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|
/* rocks.cpp: coordinates of inner moons of Mars through Pluto
Copyright (C) 2010, Project Pluto
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA. */
/* ROCKS.CPP
This code generates positions for "rocks" (faint inner satellites
that can be modelled, at least passably well, as precessing ellipses).
The currently listed "rocks" are:
505: Amalthea 706: 1986U7 Cordelia 801: Triton (Neptune I)
514: 1979J2 Thebe 707: 1986U8 Ophelia 803: 1989 N6 Naiad
515: 1979J1 Adrastea 708: 1986U9 Bianca 804: 1989 N5 Thalassa
516: 1979J3 Metis 709: 1986U3 Cressida 805: 1989 N3 Despina
710: 1986U6 Desdemona 806: 1989 N4 Galatea
610: Janus (+) 711: 1986U2 Juliet 807: 1989 N2 Larissa
611: Epimetheus (+) 712: 1986U1 Portia 808: 1989 N1 Proteus
612: Helene (+) 713: 1986U4 Rosalind
613: Telesto (+) 714: 1986U5 Belinda
614: Calypso (+) 715: 1986U1 Puck
615: 1980S28 Atlas 725: 1986U10 = Perdita 401: Phobos (+)
616: 1980S27 Prometheus 726: Mab (+) 402: Deimos (+)
617: 1980S26 Pandora 727: Cupid (+)
618: 1981S13 Pan
635: Daphnis (+)
The orbital elements were provided by Mark Showalter (some updates from
Bob Jacobson), along with the following comments:
(1) The listing refers to JPL ephemeris IDs JUP120, SAT080, URA039, and
NEP022(*). If you select the SPICE ephemerides of the same name in
Horizons, then you really should get almost identical results, because
the SPICE files were generated using these exact elements.
(2) Be aware that Saturn's moons Prometheus and Pandora are exhibiting
peculiar variations in longitude that are not currently understood,
probably related to interactions with the other nearby moons and rings.
So don't expect your results for these bodies to be particularly
accurate.
Regards, Mark Showalter
-------------------------
(+) Data is provided for this object, but I've not tried it out in Guide yet.
(*) replaced with JUP250 data 3 Nov 2007, NEP050 data 8 Jan 2008
(and Triton added), URA086X on 8 Jan 2008, MAR080 on 13 Feb 2009.
Some others updated as noted in comments. All Uranians replaced
with URA091 on 22 Dec 2009.
2012 Mar 9: updated Pan & Daphnis with SAT353.
2013 May 8: updated Pan & Daphnis with SAT357eq.
2015 Apr 15: updated Pan & Daphnis with SAT363eq_b. Flipped signs on
p and q for Triton, which caused me to get values within 300 to
500 km of Horizons. Added comments converting epoch JDs to
calendar dates. Improved the test routine. */
#include <math.h>
#define ROCK struct rock
ROCK
{
int jpl_id;
double epoch_jd, a, h, k, mean_lon0, p, q, apsis_rate, mean_motion;
double node_rate, laplacian_pole_ra, laplacian_pole_dec;
};
#define PI 3.1415926535897932384626433832795028841971693993751058209749445923
#define N_ROCKS 36
static const ROCK rocks[N_ROCKS] = {
{ 401, /* Phobos: MAR080 data */
2433282.50, /* 1950 Jan 1: element epoch Julian date */
9.376164153345777E+03, /* a = semi-major axis (km) */
-5.689907327111091E-04, /* h = e sin(periapsis longitude)*/
1.508976478046249E-02, /* k = e cos(periapsis longitude)*/
8.889912565234037E+01 * PI / 180., /* l = mean longitude (deg) */
-4.374861644190954E-03, /* p = tan(i/2) sin(node) */
-8.303312581096576E-03, /* q = tan(i/2) cos(node) */
5.037011787882128E-06 * PI / 180., /* apsis rate (deg/sec) */
1.306533283449532E-02 * PI / 180., /* mean motion (deg/sec) */
-5.043841563630776E-06 * PI / 180., /* node rate (deg/sec) */
3.176707407767539E+02 * PI / 180., /* Laplacian plane pole ra (deg) */
5.289299367003886E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 402, /* Deimos: MAR080 data */
2433282.50, /* 1950 Jan 1: element epoch Julian date */
2.345766038183417E+04, /* a = semi-major axis (km) */
-2.390285567613731E-04, /* h = e sin(periapsis longitude)*/
6.518182753851608E-05, /* k = e cos(periapsis longitude)*/
2.505824379527014E+02 * PI / 180., /* l = mean longitude (deg) */
6.477849519349295E-03, /* p = tan(i/2) sin(node) */
1.419810985499536E-02, /* q = tan(i/2) cos(node) */
2.076162603566793E-07 * PI / 180., /* apsis rate (deg/sec) */
3.300484710930912E-03 * PI / 180., /* mean motion (deg/sec) */
-2.091750616728367E-07 * PI / 180., /* node rate (deg/sec) */
3.166569791010836E+02 * PI / 180., /* Laplacian plane pole ra (deg) */
5.352937471037383E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 505, /* Amalthea: JUP250 */
