The Ephemerides server MULTI-SAT

Theories used to model the motion of the satellites Our computations for the ephemerides are based on the most precise satellite theories and the most perfect calculating methods. Parameters and constants (which are provided) for the satellite motions are defined on the basis of all published observations. We follow the IAU recommendations concerning the reference frames. Summary: The three different groups of satellites. Original numerical models of motion for outer planetary satellites. References on theories and models for each natural satellites. The planetary theories used for satellites ephemerides purpose.   The natural planetary satellites are of different kinds: the Galileans, as large as small planets, are very different from the irregular outer satellites similar to asteroids. Besides the physical nature of the satellites, their dynamics are very different too. The natural planetary satellites are divided into the following three groups: Major satellites. These are the most massive satellites. They move on almost circular orbits near the planet's equatorial plane. The motion of major satellites is influenced by the planet's oblateness, solar and planetary perturbations and mutual interactions among satellites themselves. Calculation of mutual interactions of major satellites is very complicated because of resonances between their mean motions. For major satellites, as a rule, analytical theories have been first elaborated. Since major satellites are relatively bright, their observations have a very good precision and the number of observations may be as much as tens of thousands. Analytical theories of motion are very complicated also. One has to take into account perturbations from different factors including mutual resonant interactions. influence of satellite rotation and tidal effects on its orbital motion. Note that the satellites of Mars, even they are small, are considered as major satellites. Inner satellites (satellites close to their planet). They are much smaller than the major satellites but they also move in almost circular orbits near the planet's equatorial plane. Orbits of the inner satellites are mainly perturbed by planet's oblateness and attraction of major satellites. Solar perturbations are very faint. Mutual interactions are significant only in the case of the coorbital satellites of Saturn. Because of the proximity of a bright planet and because of the small sizes of the inner satellites themselves, their observations are very difficult abd less precise than those of major satellites. So the motion of the inner satellites is mostly modelled by a Keplerian orbit having uniformly precessing pericenter and node. Such an analytical theory of motion is quite simple. The rates of precession of pericenter and node are usually defined from observations, not from the theory of perturbations. In this case, mean motions and semi-major axes are defined from observations independently. Outer satellites (irregular). These are fairly small bodies of our solar system. They look like asteroids but their orbits have large eccentricities. Orbit planes may have large inclinations relative to the planet's equatorial plane. Their motion is greatly influenced by solar perturbations. When making high-precision models of their motion, one has to take into account planet's obliquity, perturbations from major satellites and other planets. The building of analytical theories for outer satellites is theoretically possible (and there were such attempts), but large solar perturbations make this process very difficult. Orbital periods of outer satellites are from several months to several years. During the whole period of their observations these satellites made less than two hundred revolutions and the sample of data is not the best. Therefore, modern methods of numerical integration allow successful modelling of motion of outer satellites based on their observations. We developed original models for the motion of these bodies. Original numerical models. For the ephemerides of all outer planetary satellites, original numerical models of motion are used which are based on all