H0 = acos($arg)*$r2d;
259 my $aa=$alpha2-$alpha1;
260 my $ba=$alpha3-$alpha2;
261 $aa=$aa+360 if ($aa < -180);
262 $aa=$aa-360 if ($aa > 180);
263 $ba=$ba+360 if ($ba < -180);
264 $ba=$ba-360 if ($ba > 180);
267 my $ad=$delta2-$delta1;
268 my $bd=$delta3-$delta2;
269 $ad=$ad+360 if ($ad < -180);
270 $ad=$ad-360 if ($ad > 180);
271 $bd=$bd+360 if ($bd < -180);
272 $bd=$bd-360 if ($bd > 180);
275 $m0 = ($alpha2 + $lon - $theta0)/360.;
276 $m0=$m0+1 if( $m0 < 0 );
277 $m0=$m0-1 if( $m0 > 1 );
278 for ($i=1; $i<=2; $i++) {
279 $theta = $theta0+360.985647*$m0;
280 $alpha=$alpha2+$m0*($aa+$ba+$m0*$ca)/2;
281 $delta=$delta2+$m0*($ad+$bd+$m0*$cd)/2;
282 $H=$theta-$lon-$alpha;
283 $H=reduce_angle_to_360($H);
284 $H=$H-360 if ($H > 180);
285 ($az,$h)=get_az_el($H,$delta,$lat);
288 $m0=$m0+1 if( $m0 < 0 );
289 $m0=$m0-1 if( $m0 >= 1 );
294 $m1 = $m0 - $H0/360.;
295 $m1=$m1+1 if( $m1 < 0 );
296 $m1=$m1-1 if( $m1 > 1 );
297 for ($i=1; $i<=2; $i++) {
298 $theta = $theta0+360.985647*$m1;
299 $alpha=$alpha2+$m1*($aa+$ba+$m1*$ca)/2;
300 $delta=$delta2+$m1*($ad+$bd+$m1*$cd)/2;
301 $H=$theta-$lon-$alpha;
302 $H=reduce_angle_to_360($H);
303 ($az,$h)=get_az_el($H,$delta,$lat);
304 $corr=($h-$h0)/(360*(cosdeg($delta)*cosdeg($lat)*sindeg($H)));
306 # $norise=1 if( $m1 < 0 || $m1 > 1);
307 $m1=$m1-1 if( $m1 >= 1);
308 $m1=$m1+1 if( $m1 < 0);
314 $risemin=($m1*24-int($m1*24))*60+0.5;
315 if ( $risemin >= 60 ) {
316 $risemin=$risemin-60;
319 $risehr=0 if($risehr==24);
320 $risetime=sprintf("%02d:%02dZ",$risehr,$risemin);
326 $m2 = $m0 + $H0/360.;
327 $m2=$m2+1 if( $m2 < 0 );
328 $m2=$m2-1 if( $m2 >= 1 );
329 for ($i=1; $i<=2; $i++) {
330 $theta = $theta0+360.985647*$m2;
331 $alpha=$alpha2+$m2*($aa+$ba+$m2*$ca)/2;
332 $delta=$delta2+$m2*($ad+$bd+$m2*$cd)/2;
333 $H=$theta-$lon-$alpha;
334 $H=reduce_angle_to_360($H);
335 ($az,$h)=get_az_el($H,$delta,$lat);
336 $corr=($h-$h0)/(360*(cosdeg($delta)*cosdeg($lat)*sindeg($H)));
338 # $noset=1 if( $m2 < 0 || $m2 > 1);
339 $m2=$m2-1 if( $m2 >= 1);
340 $m2=$m2+1 if( $m2 < 0);
346 $setmin=($m2*24-int($m2*24))*60+0.5;
347 if ( $setmin >= 60 ) {
351 $sethr=0 if($sethr==24);
352 $settime=sprintf("%02d:%02dZ",$sethr,$setmin);
356 return $risetime,$settime;
361 sub get_moon_alpha_delta
364 # Calculate the moon's right ascension and declination
366 # As of October 2001, also calculate the illuminated fraction of the
367 # moon's disk... (why not?)