2450000.500000000, /* 1995 Oct 10: element epoch Julian date */
1.813655512465877E+05, /* a = semi-major axis (km) */
3.524243705442326E-04, /* h = e sin(periapsis longitude)*/
-3.060388597797567E-03, /* k = e cos(periapsis longitude)*/
3.088979995508090E+02 * PI / 180., /* l = mean longitude (deg) */
-8.524633361449484E-04, /* p = tan(i/2) sin(node) */
-3.277584681172060E-03, /* q = tan(i/2) cos(node) */
2.908651473226303E-05 * PI / 180., /* apsis rate (deg/sec) */
8.363792987058621E-03 * PI / 180., /* mean motion (deg/sec) */
-2.898772964219916E-05 * PI / 180., /* node rate (deg/sec) */
2.680573067077756E+02 * PI / 180., /* Laplacian plane pole ra (deg) */
6.449433514883954E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 514, /* Thebe: JUP250 */
2450000.500000000, /* 1995 Oct 10: element epoch Julian date */
2.218882574500956E+05, /* a = semi-major axis (km) */
-1.707742712451856E-02, /* h = e sin(periapsis longitude)*/
-4.631931271882844E-03, /* k = e cos(periapsis longitude)*/
2.889925861272768E+02 * PI / 180., /* l = mean longitude (deg) */
9.336528660574965E-03, /* p = tan(i/2) sin(node) */
7.503268096368817E-05, /* q = tan(i/2) cos(node) */
1.433399183927280E-05 * PI / 180., /* apsis rate (deg/sec) */
6.177086242379696E-03 * PI / 180., /* mean motion (deg/sec) */
-1.430832006152276E-05 * PI / 180., /* node rate (deg/sec) */
2.680573566856980E+02 * PI / 180., /* Laplacian plane pole ra (deg) */
6.449436369487705E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 515, /* Adrastea: JUP250 */
2450000.500000000, /* 1995 Oct 10: element epoch Julian date */
1.289847619277409E+05, /* a = semi-major axis (km) */
7.733436951055491E-05, /* h = e sin(periapsis longitude)*/
-7.119915620542968E-04, /* k = e cos(periapsis longitude)*/
8.469076821476101E+01 * PI / 180., /* l = mean longitude (deg) */
7.291459020134167E-04, /* p = tan(i/2) sin(node) */
2.676849686756846E-04, /* q = tan(i/2) cos(node) */
9.721724518582802E-05 * PI / 180., /* apsis rate (deg/sec) */
1.396989430143032E-02 * PI / 180., /* mean motion (deg/sec) */
-9.865593193437598E-05 * PI / 180., /* node rate (deg/sec) */
2.680565964128937E+02 * PI / 180., /* Laplacian plane pole ra (deg) */
6.449530295172036E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 516, /* Metis: JUP250 */
2450000.500000000, /* 1995 Oct 10: element epoch Julian date */
1.279996083074168E+05, /* a = semi-major axis (km) */
4.232619343306958E-04, /* h = e sin(periapsis longitude)*/
-6.389823783865655E-04, /* k = e cos(periapsis longitude)*/
3.380483431923231E+02 * PI / 180., /* l = mean longitude (deg) */
2.332741944310790E-04, /* p = tan(i/2) sin(node) */
5.651570478951611E-04, /* q = tan(i/2) cos(node) */
9.905391637419158E-05 * PI / 180., /* apsis rate (deg/sec) */
1.413489189624821E-02 * PI / 180., /* mean motion (deg/sec) */
-9.817915317723091E-05 * PI / 180., /* node rate (deg/sec) */
2.680565964128937E+02 * PI / 180., /* Laplacian plane pole ra (deg) */
6.449530295172036E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 610, /* Janus: SAT080 data */
2444786.5, /* 1981 Jul 1: element epoch Julian date */
1.514471646942220E+05, /* a = semi-major axis (km) */
-3.356112346396347E-03, /* h = e sin(periapsis longitude)*/
5.663424289609894E-03, /* k = e cos(periapsis longitude)*/
1.993639755564592E+02 * PI / 180., /* l = mean longitude (deg) */
-1.210639146126198E-03, /* p = tan(i/2) sin(node) */
8.350119519512047E-04, /* q = tan(i/2) cos(node) */
2.378317712273239E-05 * PI / 180., /* apsis rate (deg/sec) */
5.998806000756397E-03 * PI / 180., /* mean motion (deg/sec) */
-2.367392401124433E-05 * PI / 180., /* node rate (deg/sec) */
4.057999864473820E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
8.353999955183330E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 611, /* Epimetheus: SAT080 data */
2444786.5, /* 1981 Jul 1: element epoch Julian date */
1.513991905498270E+05, /* a = semi-major axis (km) */
1.244955044467311E-02, /* h = e sin(periapsis longitude)*/
1.689723618147796E-03, /* k = e cos(periapsis longitude)*/
1.438890791888553E+02 * PI / 180., /* l = mean longitude (deg) */
-1.212371038828309E-03, /* p = tan(i/2) sin(node) */
2.571443713031926E-03, /* q = tan(i/2) cos(node) */
2.379040740977320E-05 * PI / 180., /* apsis rate (deg/sec) */
6.001665785000491E-03 * PI / 180., /* mean motion (deg/sec) */