observations available in our database at the time of its last update (Emelyanov, 2005; Emel'yanov, Kanter, 2005). To calculate ephemerides of outer planetary satellites, a representation of satellite planetocentric rectangular coordinates by Chebyshev polynomials was used. For all outer satellites, the interval where coordinates were approximated by series was chosen to be 20 days, while the polynomial degree was 13. Ephemerides of all outer satellites are calculated using models built for given time intervals. If the user wants to get ephemerides for a date within such interval, the ephemerides are calculated using our numerical model and the limits of the interval are indicated. If the user enters a date out of the interval of our numerical models, the calculating program uses approximated Keplerian orbits which give some representation of the orbit but do not provide a good precision. For different satellites, the intervals of the numerical models are different and are indicated. Initial conditions of integration of the equations of the motion of the satellite defined from observations are given below. These data correspond to our model of satellite motion, and to the adopted constants referred to the planets and satellites.They correspond to our used methods and programs of numerical integration. When used with other tools and other values of constants, the provided initial conditions may lead to results slightly different from our ephemerides. However, our initial conditions may undoubtedly be used as an initial approximation for subsequent improvement of orbits of outer planetary satellites.   Initial conditions for the outer satellites of: Dates of the first and the last observations used for ephemerides and intervals of validity of the numerical ephemerides for the satellites of: Jupiter Jupiter Saturne Saturne Uranus Uranus Neptune Neptune Information on the natural satellites dynamical models and theories used in the MULTI-SAT ephemerides server.   Satellites of Mars Satellites Ephemeris designation in MULTI-SAT Bibliographic references Observations used for ephemeris fitting Time periode of the ephemeris representa- tion Dynamical model Satellites of Mars Lainey 2020 Lainey et al., 2020 1877 to 1014 Ground-based, recent spacecraft observations and the very last MEX SRC data. 1869/12/31 to 2060/01/16 Numerical integration   Lainey 2015 Arlot et al., 2017 1877 to 2014 Ground-based, recent spacecraft observations and the very last MEX SRC data. 1869/12/31 to 2123/07/03 Numerical integration   Lainey 2007 Lainey et al., 2007 1877 to 2005 Ground-based and recent spacecraft observations by Mars Global Surveyor and Mars Express. Limited only by the planetary ephemerides period Analytical representa- tion of numerical integration   Kudryavtsev 1997 Kudryavtsev et al.,1997 1877-1988 Ground-based and TV measurements from the spacecrafts Mariner 9, Viking 1, 2 and Phobos 2. Limited only by the planetary ephemerides period Analytical theory and representa- tion   Chapront -Touze 1990 Chapront-Touze, 1990 1877-1988 Ground-based and observations from the spacecrafts Mariner 9, Viking 1, 2 and Phobos 2. Limited only by the planetary ephemerides period Analytical theory and representa- tion Galilean satellites of Jupiter Satellites Ephemeris designation in MULTI-SAT Biblio- graphic references Observations used for ephemeris fitting Time periode of the ephemeris representation Dynamical model Galilean satellites of Jupiter J1-J4 Lainey 2009, V2.0 Lainey et al., 2009 1891-2007 Ground-based photographic data, transit circle and mutual events observations 1973-2003 01/06/1903 at 12h to 13/02/2043 at 12h, TDB Numerical integration   J1-J4 Lainey 2004, V1.1 Lainey V., Duriez L., Vienne A., 2004; Lainey V., Arlot J.