371 my $Lp=218.3164477+481267.88123421*$tt-
372 0.0015786*$tt*$tt+$tt*$tt*$tt/538841-$tt*$tt*$tt*$tt/65194000;
373 $Lp=reduce_angle_to_360($Lp);
375 my $D = 297.8501921+445267.1114034*$tt-0.0018819*$tt*$tt+
376 $tt*$tt*$tt/545868.-$tt*$tt*$tt*$tt/113065000.;
377 $D=reduce_angle_to_360($D);
379 my $M = 357.5291092 + 35999.0502909*$tt-0.0001536*$tt*$tt+
380 $tt*$tt*$tt/24490000.;
381 $M=reduce_angle_to_360($M);
383 my $Mp = 134.9633964 + 477198.8675055*$tt+0.0087414*$tt*$tt+
384 $tt*$tt*$tt/69699-$tt*$tt*$tt*$tt/14712000;
385 $Mp=reduce_angle_to_360($Mp);
387 my $F = 93.2720950 + 483202.0175233*$tt - 0.0036539*$tt*$tt-
388 $tt*$tt*$tt/3526000 + $tt*$tt*$tt*$tt/863310000;
389 $F=reduce_angle_to_360($F);
391 my $A1 = 119.75 + 131.849 * $tt;
392 $A1=reduce_angle_to_360($A1);
394 my $A2 = 53.09 + 479264.290 * $tt;
395 $A2=reduce_angle_to_360($A2);
397 my $A3 = 313.45 + 481266.484 * $tt;
398 $A3=reduce_angle_to_360($A3);
400 my $E = 1 - 0.002516 * $tt - 0.0000074 * $tt * $tt;
402 my $Sl= 6288774*sindeg( 1 * $Mp ) +
403 1274027*sindeg(2 * $D + -1 * $Mp ) +
404 658314 *sindeg(2 * $D ) +
405 213618 *sindeg( 2 * $Mp ) +
406 -185116 *sindeg( 1 * $M )*$E +
407 -114332 *sindeg( 2 * $F ) +
408 58793 *sindeg(2 * $D + -2 * $Mp ) +
409 57066 *sindeg(2 * $D - 1 * $M -1 * $Mp )*$E +
410 53322 *sindeg(2 * $D + 1 * $Mp ) +
411 45758 *sindeg(2 * $D - 1 * $M )*$E +
412 -40923 *sindeg( + 1 * $M -1 * $Mp )*$E +
413 -34720 *sindeg(1 * $D ) +
414 -30383 *sindeg( + 1 * $M + 1 * $Mp )*$E +
415 15327 *sindeg(2 * $D + -2 * $F ) +
416 -12528 *sindeg( 1 * $Mp + 2 * $F ) +
417 10980 *sindeg( 1 * $Mp - 2 * $F ) +
418 10675 *sindeg(4 * $D + -1 * $Mp ) +
419 10034 *sindeg( 3 * $Mp ) +
420 8548 *sindeg(4 * $D + 0 * $M - 2 * $Mp + 0 * $F ) +
421 -7888 *sindeg(2 * $D + 1 * $M - 1 * $Mp + 0 * $F )*$E +
422 -6766 *sindeg(2 * $D + 1 * $M + 0 * $Mp + 0 * $F )*$E +
423 -5163 *sindeg(1 * $D + 0 * $M - 1 * $Mp + 0 * $F ) +
424 4987 *sindeg(1 * $D + 1 * $M + 0 * $Mp + 0 * $F )*$E +
425 4036 *sindeg(2 * $D - 1 * $M + 1 * $Mp + 0 * $F )*$E +
426 3994 *sindeg(2 * $D + 0 * $M + 2 * $Mp + 0 * $F ) +
427 3861 *sindeg(4 * $D + 0 * $M + 0 * $Mp + 0 * $F ) +
428 3665 *sindeg(2 * $D + 0 * $M - 3 * $Mp + 0 * $F ) +
429 -2689 *sindeg(0 * $D + 1 * $M - 2 * $Mp + 0 * $F )*$E +
430 -2602 *sindeg(2 * $D + 0 * $M - 1 * $Mp + 2 * $F ) +
431 2390 *sindeg(2 * $D - 1 * $M - 2 * $Mp + 0 * $F )*$E +
432 -2348 *sindeg(1 * $D + 0 * $M + 1 * $Mp + 0 * $F ) +
433 2236 *sindeg(2 * $D - 2 * $M + 0 * $Mp + 0 * $F )*$E*$E +
434 -2120 *sindeg(0 * $D + 1 * $M + 2 * $Mp + 0 * $F )*$E +
435 -2069 *sindeg(0 * $D + 2 * $M + 0 * $Mp + 0 * $F )*$E*$E +