-2.367577385695356E-05 * PI / 180., /* node rate (deg/sec) */
4.057999864473820E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
8.353999955183330E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 612, /* Helene: SAT080 data */
2444786.5, /* 1981 Jul 1: element epoch Julian date */
3.774166381879790E+05, /* a = semi-major axis (km) */
-9.353516152747377E-05, /* h = e sin(periapsis longitude)*/
1.583034918343283E-03, /* k = e cos(periapsis longitude)*/
1.006212707258068E+02 * PI / 180., /* l = mean longitude (deg) */
3.230333151378729E-04, /* p = tan(i/2) sin(node) */
1.710869900001995E-03, /* q = tan(i/2) cos(node) */
-6.777890900303528E-07 * PI / 180., /* apsis rate (deg/sec) */
1.522394989535369E-03 * PI / 180., /* mean motion (deg/sec) */
-9.680289928992843E-07 * PI / 180., /* node rate (deg/sec) */
4.057615013244320E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
8.354534172579820E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 613, /* Telesto: SAT080 data */
2444786.5, /* 1981 Jul 1: element epoch Julian date */
2.946735826892260E+05, /* a = semi-major axis (km) */
-5.228888695475952E-04, /* h = e sin(periapsis longitude)*/
-6.853986134369704E-04, /* k = e cos(periapsis longitude)*/
2.150026475454563E+02 * PI / 180., /* l = mean longitude (deg) */
8.124186851739944E-03, /* p = tan(i/2) sin(node) */
-5.785202572889351E-03, /* q = tan(i/2) cos(node) */
2.297061650453675E-06 * PI / 180., /* apsis rate (deg/sec) */
2.207149546064677E-03 * PI / 180., /* mean motion (deg/sec) */
-2.290176906415847E-06 * PI / 180., /* node rate (deg/sec) */
4.057999864473820E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
8.353999955183330E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 614, /* Calypso: SAT080 data */
2444786.5, /* 1981 Jul 1: element epoch Julian date */
2.946734418892560E+05, /* a = semi-major axis (km) */
2.900726601141678E-05, /* h = e sin(periapsis longitude)*/
-1.805642558770706E-04, /* k = e cos(periapsis longitude)*/
9.486345898172432E+01 * PI / 180., /* l = mean longitude (deg) */
-6.373255324934580E-03, /* p = tan(i/2) sin(node) */
-1.114711641632123E-02, /* q = tan(i/2) cos(node) */
2.297022164277979E-06 * PI / 180., /* apsis rate (deg/sec) */
2.207149553889344E-03 * PI / 180., /* mean motion (deg/sec) */
-2.289705897532556E-06 * PI / 180., /* node rate (deg/sec) */
4.057999864473820E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
8.353999955183330E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 615, /* Atlas: SAT080 data */
2444786.50, /* 1981 Jul 1: element epoch Julian date */
1.376664620000000E+05, /* a = semi-major axis (km) */
0.000000000000000E+00, /* h = e sin(periapsis longitude)*/
0.000000000000000E+00, /* k = e cos(periapsis longitude)*/
1.865410967364615E+02 * PI / 180., /* l = mean longitude (deg) */
0.000000000000000E+00, /* p = tan(i/2) sin(node) */
0.000000000000000E+00, /* q = tan(i/2) cos(node) */
3.334584985561025E-05 * PI / 180., /* apsis rate (deg/sec) */
6.924845572071244E-03 * PI / 180., /* mean motion (deg/sec) */
-3.318681015315788E-05 * PI / 180., /* node rate (deg/sec) */
4.058861887893110E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
8.352533375484340E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 616, /* Prometheus: SAT127 data */
2444940., /* 1981 Dec 1.5: element epoch Julian date */
1.393776240E+5, /* a = semi-major axis (km) */
-1.870790E-3, /* h = e sin(periapsis longitude)*/
-4.319060E-4, /* k = e cos(periapsis longitude)*/
339.155 * PI / 180., /* l = mean longitude (deg) */
0.0, /* p = tan(i/2) sin(node) */
0.0, /* q = tan(i/2) cos(node) */
3.191398148E-05 * PI / 180., /* apsis rate (deg/sec) */
6.797308681E-03 * PI / 180., /* mean motion (deg/sec) */
-3.191398148E-05 * PI / 180., /* node rate (deg/sec) */
40.5955 * PI / 180., /* Laplacian plane pole ra (deg) */
83.53812 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 617, /* Pandora: SAT127 data */
2444940.0, /* 1981 Dec 1.5: element epoch Julian date */
1.417131075E+05, /* a = semi-major axis (km) */
-7.853582898E-05, /* h = e sin(periapsis longitude)*/
4.499314628E-03, /* k = e cos(periapsis longitude)*/
96.023 * PI / 180., /* l = mean longitude (deg) */
0.000000000E+00, /* p = tan(i/2) sin(node) */
0.000000000E+00, /* q = tan(i/2) cos(node) */
3.008501157E-05 * PI / 180., /* apsis rate (deg/sec) */