-E., Vienne A., 2004 1891-2003 Ground-based photographic data and transit circle Limited only by the planetary ephemerides period Analytical representa- tion of numerical integration   J1-J4 Arlot 1982, G-5 Arlot, 1982 1891-1978 Earth-based photographic observations Limited only by the planetary ephemerides period Analytical theory and representa- tion   J1-J4 Lieske 1998, E-5 Lieske, 1998 1967-1991: Earth-based photographic observations 1993-1995: CCD data from Flagstaff 1652-1983: Eclipse timings 1973-1991: Mutual event data; Voyager data. Limited only by the planetary ephemerides period Analytical theory and representa- tion Inner satellites of Jupiter Satellites Ephemeris designation in MULTI-SAT Biblio- graphic references Observations used for ephemeris fitting Time periode of the ephemeris representa- tion Dynamical model Small inner satellites of Jupiter J5,J14-J16 Adjusted on (Jacobson, 2009) Emel'yanov 2015; Jacobson, 2013 Precessing ellipses fitted by Emel'yanov (2015) to the JPL ephemerides based on a variety of Earth-based and spacecraft observations (Jacobson, 2013). Limited only by the planetary ephemerides period Precessing ellipses fitted by Emel'yanov (2015) to JPL ephemerides   J5,J14-J16 Avdyushev, Ban'shikova 2008 Avdyushev, Ban'shikova, 2008 Earth-based observations. Amalthea: 1954-2001 Thebe: 1995-2001 Adrastea:1988-2000 Metis:1988-2000 1954/02/14 to 2034/12/04 Numerical integration Outer irregular satellites of Jupiter Satellites Ephemeris designation in MULTI-SAT Biblio- graphic references Observations used for ephemeris fitting Time periode of the ephemeris representa- tion Dynamical model Eight outer satellites of Jupiter No choice Emelyanov, 2005 Earth-based observations 1905-2011. 1905/01/01.0 to 2025/07/10.0 Numerical integration New outer satellites of Jupiter No choice Emel'yanov, Kanter, 2005. A variety of intervals for different satellites (from 30 days to 12 years) 1974/12/31.0 to 2027/02/16.0 Numerical integration Main satellites of Saturn Satellites Ephemeris designation in MULTI-SAT Biblio- graphic references Observations used for ephemeris fitting Time periode of the ephemeris representa- tion Dynamical model Major satellites of Saturn S1-S8 Lainey 2015 Arlot et al., 2017 Earth-based astrometric from 1885 to 2009. Mutual phenomena observations in 1995 and in 2009. Cassini imaging 2004-2012 1950/01/01.0 to 2048/01/01.5 Numerical integration.   S1-S8 Lainey 2012 Lainey et al., 2012 Earth-based astrometric from 1874 to 2009. Mutual phenomena observations in 1995 and in 2009. 1875/01/08.8 to 2022/07/10.8 Numerical integration.   S1-S8 Vienne, Duriez 1995, 1997 Vienne and Duriez, 1995; Duriez and Vienne, 1997 Earth-based astrometric 1874-1989 Limited only by the planetary ephemerides period Analytical (synthetic) theory   S1-S8 Dourneau 1987 Dourneau G., 1987 Earth-based astrometric 1874-1986 Limited only by the planetary ephemerides period Analytical theory   S1-S8 Harper, Taylor 1993, 1997 Harper and Taylor, 1993; Taylor et al., 1987 Earth-based astrometric 1874-1986 Limited only by the planetary ephemerides period Analytical theory Inner satellites of Saturn Satellites Ephemeris designation in MULTI-SAT Bibliographic references Observations used for ephemeris fitting Time periode of the ephemeris representa- tion Dynamical model Helene S12, Telesto S13, Calypso S14, S12-S14 Lainey 2015 Arlot et al., 2017 Earth-based 1980-1996 Cassini imaging 2004-2012 1950/01/01.0 to 2049/05/16.7 Numerical integration.   S12-S14 Oberti, Vienne 2003 Oberti, Vienne, 2003 Earth-based 1980-1996 Limited only by the planetary ephemerides period Analytical theory   S12-S14 Oberti 1990 Oberti, 1990 Earth-based 1980-1987 Limited only by the planetary ephemerides period Analytical theory S15-S18 S15 Atlas, S16 Prometheus, S17 Pandora, S18 Pan S15-S18 Jacobson 2008 Jacobson et al., 2008 Cassini imaging 2004-2012 Limited only by the planetary ephemerides period Precessing ellipse   S15-S18 Porco 2005 Porco et al., 2005 Cassini Imaging 2004-2012 Limited only by the planetary ephemerides period Precessing ellipse S34 Polydeuce S34 Lainey 2015 Arlot et al., 2017 Earth-based 1980-1996, Cassini imaging 2004-2012 1950/01/01.0 to 2049/05/16.7 Numerical integration   S34 Lacobson 2008 Jacobson et al., 2008 Cassini imaging 2004-2012 Limited only by the planetary ephemerides period Precessing ellipse Outer irregular satellites of Saturn Satellites Ephemeris designation in MULTI-SAT Biblio- graphic references Observations used for ephemeris fitting Time periode of the ephemeris representa- tion Dynamical model Phoebe