436 2048 *sindeg(2 * $D - 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
437 -1773 *sindeg(2 * $D + 0 * $M + 1 * $Mp - 2 * $F ) +
438 -1595 *sindeg(2 * $D + 0 * $M + 0 * $Mp + 2 * $F ) +
439 1215 *sindeg(4 * $D - 1 * $M - 1 * $Mp + 0 * $F )*$E +
440 -1110 *sindeg(0 * $D + 0 * $M + 2 * $Mp + 2 * $F ) +
441 -892 *sindeg(3 * $D + 0 * $M - 1 * $Mp + 0 * $F ) +
442 -810 *sindeg(2 * $D + 1 * $M + 1 * $Mp + 0 * $F )*$E +
443 759 *sindeg(4 * $D - 1 * $M - 2 * $Mp + 0 * $F )*$E +
444 -713 *sindeg(0 * $D + 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
445 -700 *sindeg(2 * $D + 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
446 691 *sindeg(2 * $D + 1 * $M - 2 * $Mp + 0 * $F )*$E +
447 596 *sindeg(2 * $D - 1 * $M + 0 * $Mp - 2 * $F )*$E +
448 549 *sindeg(4 * $D + 0 * $M + 1 * $Mp + 0 * $F ) +
449 537 *sindeg(0 * $D + 0 * $M + 4 * $Mp + 0 * $F ) +
450 520 *sindeg(4 * $D - 1 * $M + 0 * $Mp + 0 * $F )*$E +
451 -487 *sindeg(1 * $D + 0 * $M - 2 * $Mp + 0 * $F ) +
452 -399 *sindeg(2 * $D + 1 * $M + 0 * $Mp - 2 * $F )*$E +
453 -381 *sindeg(0 * $D + 0 * $M + 2 * $Mp - 2 * $F ) +
454 351 *sindeg(1 * $D + 1 * $M + 1 * $Mp + 0 * $F )*$E +
455 -340 *sindeg(3 * $D + 0 * $M - 2 * $Mp + 0 * $F ) +
456 330 *sindeg(4 * $D + 0 * $M - 3 * $Mp + 0 * $F ) +
457 327 *sindeg(2 * $D - 1 * $M + 2 * $Mp + 0 * $F )*$E +
458 -323 *sindeg(0 * $D + 2 * $M + 1 * $Mp + 0 * $F )*$E*$E +
459 299 *sindeg(1 * $D + 1 * $M - 1 * $Mp + 0 * $F )*$E +
460 294 *sindeg(2 * $D + 0 * $M + 3 * $Mp + 0 * $F ) +
461 3958 *sindeg($A1) + 1962*sindeg($Lp - $F) + 318*sindeg($A2);
463 my $Sr=-20905355 *cosdeg( 1 * $Mp ) +
464 -3699111 *cosdeg(2 * $D + -1 * $Mp ) +
465 -2955968 *cosdeg(2 * $D ) +
466 -569925 *cosdeg( 2 * $Mp ) +
467 48888 *cosdeg( 1 * $M )*$E +
468 -3149 *cosdeg( 2 * $F ) +
469 246158 *cosdeg(2 * $D + -2 * $Mp ) +
470 -152138 *cosdeg(2 * $D - 1 * $M -1 * $Mp )*$E +
471 -170733 *cosdeg(2 * $D + 1 * $Mp ) +
472 -204586 *cosdeg(2 * $D - 1 * $M )*$E +
473 -129620 *cosdeg( + 1 * $M -1 * $Mp )*$E +
474 108743 *cosdeg(1 * $D ) +
475 104755 *cosdeg( + 1 * $M + 1 * $Mp )*$E +
476 10321 *cosdeg(2 * $D + -2 * $F ) +
477 79661 *cosdeg( 1 * $Mp - 2 * $F ) +
478 -34782 *cosdeg(4 * $D + -1 * $Mp ) +
479 -23210 *cosdeg( 3 * $Mp ) +
480 -21636 *cosdeg(4 * $D + 0 * $M - 2 * $Mp + 0 * $F ) +
481 24208 *cosdeg(2 * $D + 1 * $M - 1 * $Mp + 0 * $F )*$E +
482 30824 *cosdeg(2 * $D + 1 * $M + 0 * $Mp + 0 * $F )*$E +
483 -8379 *cosdeg(1 * $D + 0 * $M - 1 * $Mp + 0 * $F ) +
484 -16675 *cosdeg(1 * $D + 1 * $M + 0 * $Mp + 0 * $F )*$E +
485 -12831 *cosdeg(2 * $D - 1 * $M + 1 * $Mp + 0 * $F )*$E +
486 -10445 *cosdeg(2 * $D + 0 * $M + 2 * $Mp + 0 * $F ) +