6.629462963E-03 * PI / 180., /* mean motion (deg/sec) */
-3.008501157E-05 * PI / 180., /* node rate (deg/sec) */
40.5955 * PI / 180., /* Laplacian plane pole ra (deg) */
83.53812 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 618, /* Pan SAT363eq_b: for 2010 Jan 1 and later only! */
2451545.000000000, /* 2000 Jan 1.5: element epoch Julian date */
1.335844767617734E+05, /* a = semi-major axis (km) */
6.573230396213189E-07, /* h = e sin(periapsis longitude)*/
-3.834742374741285E-06, /* k = e cos(periapsis longitude)*/
1.465930214018767E+02 * PI / 180., /* l = mean longitude (deg) */
2.874273755616854E-06, /* p = tan(i/2) sin(node) */
1.786179828249530E-06, /* q = tan(i/2) cos(node) */
3.711667877073790E-05 * PI / 180., /* apsis rate (deg/sec) */
7.245737665179854E-03 * PI / 180., /* mean motion (deg/sec) */
-3.692848989739440E-05 * PI / 180., /* node rate (deg/sec) */
4.058266021370071E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
8.353762557532015E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 635, /* Daphnis SAT363eq_b: for 2010 Jan 1 and later only! */
2451545.0, /* 2000 Jan 1.5: element epoch Julian date */
1.365074939615504E+05, /* a = semi-major axis (km) */
-1.315672990237585E-05, /* h = e sin(periapsis longitude)*/
9.642045594783008E-06, /* k = e cos(periapsis longitude)*/
1.715596048001493E+02 * PI / 180., /* l = mean longitude (deg) */
7.531461278368427E-06, /* p = tan(i/2) sin(node) */
1.795515998708297E-07, /* q = tan(i/2) cos(node) */
3.436668768688540E-05 * PI / 180., /* apsis rate (deg/sec) */
7.013639183255008E-03 * PI / 180., /* mean motion (deg/sec) */
-3.419991514627601E-05 * PI / 180., /* node rate (deg/sec) */
4.058266021370071E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
8.353762557532015E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 706, /* Cordelia URA091*/
2446450.0, /* 1986 Jan 19.5: element epoch Julian date */
4.975278376008903E+04, /* a = semi-major axis (km) */
3.397026389377096E-05, /* h = e sin(periapsis longitude)*/
-2.515254211787496E-04, /* k = e cos(periapsis longitude)*/
7.000215607027029E+01 * PI / 180., /* l = mean longitude (deg) */
3.704615503525648E-04, /* p = tan(i/2) sin(node) */
5.853261080355042E-04, /* q = tan(i/2) cos(node) */
1.738799696981362E-05 * PI / 180., /* apsis rate (deg/sec) */
1.243656183299048E-02 * PI / 180., /* mean motion (deg/sec) */
-1.736377492435019E-05 * PI / 180., /* node rate (deg/sec) */
7.731359116506646E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
1.517445781731228E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 707, /* Ophelia URA091*/
2446450.0, /* 1986 Jan 19.5: element epoch Julian date */
5.377236269476546E+04, /* a = semi-major axis (km) */
-2.150301507347647E-04, /* h = e sin(periapsis longitude)*/
-9.999740581692736E-03, /* k = e cos(periapsis longitude)*/
2.980775969867487E+02 * PI / 180., /* l = mean longitude (deg) */
-2.020628913672490E-05, /* p = tan(i/2) sin(node) */
-3.602825478615738E-04, /* q = tan(i/2) cos(node) */
1.324712040631912E-05 * PI / 180., /* apsis rate (deg/sec) */
1.106966008118268E-02 * PI / 180., /* mean motion (deg/sec) */
-1.323133607399601E-05 * PI / 180., /* node rate (deg/sec) */
7.731359116506646E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
1.517445781731228E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 708, /* Bianca URA091*/
2446450.0, /* 1986 Jan 19.5: element epoch Julian date */
5.916601845295852E+04, /* a = semi-major axis (km) */
8.477231065799786E-04, /* h = e sin(periapsis longitude)*/
-1.956287335001066E-04, /* k = e cos(periapsis longitude)*/
2.399994222705358E+02 * PI / 180., /* l = mean longitude (deg) */
1.589300498661261E-03, /* p = tan(i/2) sin(node) */
6.379647873951716E-05, /* q = tan(i/2) cos(node) */
9.467105548594393E-06 * PI / 180., /* apsis rate (deg/sec) */
9.587823207439880E-03 * PI / 180., /* mean motion (deg/sec) */
-9.457950543934906E-06 * PI / 180., /* node rate (deg/sec) */
7.731359116506646E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
1.517445781731228E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 709, /* Cressida URA091*/
2446450.0, /* 1986 Jan 19.5: element epoch Julian date */
6.176701274125071E+04, /* a = semi-major axis (km) */
1.280325717493410E-04, /* h = e sin(periapsis longitude)*/