Any choice Desmars et al., 2013 Earth-based 1898-2012, Cassini imaging 2004-2012 1875/07/01.0 to 2022/06/30.0 Numerical integration. New outer satellites of Saturn Any choice Emel'yanov, Kanter, 2005. A variety of intervals for different satellites (from 30 days to 12 years) 1974/12/29.0 to 2028/03/20.0 Numerical integration Satellites of Uranus Satellites Ephemeris designation in MULTI-SAT Bibliographic references Observations used for ephemeris fitting Time periode of the ephemeris representa- tion Dynamical model Major satellites of Uranus U1-U5 Lainey 2015 Lainey, 2008 & Arlot et al., 2017 Earth-based 1874-2012, Voyager 2, Mutual events 2007-2008 1847/01/00.5 to 2145/01/02.0 Numerical integration   U1-U5 Emelyanov, Nikonchuk 2013 Emelyanov, Nikonchuk, 2013 Earth-based 1847-2008, Voyager 2, Mutual events 2007-2008 1787/02/12.0 to 2032/01/09.0 Numerical integration   U1-U5 Laskar, Jacobson 1987, GUST86 Laskar, Jacobson, 1987 Earth-based 1911-1986, Voyager 2 Limited only by the used planetary ephemerides period Analytical theory Inner satellites of Uranus Any choice Jacobson, 1998; Pascu et al., 1998. HST 1994, Voyager-2 1985-1986 Limited only by the planetary ephemerides period Precessing ellipse New outer satellites of Uranus Any choice Emel'yanov, Kanter, 2005. Earth-based observations. For U16-U17: 1984-2012, U18-U20: 1999-2010, U21-U24: 2001-2010 1974/12/30.0 to 2025/06/25.0 Numerical integration Satellites of Neptune Satellites Ephemeris designation in MULTI-SAT Bibliographic references Observations used for ephemeris fitting Time periode of the ephemeris representation Dynamical model Satellite of Neptune Triton Triton Emelyanov 2015 Emelyanov, Samorodov, 2015 Earth-based 1847 to 2012, Voyager-2 Limited only by the planetary ephemerides period Analytical theory   Triton Jacobson 2009 Jacobson, 2009; Emelyanov, Samorodov, 2015 Precessing ellipses fitted by Emelyanov, Samorodov (2015) to the JPL ephemerides based on a variety of Earth-based and spacecraft observations (Jacobson, 2009). Limited only by the planetary ephemerides period Precessing ellipse   Triton Zhang 2014 Zhang et al., 2014 Earth-based 1975 to 2006 1975/01/01.0 to 2033/01/03.0 Numerical integration Satellite of Neptune Nereid Any choice Emelyanov, Arlot, 2011 Earth-based 1949 to 2010, Voyager-2 1920/11/29.0 to 2029/05/01.0 Numerical integration Inner satellites of Neptune Any choice Owen et al., 1991; Pascu et al., 2004; Jacobson, 2009 Voyager-2, HST 1997 Limited only by the planetary ephemerides period Precessing ellipse Outer satellites of Neptune Any choice Emel'yanov, Kanter, 2005. Earth-based 1999 to 2009 1974/12/31.0 to 2026/03/13.0 Numerical integration Satellites of Pluto Satellites Ephemeris designation in MULTI-SAT Bibliographic references Observations used for ephemeris fitting Time periode of the ephemeris representation Dynamical model Satellites of Pluto P1-P3 Beauvalet 2013 Beauvalet et al., 2013 HST, VLT-UT4 Charon: 1992-2010 Nix, Hydra: 2002-2006 1950/01/01.1 to 2029/12/31.7 Numerical integration   P1-P3 Buie 2006 Buie et al., 2006 HST 2002, 2003 Limited only by the planetary ephemerides period Precessing ellipse   P1-P3 Tholen 2008 Tholen et al., 2008 For Charon: speckle interferometric data 1985. For Charon Nix, Hydra: Magellan telescope, VLT 2002-2006 Limited only by the planetary ephemerides period Precessing ellipse References Arlot, J. -E. New constants for Sampson-Lieske theory of the Galilean Satellites of Jupiter. Astronomy and Astrophysics. 1982. V. 107. N. 2. P. 305-310. Arlot J.E., Cooper N., Emelyanov N., Lainey V., Meunier L.E., Murray C., Oberst J., Pascu D., Pasewaldt A., Robert V., Tajeddine R., Willner K. (2017) Natural satellites astrometric data from either space probes and ground-based observatories produced by the European consortium "ESPaCE". Notes Scientifiques et Techniques de l'Institut de mécanique céleste. 2017. S105. P. 1-49. Avdyushev V. A., Ban'shikova M. A. (2008) Determination of the orbits of inner Jupiter satellites Solar System Research. V. 42. P.296-318. Beauvalet L., Robert V., Lainey V., Arlot J.