487 -11650 *cosdeg(4 * $D + 0 * $M + 0 * $Mp + 0 * $F ) +
488 14403 *cosdeg(2 * $D + 0 * $M - 3 * $Mp + 0 * $F ) +
489 -7003 *cosdeg(0 * $D + 1 * $M - 2 * $Mp + 0 * $F )*$E +
490 10056 *cosdeg(2 * $D - 1 * $M - 2 * $Mp + 0 * $F )*$E +
491 6322 *cosdeg(1 * $D + 0 * $M + 1 * $Mp + 0 * $F ) +
492 -9884 *cosdeg(2 * $D - 2 * $M + 0 * $Mp + 0 * $F )*$E*$E +
493 5751 *cosdeg(0 * $D + 1 * $M + 2 * $Mp + 0 * $F )*$E +
494 -4950 *cosdeg(2 * $D - 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
495 4130 *cosdeg(2 * $D + 0 * $M + 1 * $Mp - 2 * $F )+
496 -3958 *cosdeg(4 * $D - 1 * $M - 1 * $Mp + 0 * $F )*$E +
497 3258 *cosdeg(3 * $D + 0 * $M - 1 * $Mp + 0 * $F )+
498 2616 *cosdeg(2 * $D + 1 * $M + 1 * $Mp + 0 * $F )*$E +
499 -1897 *cosdeg(4 * $D - 1 * $M - 2 * $Mp + 0 * $F )*$E +
500 -2117 *cosdeg(0 * $D + 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
501 2354 *cosdeg(2 * $D + 2 * $M - 1 * $Mp + 0 * $F )*$E*$E +
502 -1423 *cosdeg(4 * $D + 0 * $M + 1 * $Mp + 0 * $F )+
503 -1117 *cosdeg(0 * $D + 0 * $M + 4 * $Mp + 0 * $F )+
504 -1571 *cosdeg(4 * $D - 1 * $M + 0 * $Mp + 0 * $F )*$E +
505 -1739 *cosdeg(1 * $D + 0 * $M - 2 * $Mp + 0 * $F )+
506 -4421 *cosdeg(0 * $D + 0 * $M + 2 * $Mp - 2 * $F )+
507 1165 *cosdeg(0 * $D + 2 * $M + 1 * $Mp + 0 * $F )*$E*$E +
508 8752 *cosdeg(2 * $D + 0 * $M - 1 * $Mp - 2 * $F );
510 my $Sb= 5128122 *sindeg( 1 * $F ) +
511 280602 *sindeg( 1 * $Mp + 1 * $F ) +
512 277693 *sindeg( 1 * $Mp - 1 * $F ) +
513 173237 *sindeg(2 * $D - 1 * $F ) +
514 55413 *sindeg(2 * $D -1 * $Mp + 1 * $F ) +
515 46271 *sindeg(2 * $D + -1 * $Mp - 1 * $F ) +
516 32573 *sindeg(2 * $D + 1 * $F ) +
517 17198 *sindeg( 2 * $Mp + 1 * $F )+
518 9266 *sindeg(2 * $D + 0 * $M + 1 * $Mp - 1 * $F ) +
519 8822 *sindeg(0 * $D + 0 * $M + 2 * $Mp - 1 * $F ) +
520 8216 *sindeg(2 * $D - 1 * $M + 0 * $Mp - 1 * $F )*$E +
521 4324 *sindeg(2 * $D + 0 * $M - 2 * $Mp - 1 * $F ) +
522 4200 *sindeg(2 * $D + 0 * $M + 1 * $Mp + 1 * $F ) +
523 -3359 *sindeg(2 * $D + 1 * $M + 0 * $Mp - 1 * $F )*$E +
524 2463 *sindeg(2 * $D - 1 * $M - 1 * $Mp + 1 * $F )*$E +
525 2211 *sindeg(2 * $D - 1 * $M + 0 * $Mp + 1 * $F )*$E +
526 2065 *sindeg(2 * $D - 1 * $M - 1 * $Mp - 1 * $F )*$E +
527 -1870 *sindeg(0 * $D + 1 * $M - 1 * $Mp - 1 * $F )*$E +
528 1828 *sindeg(4 * $D + 0 * $M - 1 * $Mp - 1 * $F ) +
529 -1794 *sindeg(0 * $D + 1 * $M + 0 * $Mp + 1 * $F )*$E +
530 -1749 *sindeg(0 * $D + 0 * $M + 0 * $Mp + 3 * $F ) +
531 -1565 *sindeg(0 * $D + 1 * $M - 1 * $Mp + 1 * $F )*$E +
532 -1491 *sindeg(1 * $D + 0 * $M + 0 * $Mp + 1 * $F ) +
533 -1475 *sindeg(0 * $D + 1 * $M + 1 * $Mp + 1 * $F )*$E +
534 -1410 *sindeg(0 * $D + 1 * $M + 1 * $Mp - 1 * $F )*$E +