-3.492016953899938E-04, /* k = e cos(periapsis longitude)*/
1.744231642592986E+01 * PI / 180., /* l = mean longitude (deg) */
-8.721221306573636E-05, /* p = tan(i/2) sin(node) */
-5.691312570236423E-05, /* q = tan(i/2) cos(node) */
8.142357893631056E-06 * PI / 180., /* apsis rate (deg/sec) */
8.988222143978887E-03 * PI / 180., /* mean motion (deg/sec) */
-8.135007925901379E-06 * PI / 180., /* node rate (deg/sec) */
7.731359116506646E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
1.517445781731228E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 710, /* Desdemona URA091*/
2446450.0, /* 1986 Jan 19.5: element epoch Julian date */
6.265802480732047E+04, /* a = semi-major axis (km) */
6.122707189532604E-05, /* h = e sin(periapsis longitude)*/
-7.493551564088767E-05, /* k = e cos(periapsis longitude)*/
3.140089739140928E+02 * PI / 180., /* l = mean longitude (deg) */
-8.205209935503686E-04, /* p = tan(i/2) sin(node) */
2.858562925749050E-04, /* q = tan(i/2) cos(node) */
7.743633229159851E-06 * PI / 180., /* apsis rate (deg/sec) */
8.796938545302438E-03 * PI / 180., /* mean motion (deg/sec) */
-7.736867825787147E-06 * PI / 180., /* node rate (deg/sec) */
7.731359116506646E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
1.517445781731228E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 711, /* Juliet URA091*/
2446450.0, /* 1986 Jan 19.5: element epoch Julian date */
6.435798256249492E+04, /* a = semi-major axis (km) */
5.727123336968831E-04, /* h = e sin(periapsis longitude)*/
2.769692434848892E-04, /* k = e cos(periapsis longitude)*/
3.086610831200759E+02 * PI / 180., /* l = mean longitude (deg) */
1.979873455981514E-06, /* p = tan(i/2) sin(node) */
-3.519679830363237E-04, /* q = tan(i/2) cos(node) */
7.050789555402506E-06 * PI / 180., /* apsis rate (deg/sec) */
8.450533525589351E-03 * PI / 180., /* mean motion (deg/sec) */
-7.044928085318312E-06 * PI / 180., /* node rate (deg/sec) */
7.731359116506646E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
1.517445781731228E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 712, /* Portia URA091*/
2446450.0, /* 1986 Jan 19.5: element epoch Julian date */
6.609699016546280E+04, /* a = semi-major axis (km) */
-1.561120967532852E-05, /* h = e sin(periapsis longitude)*/
-1.037014963876101E-05, /* k = e cos(periapsis longitude)*/
3.408196917514196E+02 * PI / 180., /* l = mean longitude (deg) */
-6.171045740059509E-04, /* p = tan(i/2) sin(node) */
-3.299300587868204E-05, /* q = tan(i/2) cos(node) */
6.422466432321616E-06 * PI / 180., /* apsis rate (deg/sec) */
8.119056168010097E-03 * PI / 180., /* mean motion (deg/sec) */
-6.417420983992342E-06 * PI / 180., /* node rate (deg/sec) */
7.731359116506646E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
1.517445781731228E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 713, /* Rosalind URA091*/
2446450.0, /* 1986 Jan 19.5: element epoch Julian date */
6.992700696485957E+04, /* a = semi-major axis (km) */
-1.403276497951949E-06, /* h = e sin(periapsis longitude)*/
-2.648962937429079E-04, /* k = e cos(periapsis longitude)*/
2.895216219202660E+02 * PI / 180., /* l = mean longitude (deg) */
1.425386769737830E-04, /* p = tan(i/2) sin(node) */
1.380714624815777E-03, /* q = tan(i/2) cos(node) */
5.273919837749587E-06 * PI / 180., /* apsis rate (deg/sec) */
7.460999947254308E-03 * PI / 180., /* mean motion (deg/sec) */
-5.270264644406115E-06 * PI / 180., /* node rate (deg/sec) */
7.731359116506646E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
1.517445781731228E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 714, /* Belinda URA091*/
2446450.0, /* 1986 Jan 19.5: element epoch Julian date */
7.525599298568144E+04, /* a = semi-major axis (km) */
-1.133077752423965E-04, /* h = e sin(periapsis longitude)*/
9.095450345916166E-05, /* k = e cos(periapsis longitude)*/
3.189638319876507E+02 * PI / 180., /* l = mean longitude (deg) */
-2.319689561589446E-04, /* p = tan(i/2) sin(node) */
1.836879475556537E-04, /* q = tan(i/2) cos(node) */
4.080592112111099E-06 * PI / 180., /* apsis rate (deg/sec) */
6.682410769071078E-03 * PI / 180., /* mean motion (deg/sec) */
-4.078118716334471E-06 * PI / 180., /* node rate (deg/sec) */
7.731359116506646E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
1.517445781731228E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 715, /* Puck URA091*/