535 -1344 *sindeg(0 * $D + 1 * $M + 0 * $Mp - 1 * $F )*$E +
536 -1335 *sindeg(1 * $D + 0 * $M + 0 * $Mp - 1 * $F ) +
537 1107 *sindeg(0 * $D + 0 * $M + 3 * $Mp + 1 * $F ) +
538 1021 *sindeg(4 * $D + 0 * $M + 0 * $Mp - 1 * $F ) +
539 833 *sindeg(4 * $D + 0 * $M - 1 * $Mp + 1 * $F ) +
540 777 *sindeg(0 * $D + 0 * $M + 1 * $Mp - 3 * $F ) +
541 671 *sindeg(4 * $D + 0 * $M - 2 * $Mp + 1 * $F ) +
542 607 *sindeg(2 * $D + 0 * $M + 0 * $Mp - 3 * $F ) +
543 596 *sindeg(2 * $D + 0 * $M + 2 * $Mp - 1 * $F ) +
544 491 *sindeg(2 * $D - 1 * $M + 1 * $Mp - 1 * $F )*$E +
545 -451 *sindeg(2 * $D + 0 * $M - 2 * $Mp + 1 * $F ) +
546 439 *sindeg(0 * $D + 0 * $M + 3 * $Mp - 1 * $F ) +
547 422 *sindeg(2 * $D + 0 * $M + 2 * $Mp + 1 * $F ) +
548 421 *sindeg(2 * $D + 0 * $M - 3 * $Mp - 1 * $F ) +
549 -366 *sindeg(2 * $D + 1 * $M - 1 * $Mp + 1 * $F )*$E +
550 -351 *sindeg(2 * $D + 1 * $M + 0 * $Mp + 1 * $F )*$E +
551 331 *sindeg(4 * $D + 0 * $M + 0 * $Mp + 1 * $F ) +
552 315 *sindeg(2 * $D - 1 * $M + 1 * $Mp + 1 * $F )*$E +
553 302 *sindeg(2 * $D - 2 * $M + 0 * $Mp - 1 * $F )*$E*$E +
554 -283 *sindeg(0 * $D + 0 * $M + 1 * $Mp + 3 * $F ) +
555 -229 *sindeg(2 * $D + 1 * $M + 1 * $Mp - 1 * $F )*$E +
556 223 *sindeg(1 * $D + 1 * $M + 0 * $Mp - 1 * $F )*$E +
557 223 *sindeg(1 * $D + 1 * $M + 0 * $Mp + 1 * $F )*$E +
558 -220 *sindeg(0 * $D + 1 * $M - 2 * $Mp - 1 * $F )*$E +
559 -220 *sindeg(2 * $D + 1 * $M - 1 * $Mp - 1 * $F )*$E +
560 -185 *sindeg(1 * $D + 0 * $M + 1 * $Mp + 1 * $F ) +
561 181 *sindeg(2 * $D - 1 * $M - 2 * $Mp - 1 * $F )*$E +
562 -177 *sindeg(0 * $D + 1 * $M + 2 * $Mp + 1 * $F )*$E +
563 176 *sindeg(4 * $D + 0 * $M - 2 * $Mp - 1 * $F ) +
564 166 *sindeg(4 * $D - 1 * $M - 1 * $Mp - 1 * $F )*$E +
565 -164 *sindeg(1 * $D + 0 * $M + 1 * $Mp - 1 * $F ) +
566 132 *sindeg(4 * $D + 0 * $M + 1 * $Mp - 1 * $F ) +
567 -119 *sindeg(1 * $D + 0 * $M - 1 * $Mp - 1 * $F ) +
568 115 *sindeg(4 * $D - 1 * $M + 0 * $Mp - 1 * $F )*$E +
569 107 *sindeg(2 * $D - 2 * $M + 0 * $Mp + 1 * $F )*$E*$E
570 -2235 *sindeg($Lp) + 382*sindeg($A3) +
571 175 *sindeg($A1-$F) + 175*sindeg($A1+$F) +
572 127 *sindeg($Lp-$Mp) - 115*sindeg($Lp+$Mp);
574 my $lambda=$Lp+$Sl/1000000.;
576 my $beta=$Sb/1000000.;
578 my $distance=385000.56 + $Sr/1000.;
580 my $epsilon = 23+26./60.+21.448/(60.*60.);
582 my $alpha=atan2(cosdeg($epsilon)*sindeg($lambda)-tandeg($beta)*sindeg($epsilon),cosdeg($lambda))*$r2d;
583 $alpha = reduce_angle_to_360($alpha);
585 my $delta=asin(cosdeg($beta)*sindeg($epsilon)*sindeg($lambda)+sindeg($beta)*cosdeg($epsilon))*$r2d;
586 $delta = reduce_angle_to_360($delta);
588 # $phase will be the "moon phase angle" from p. 346 of Meeus' book...