2446450.0, /* 1986 Jan 19.5: element epoch Julian date */
8.600500570186481E+04, /* a = semi-major axis (km) */
2.408105269975341E-05, /* h = e sin(periapsis longitude)*/
4.402601703153761E-05, /* k = e cos(periapsis longitude)*/
3.316332080099892E+02 * PI / 180., /* l = mean longitude (deg) */
-2.920341971029460E-03, /* p = tan(i/2) sin(node) */
-1.546045006884095E-04, /* q = tan(i/2) cos(node) */
2.563927692592904E-06 * PI / 180., /* apsis rate (deg/sec) */
5.469265726829639E-03 * PI / 180., /* mean motion (deg/sec) */
-2.562898939602568E-06 * PI / 180., /* node rate (deg/sec) */
7.731359116506646E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
1.517445781731228E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 725, /* Perdita URA091*/
2453243.0, /* 2004 Aug 25.5: element epoch Julian date */
7.724773127464541E+04, /* a = semi-major axis (km) */
1.390656943538988E-02, /* h = e sin(periapsis longitude)*/
3.764212415028709E-03, /* k = e cos(periapsis longitude)*/
3.595150462692501E+01 * PI / 180., /* l = mean longitude (deg) */
-3.980139862871680E-03, /* p = tan(i/2) sin(node) */
2.570818282326076E-03, /* q = tan(i/2) cos(node) */
7.254635422562736E-06 * PI / 180., /* apsis rate (deg/sec) */
6.530622640638519E-03 * PI / 180., /* mean motion (deg/sec) */
-1.264570087799819E-06 * PI / 180., /* node rate (deg/sec) */
7.731359116506646E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
1.517445781731228E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 726, /* Mab URA091*/
2453243.0, /* 2004 Aug 25.5: element epoch Julian date */
9.775566743468499E+04, /* a = semi-major axis (km) */
-4.588659276539662E-03, /* h = e sin(periapsis longitude)*/
1.692530123450800E-04, /* k = e cos(periapsis longitude)*/
1.541172205352909E+02 * PI / 180., /* l = mean longitude (deg) */
-6.759365158371933E-04, /* p = tan(i/2) sin(node) */
1.062018029025279E-03, /* q = tan(i/2) cos(node) */
2.045092348282713E-06 * PI / 180., /* apsis rate (deg/sec) */
4.514456799305884E-03 * PI / 180., /* mean motion (deg/sec) */
-1.920887916143170E-06 * PI / 180., /* node rate (deg/sec) */
7.731359116506646E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
1.517445781731228E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 727, /* Cupid URA091*/
2453243.0, /* 2004 Aug 25.5: element epoch Julian date */
7.450315104822017E+04, /* a = semi-major axis (km) */
1.837706282342717E-03, /* h = e sin(periapsis longitude)*/
1.041837588715111E-03, /* k = e cos(periapsis longitude)*/
2.341997642137053E+02 * PI / 180., /* l = mean longitude (deg) */
-2.742799982489807E-04, /* p = tan(i/2) sin(node) */
-1.085742482179855E-03, /* q = tan(i/2) cos(node) */
4.009533113969465E-06 * PI / 180., /* apsis rate (deg/sec) */
6.799110491893427E-03 * PI / 180., /* mean motion (deg/sec) */
-3.448340803322791E-06 * PI / 180., /* node rate (deg/sec) */
7.731359116506646E+01 * PI / 180., /* Laplacian plane pole ra (deg) */
1.517445781731228E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
/* NOTE that in the following elements for Triton, I */
/* reversed the signs for p and q from the original values. */
/* That led to results matching Horizons, my own derivation */
/* from observations, and 'triton.cpp'... pretty closely. I */
/* wouldn't be amazed if there's something else going on as */
/* well, but if so, it's a much lesser effect. */
{ 801, /* Triton, aka Neptune I: NEP050 */
2447763.5, /* 1989 Aug 25: element epoch Julian date */
3.547591460000000E+05, /* a = semi-major axis (km) */
2.183485420000000E-06, /* h = e sin(periapsis longitude)*/
-1.543648510000000E-05, /* k = e cos(periapsis longitude)*/
-7.672436890000000E+01 * PI / 180., /* l = mean longitude (deg) */
-2.818138250000000E-02, /* p = tan(i/2) sin(node) */
2.030103396000000E-01, /* q = tan(i/2) cos(node) */
1.211953824000000E-08 * PI / 180., /* apsis rate (deg/sec) */
-7.089961076000000E-04 * PI / 180., /* mean motion (deg/sec) */
1.657793254000000E-08 * PI / 180., /* node rate (deg/sec) */
2.989472940000000E+02 * PI / 180., /* Laplacian plane pole ra (deg) */
4.331890600000000E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 803, /* Naiad, a.k.a. 1989N6: NEP050 */
2447757.0, /* 1989 Aug 18.5: element epoch Julian date */
4.822701435905355E+04, /* a = semi-major axis (km) */
3.620224770838396E-04, /* h = e sin(periapsis longitude)*/