589 my $phase=180.0 - $D - 6.289 *sindeg($Mp)
591 - 1.274 *sindeg(2.*$D - $Mp)
592 - 0.658 *sindeg(2.*$D)
593 - 0.214 *sindeg(2.*$Mp)
596 # $illum_frac is the fraction of the disk that is illuminated, and will be
597 # zero at new moon and 1.0 at full moon.
599 my $illum_frac = (1.0 + cosdeg( $phase ))/2.;
601 return ($alpha,$delta,$distance,$illum_frac);
604 sub get_sun_alpha_delta
607 # Calculate Sun's right ascension and declination
611 my $L0 = 280.46646+36000.76983*$tt+0.0003032*($tt^2);
612 $L0=reduce_angle_to_360($L0);
614 my $M = 357.52911 + 35999.05029*$tt-0.0001537*($tt^2);
615 $M=reduce_angle_to_360($M);
617 my $C = (1.914602 - 0.004817*$tt-0.000014*($tt^2))*sindeg($M) +
618 (0.019993 - 0.000101*$tt)*sindeg(2*$M) +
619 0.000289*sindeg(3*$M);
621 my $OMEGA = 125.04 - 1934.136*$tt;
623 my $lambda=$L0+$C-0.00569-0.00478*sindeg($OMEGA);
625 my $epsilon = 23+26./60.+21.448/(60.*60.);
627 my $alpha=atan2(cosdeg($epsilon)*sindeg($lambda),cosdeg($lambda))*$r2d;
628 $alpha = reduce_angle_to_360($alpha);
630 my $delta=asin(sin($epsilon*$d2r)*sin($lambda*$d2r))*$r2d;
631 $delta = reduce_angle_to_360($delta);
633 return ($alpha,$delta);
635 sub get_satellite_pos
638 # This code was translated more-or-less directly from the Pascal
639 # routines contained in a report compiled by TS Kelso and based on:
640 # Spacetrack Report No. 3
641 # "Models for Propagation of NORAD Element Sets"
642 # Felix R. Hoots, Ronald L Roehrich
645 # See TS Kelso's web site for more details...
646 # Only the SGP propagation model is implemented.
648 # Steve Franke, K9AN. 9 Dec 1999.
652 #1 25338U 98030A 99341.00000000 +.00000376 +00000-0 +18612-3 0 05978
653 #2 25338 098.6601 008.2003 0011401 112.4684 042.5140 14.23047277081382
655 #1 21639U 91054B 99341.34471854 .00000095 00000-0 10000-3 0 4928
656 #2 21639 1.5957 88.4884 0003028 161.6582 135.4323 1.00277774 30562
658 #1 20439U 90005D 99341.14501399 +.00000343 +00000-0 +14841-3 0 02859
659 #2 20439 098.4690 055.0032 0012163 066.4615 293.7842 14.30320285515297
661 #Temporary keps database...
668 my $sat_ref = $keps{$satname};
669 #printf("$jtime $lat $lon $alt Satellite name = $satname\n");
676 my $xke=.743669161e-1;
680 my $ck2=.5*$xj2*$ae**2;
681 my $ck4=-.375*$xj4*$ae**4;
682 my $qoms2t=(($qo-$so)*$ae/$xkmper)**4;
683 my $s=$ae*(1+$so/$xkmper);
685 my $epoch = $sat_ref ->{epoch};
686 #printf("epoch = %10.2f\n",$epoch);
687 my $jt_epoch=Julian_Date_of_Epoch($epoch);
688 #printf("JT for epoch = %17.12f\n",$jt_epoch);
689 my $tsince=($jtime-$jt_epoch)*24*60;
690 #printf("tsince (min) = %17.12f\n",$tsince);
692 my $mm1 = $sat_ref ->{mm1};
693 my $mm2 = $sat_ref ->{mm2};
694 my $bstar=$sat_ref ->{bstar}; # drag term for sgp4 model
695 my $inclination=$sat_ref->{inclination}; # inclination in degrees
696 my $raan=$sat_ref->{raan}; # right ascension of ascending node in degs
697 my $eccentricity=$sat_ref ->{eccentricity}; # eccentricity - dimensionless
698 my $omegao=$sat_ref ->{argperigee}; # argument of perigee in degs
699 my $xmo=$sat_ref ->{meananomaly}; # mean anomaly in degrees
700 my $xno=$sat_ref ->{meanmotion}; # mean motion in revs per day
702 #printf("%10.6f %10.6f %10.6f %10.6f %10.6f %10.6f %10.6f %10.6f %10.6f\n",
703 #$mm1,$mm2,$bstar,$inclination,$raan,$eccentricity,$omegao,$xmo,$xno);
705 $omegao=$omegao*$d2r;
707 $inclination=$inclination*$d2r;
708 my $temp=2*$pi/$xmnpda/$xmnpda;
709 $xno=$xno*$temp*$xmnpda;
711 $mm2=$mm2*$temp/$xmnpda;
716 my $c4=$xj3*$ae**3/(4*$ck2);
717 my $cosio=cos($inclination);
718 my $sinio=sin($inclination);
719 my $a1=($xke/$xno)**(2./3.);
720 my $d1=$c1/$a1/$a1*(3*$cosio*$cosio-1)/(1-$eccentricity*$eccentricity)**1.5;
721 my $ao=$a1*(1-1./3.*$d1-$d1*$d1-134./81.*$d1*$d1*$d1);
722 my $po=$ao*(1-$eccentricity*$eccentricity);
723 $qo=$ao*(1-$eccentricity);
724 my $xlo=$xmo+$omegao+$raan;
725 my $d10=$c3*$sinio*$sinio;
726 my $d20=$c2*(7.*$cosio*$cosio-1);
729 my $po2no=$xno/($po*$po);
730 my $omgdt=$c1*$po2no*(5.*$cosio*$cosio-1);
731 my $xnodot=-2.*$d30*$po2no;
732 my $c5=0.5*$c4*$sinio*(3+5*$cosio)/(1+$cosio);
735 my $a=$xno+(2*$mm1+3*$mm2*$tsince)*$tsince;
736 $a=$ao*($xno/$a)**(2./3.);
738 $e =1-$qo/$a if ($a > $qo);
740 my $xnodes=$raan+$xnodot*$tsince;
741 my $omgas=$omegao+$omgdt*$tsince;
742 my $xls=mod2p($xlo+($xno+$omgdt+$xnodot+($mm1+$mm2*$tsince)*$tsince)*$tsince);
744 my $axnsl=$e*cos($omgas);
745 my $aynsl=$e*sin($omgas)-$c6/$p;
746 my $xl=mod2p($xls-$c5/$p*$axnsl);
748 my $u=mod2p($xl-$xnodes);
754 for ($item3=0; abs($tem5) >= 1e-6 && $item3 < 10; $item3++ )
758 $tem5=1-$coseo1*$axnsl-$sineo1*$aynsl;
759 $tem5=($u-$aynsl*$coseo1+$axnsl*$sineo1-$eo1)/$tem5;
761 $tem5=$tem2/$tem5 if ($tem2 > 1);
767 my $ecose=$axnsl*$coseo1+$aynsl*$sineo1;
768 my $esine=$axnsl*$sineo1-$aynsl*$coseo1;
769 my $el2=$axnsl*$axnsl+$aynsl*$aynsl;
773 my $rdot=$xke*sqrt($a)/$r*$esine;
774 my $rvdot=$xke*sqrt($pl)/$r;
775 $temp=$esine/(1+sqrt(1-$el2));
776 my $sinu=$a/$r*($sineo1-$aynsl-$axnsl*$temp);
777 my $cosu=$a/$r*($coseo1-$axnsl+$aynsl*$temp);
778 my $su=atan2($sinu,$cosu);
780 my $sin2u=($cosu+$cosu)*$sinu;
781 my $cos2u=1-2*$sinu*$sinu;
782 my $rk=$r+$d10/$pl*$cos2u;
783 my $uk=$su-$d20/$pl2*$sin2u;
784 my $xnodek=$xnodes+$d30*$sin2u/$pl2;
785 my $xinck=$inclination+$d40/$pl2*$cos2u;
789 my $sinnok=sin($xnodek);
790 my $cosnok=cos($xnodek);
791 my $sinik=sin($xinck);
792 my $cosik=cos($xinck);
793 my $xmx=-$sinnok*$cosik;
794 my $xmy=$cosnok*$cosik;
795 my $ux=$xmx*$sinuk+$cosnok*$cosuk;
796 my $uy=$xmy*$sinuk+$sinnok*$cosuk;
797 my $uz=$sinik*$sinuk;
798 my $vx=$xmx*$cosuk-$cosnok*$sinuk;
799 my $vy=$xmy*$cosuk-$sinnok*$sinuk;
800 my $vz=$sinik*$cosuk;
802 my $x=$rk*$ux*$xkmper/$ae;
803 my $y=$rk*$uy*$xkmper/$ae;
804 my $z=$rk*$uz*$xkmper/$ae;
808 $xdot=($rvdot*$vx+$xdot)*$xkmper/$ae*$xmnpda/86400;
809 $ydot=($rvdot*$vy+$ydot)*$xkmper/$ae*$xmnpda/86400;
810 $zdot=($rvdot*$vz+$zdot)*$xkmper/$ae*$xmnpda/86400;
811 #printf("x=%17.6f y=%17.6f z=%17.6f \n",$x,$y,$z);
812 #printf("xdot=%17.6f ydot=%17.6f zdot=%17.6f \n",$xdot,$ydot,$zdot);
813 my ($sat_lat,$sat_lon,$sat_alt,$sat_theta)=Calculate_LatLonAlt($x,$y,$z,$jtime);
814 my ($az, $el, $distance) = Calculate_Obs($x,$y,$z,$sat_theta,$xdot,$ydot,$zdot,$jtime,$lat,$lon,$alt);
815 return ($sat_lat,$sat_lon,$sat_alt,$az,$el,$distance);
818 sub Calculate_LatLonAlt
821 # convert from ECI coordinates to latitude, longitude and altitude.