1.156185304588290E-05, /* k = e cos(periapsis longitude)*/
6.810339767839658E+01 * PI / 180., /* l = mean longitude (deg) */
3.452822063733985E-02, /* p = tan(i/2) sin(node) */
2.290770169216655E-02, /* q = tan(i/2) cos(node) */
1.964161049323076E-05 * PI / 180., /* apsis rate (deg/sec) */
1.415326558087714E-02 * PI / 180., /* mean motion (deg/sec) */
-1.985180471594082E-05 * PI / 180., /* node rate (deg/sec) */
2.993634890000000E+02 * PI / 180., /* Laplacian plane pole ra (deg) */
4.344909600000000E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 804, /* Thalassa, a.k.a. 1989N5: NEP050 */
2447757.0, /* 1989 Aug 18.5: element epoch Julian date */
5.007495130640859E+04, /* a = semi-major axis (km) */
1.881434320556790E-04, /* h = e sin(periapsis longitude)*/
1.033517936279606E-04, /* k = e cos(periapsis longitude)*/
2.475810361721285E+02 * PI / 180., /* l = mean longitude (deg) */
1.808988491806543E-03, /* p = tan(i/2) sin(node) */
-2.572520444193769E-04, /* q = tan(i/2) cos(node) */
1.745544005794959E-05 * PI / 180., /* apsis rate (deg/sec) */
1.337678870805562E-02 * PI / 180., /* mean motion (deg/sec) */
-1.746377282651943E-05 * PI / 180., /* node rate (deg/sec) */
2.993634890000000E+02 * PI / 180., /* Laplacian plane pole ra (deg) */
4.344909600000000E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 805, /* Despina, a.k.a. 1989N3: NEP050 */
2447757.0, /* 1989 Aug 18.5: element epoch Julian date */
5.252607405757254E+04, /* a = semi-major axis (km) */
2.232930551031250E-04, /* h = e sin(periapsis longitude)*/
-1.115774312255063E-05, /* k = e cos(periapsis longitude)*/
9.311343295481528E+01 * PI / 180., /* l = mean longitude (deg) */
1.944862825322830E-04, /* p = tan(i/2) sin(node) */
-5.200679669272585E-04, /* q = tan(i/2) cos(node) */
1.475565828888696E-05 * PI / 180., /* apsis rate (deg/sec) */
1.245059755574818E-02 * PI / 180., /* mean motion (deg/sec) */
-1.476785707594837E-05 * PI / 180., /* node rate (deg/sec) */
2.993634890000000E+02 * PI / 180., /* Laplacian plane pole ra (deg) */
4.344909600000000E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 806, /* Galatea, a.k.a. 1989N4: NEP050 */
2447757.0, /* 1989 Aug 18.5: element epoch Julian date */
6.195297903638693E+04, /* a = semi-major axis (km) */
1.674342888688514E-05, /* h = e sin(periapsis longitude)*/
-3.311081056771463E-05, /* k = e cos(periapsis longitude)*/
5.448813192644227E+01 * PI / 180., /* l = mean longitude (deg) */
4.358773699437865E-04, /* p = tan(i/2) sin(node) */
-3.132950150251619E-04, /* q = tan(i/2) cos(node) */
8.264989830842901E-06 * PI / 180., /* apsis rate (deg/sec) */
9.718285365249440E-03 * PI / 180., /* mean motion (deg/sec) */
-8.284262531923991E-06 * PI / 180., /* node rate (deg/sec) */
2.993634890000000E+02 * PI / 180., /* Laplacian plane pole ra (deg) */
4.344909600000000E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 807, /* Larissa, a.k.a. 1989N2: NEP050 */
2447757.0, /* 1989 Aug 18.5: element epoch Julian date */
7.354791709303492E+04, /* a = semi-major axis (km) */
5.742600597431634E-04, /* h = e sin(periapsis longitude)*/
-1.269545891017604E-03, /* k = e cos(periapsis longitude)*/
1.926654222778896E+02 * PI / 180., /* l = mean longitude (deg) */
5.395612235869184E-04, /* p = tan(i/2) sin(node) */
1.702120710409934E-03, /* q = tan(i/2) cos(node) */
4.526939181068548E-06 * PI / 180., /* apsis rate (deg/sec) */
7.512183377052987E-03 * PI / 180., /* mean motion (deg/sec) */
-4.555573945715664E-06 * PI / 180., /* node rate (deg/sec) */
2.993634890000000E+02 * PI / 180., /* Laplacian plane pole ra (deg) */
4.344909600000000E+01 * PI / 180. }, /* Laplacian plane pole dec (deg)*/
{ 808, /* Proteus, a.k.a. 1989N1: NEP050 */
2447757.0, /* 1989 Aug 18.5: element epoch Julian date */
1.176468148802116E+05, /* a = semi-major axis (km) */
5.138756385126203E-04, /* h = e sin(periapsis longitude)*/
-1.319038194876358E-04, /* k = e cos(periapsis longitude)*/
2.214459710358717E+02 * PI / 180., /* l = mean longitude (deg) */
6.691721009767980E-05, /* p = tan(i/2) sin(node) */
-2.147144625701844E-04, /* q = tan(i/2) cos(node) */
8.764111065373391E-07 * PI / 180., /* apsis rate (deg/sec) */
3.712548540365151E-03 * PI / 180., /* mean motion (deg/sec) */
-9.086814828264133E-07 * PI / 180., /* node rate (deg/sec) */
2.993634890000000E+02 * PI / 180., /* Laplacian plane pole ra (deg) */
4.344909600000000E+01 * PI / 180. } /* Laplacian plane pole dec (deg)*/
};
/* In Win32, if this function is in a DLL, we gotta */
/* mention that fact up front. The following #ifdef */
/* lets us do that without confusing OSes that are */
/* blessedly ignorant of the weirdnesses of Windoze DLLs: */
#ifdef _WIN32
#define DLL_FUNC __stdcall
#else
#define DLL_FUNC
#endif
/* Given a JDE and a JPL ID number (see list at the top of this file), */
/* evaluate_rock( ) will compute the J2000 equatorial Cartesian */
/* position for that "rock" and will return 0. Otherwise, it returns */
/* -1 as an error condition. No other errors are returned... though */
/* hypothetically, something indicating you're outside the valid time */
/* coverage for the orbit in question would be nice. */
#ifdef __cplusplus
extern "C" {
#endif
int DLL_FUNC evaluate_rock( const double jde, const int jpl_id,
double *output_vect)
{
int i;
const ROCK *rptr = rocks;
for( i = N_ROCKS; i; i--, rptr++)
if( rptr->jpl_id == jpl_id)
{
const double seconds_per_day = 86400.;
const double dt_seconds = (jde - rptr->epoch_jd) * seconds_per_day;
const double mean_lon =
rptr->mean_lon0 + dt_seconds * rptr->mean_motion;
double avect[3], bvect[3], cvect[3];
double h, k, p, q, tsin, tcos, r, e, omega, true_lon;
double a_fraction, b_fraction, c_fraction, dot_prod;
/* avect is at right angles to Laplacian pole, */
/* but in plane of the J2000 equator: */
avect[0] = -sin( rptr->laplacian_pole_ra);
avect[1] = cos( rptr->laplacian_pole_ra);
avect[2] = 0.;
/* bvect is at right angles to Laplacian pole */
/* _and_ to avect: */
tsin = sin( rptr->laplacian_pole_dec);
tcos = cos( rptr->laplacian_pole_dec);
bvect[0] = -avect[1] * tsin;
bvect[1] = avect[0] * tsin;
bvect[2] = tcos;
/* cvect is the Laplacian pole vector: */
cvect[0] = avect[1] * tcos;
cvect[1] = -avect[0] * tcos;
cvect[2] = tsin;
/* Rotate the (h, k) vector to account for */
/* a constant apsidal motion: */
tsin = sin( dt_seconds * rptr->apsis_rate);
tcos = cos( dt_seconds * rptr->apsis_rate);
h = rptr->k * tsin + rptr->h * tcos;
k = rptr->k * tcos - rptr->h * tsin;
/* I'm sure there's a better way to do this... */
/* all I do here is to compute the eccentricity */
/* and omega, a.k.a. longitude of perihelion, */
/* and do a first-order correction to get the */
/* 'actual' r and true longitude values. */
e = sqrt( h * h + k * k);
omega = atan2( h, k);
true_lon = mean_lon + 2. * e * sin( mean_lon - omega)
+ 1.25 * e * e * sin( 2. * (mean_lon - omega));
r = rptr->a * (1. - e * e) / (1 + e * cos( true_lon - omega));
/* Just as we rotated (h,k), we gotta rotate */
/* the (p,q) vector to account for precession */
/* in the Laplacian plane: */
tsin = sin( dt_seconds * rptr->node_rate);
tcos = cos( dt_seconds * rptr->node_rate);
p = rptr->q * tsin + rptr->p * tcos;
q = rptr->q * tcos - rptr->p * tsin;
/* Now we evaluate the position in components */
/* along avect, bvect, cvect. I derived the */
/* formulae from scratch... sorry I can't */
/* give references: */
tsin = sin( true_lon);
tcos = cos( true_lon);
dot_prod = 2. * (q * tsin - p * tcos) / (1. + p * p + q * q);
a_fraction = tcos + p * dot_prod;
b_fraction = tsin - q * dot_prod;
c_fraction = dot_prod;
/* Now that we've got components on each axis, */
/* the remainder is trivial: */
for( i = 0; i < 3; i++)
output_vect[i] = r * (a_fraction * avect[i]
+ b_fraction * bvect[i]
+ c_fraction * cvect[i]);
return( 0);
}
return( -1);
}
#ifdef __cplusplus
}
#endif
#ifdef TEST_PROGRAM
/* A simple piece of test code that, given a JPL ID and a JD, prints out */
/* the result of evaluate_rock. Comparison to Horizons is straightforward, */
/* and indicates agreement to better than a meter. */
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define AU_IN_KM 1.495978707e+8
int main( const int argc, const char **argv)
{
double vect[3], r2 = 0.;
int i, jpl_id = atoi( argv[2]);
if( evaluate_rock( atof( argv[1]), jpl_id, vect))
printf( "Failed\n");
else
{
printf( "%f %f %f\n", vect[0], vect[1], vect[2]);
for( i = 0; i < 3; i++)
r2 += vect[i] * vect[i];
printf( "\n%lf\n", sqrt( r2));
printf( "%.9f %.9f %.9f : %.9f\n", vect[0] / AU_IN_KM,
vect[1]/ AU_IN_KM, vect[2] / AU_IN_KM,
sqrt( r2) / AU_IN_KM);
}
return( 0);
}
#endif
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