828 my $theta=atan2($y,$x);
829 my $lon=mod2p($theta-ThetaG_JD($time));
830 my $range=sqrt($x**2+$y**2);
831 my $f=1/298.26; # earth flattening constant
834 my $lat=atan2($z,$range);
839 $c=1/sqrt(1-$e2*sin($phi)**2);
840 $lat=atan2($z+$xkmper*$c*$e2*sin($phi),$range);
841 } until abs($lat-$phi) < 1e-10;
842 my $alt=$range/cos($lat)-$xkmper*$c;
843 return ($lat,$lon,$alt,$theta); # radians and kilometers
847 sub Calculate_User_PosVel
849 # change from lat/lon/alt/time coordinates to earth centered inertial (ECI)
850 # position and local hour angle.
855 my $theta=mod2p(ThetaG_JD($time)+$lon);
856 my $omega_E=1.00273790934; # earth rotations per sidereal day
858 my $mfactor=2*$pi*$omega_E/$secday;
859 my $f=1/298.26; # earth flattening constant
861 my $c=1/sqrt(1+$f*($f-2)*sin($lat)**2);
862 my $s=(1-$f)*(1-$f)*$c;
863 my $achcp=($xkmper*$c+$alt)*cos($lat);
864 my $x_user=$achcp*cos($theta);
865 my $y_user=$achcp*sin($theta);
866 my $z_user=($xkmper*$s+$alt)*sin($lat);
867 my $xdot_user=-$mfactor*$y_user;
868 my $ydot_user=$mfactor*$x_user;
870 return ($x_user,$y_user,$z_user,$xdot_user,$ydot_user,$zdot_user,$theta);
874 # calculate the azimuth/el of an object as viewed from observers position
875 # with object position given in ECI coordinates and observer in lat/long/alt.
877 # inputs: object ECI position vector (km)
878 # object velocity vector (km/s)
880 # observer lat,lon,altitude (km)
893 my ($x_o,$y_o,$z_o,$xdot_o,$ydot_o,$zdot_o,$theta)=
894 Calculate_User_PosVel($lat,$lon,$alt,$time);
898 my $xxdot=$xdot-$xdot_o;
899 my $yydot=$ydot-$ydot_o;
900 my $zzdot=$zdot-$zdot_o;
902 my $sin_lat=sin($lat);
903 my $cos_lat=cos($lat);
904 my $sin_theta=sin($theta);
905 my $cos_theta=cos($theta);
907 my $top_s=$sin_lat*$cos_theta*$xx
908 + $sin_lat*$sin_theta*$yy
911 my $top_e=-$sin_theta*$xx
914 my $top_z=$cos_lat*$cos_theta*$xx
915 + $cos_lat*$sin_theta*$yy
918 my $az=atan(-$top_e/$top_s);
919 $az=$az+$pi if ( $top_s > 0 );
920 $az=$az+2*$pi if ( $az < 0 );
922 my $range=sqrt($xx*$xx+$yy*$yy+$zz*$zz);
923 my $el=asin($top_z/$range);
924 return ($az, $el, $range);
927 sub Calendar_date_and_time_from_JD
929 my ($jd,$z,$frac,$alpha,$a,$b,$c,$d,$e,$dom,$yr,$mon,$day,$hr,$min);
934 $alpha = int( ($z-1867216.5)/36524.25 );
935 $a=$z + 1 + $alpha - int($alpha/4);
936 $a=$z if( $z < 2299161 );
938 $c=int(($b-122.1)/365.25);
940 $e=int(($b-$d)/30.6001);
941 $dom=$b-$d-int(30.6001*$e)+$frac;
943 $mon=$e-1 if( $e < 14 );
944 $mon=$e-13 if( $e == 14 || $e == 15 );
945 $yr = $c-4716 if( $mon > 2 );
946 $yr = $c-4715 if( $mon == 1 || $mon == 2 );
948 $min= int(($frac*24 - $hr)*60+0.5);
949 if ($min == 60) { # this may well prove inadequate DJK
953 return ($yr,$mon,$day,$hr,$min);