-E., Colas, F. (2013) ODIN: a new model and ephemeris for the Pluto system. Astronomy & Astrophysics. V. 553, id.A14, 22 pp. Buie M. W., Grundy W. M., Young E. F., Young L. A., Stern S. A. (2006) Orbits and photometry of Pluto's satellites: Charon, S/2005 P1, and S/2005 P2. The Astronomical Journal. V. 132. N. 1. P. 290-298. Chapront-Touze M. (1990) Orbits of the Martian satellites from ESAPHO and ESADE theories. Astronomy and Astrophysics, vol. 240, p. 159-172. Desmars J., Li S. N., Tajeddine R., Peng Q.Y., Tang Z.H. (2013) Phoebe's orbit from ground-based and space-based observations Astronomy & Astrophysics. V. 553. id. A36. 10 pp. Dourneau G. Ph.D. Thesis (1987) Duriez L., Vienne A. (1997) Theory of motion and ephemerides of Hyperion. Astronomy and Astrophysics. V. 324. P. 366-380. Emelyanov N.V. (2005) Ephemerides of the outer Jovian satellites. Astronomy and Astrophysics. V. 435, p. 1173-1179. Emel'yanov N. V., Kanter A. A. (2005) Orbits of new outer planetary satellites based on observations. Solar System Research. V. 39. N. 2. P. 112-123. Emelyanov N. V., Arlot J.-E. (2011) The orbit of Nereid based on observations. Monthly Notices of the Royal Astronomical Society. V. 417. Issue 1. P. 458-463. Emelyanov N. V., Nikonchuk D.V. (2013) Ephemerides of the main Uranian satellites. Monthly Notices of the Royal Astronomical Society. V. 436. P. 3668-3679. Emel'yanov N. V. (2015) Perturbed motion at small eccentricities Solar System Research. V. 49. No. 5. P. 346-359. Emelyanov N. V., Samorodov M. Yu. (2015) Analytical theory of motion and new ephemeris of Triton from observations Monthly Notices of the Royal Astronomical Society. V. 454. P. 2205-2215. Harper D., Taylor D. B. (1993) The orbits of the major satellites of Saturn. Astronomy and Astrophysics. V. 268. P. 326-349. Jacobson R. A. (1998) The Orbits of the Inner Uranian Satellites from Hubble Space Telescope and Voyager 2 Observations. The Astronomical Journal. V. 115. Issue 3. P. 1195-1199. Jacobson R. A., Spitale J., Porco C. C., Beurle K., Cooper N. J., Evans M. W., Murray C. D. (2008) Revised orbits of Saturn's small inner satellites. Astronomical Journal. V. 135. P. 261-263. Jacobson R. A. (2009) The orbits of the neptunian satellites and the orientation of the pole of Neptune. Astronomical Journal. V. 137. P. 4322-4329. Jacobson, R.A., The orbits of the regular Jovian satellites, their masses, and the gravity field of Jupiter, Proc. Amer. Astron. Soc. DDA Meeting, #44, #402.04, 2013. Kudryavtsev S.M., Kolyuka Y.F., Tikhonov V.F. New Analytical Theory of Motion of Phobos and Deimos for Navigation Support of Mission to Mars // ESA SP-403: Proceedings of the 12th International Symposium on Space Flight Dynamics. 1997. P. 377-382. Lainey V., Duriez L., Vienne A. (2004) New accurate ephemerides for the Galilean satellites of Jupiter. I. Numerical integration of elaborated equations of motion. Astronomy and Astrophysics. V. 420. P. 1171-1183. Lainey V., Arlot J.-E., Vienne A. (2004) New accurate ephemerides for the Galilean satellites of Jupiter. II. Fitting the observations. Astronomy and Astrophysics. V. 427. P. 371-376. Lainey V., Dehant V., Patzold M. (2007) First numerical ephemerides of the Martian moons. Astronomy and Astrophysics. V. 465. p. 1075-1084. Lainey V. (2008) A new dynamical model for the Uranian satellites. Planetary and Space Science. V. 56. P. 1766-1772. Lainey V., Arlot J.-E., Karatekin O., van Hoolst T. (2009) Strong tidal dissipation in Io and Jupiter from astrometric observations. Nature. V. 459. Issue 7249. P. 957-959. Lainey V., Karatekin O., Desmars J., Charnoz S., Arlot J.-E., Emelyanov N., Le Poncin-Lafitte Chr., Mathis S., Remus F., Tobie G., Zahn J.-P. (2012) Strong tidal dissipation in Saturn and constraints on Enceladus' thermal state from astrometry. The Astrophysical Journal. V. 752. Issue 1. Article id. 14 (2012). Lainey V., Pasewaldt A., Robert V., Rosenblatt P., Jaumann R., Oberst J., Roatsch T., Willner K., Ziese R., Thuillot W. (2020). Mars moon ephemerides after 12 years of Mars Express data. eprint arXiv:2009.06482. Laskar J., Jacobson R.A. (1987) GUST86 - an analytical ephemeris of the Uranian satellites. Astronomy and Astrophysics. V. 188. P. 212-224. Lieske J. H. (1998) Galilean satellite ephemerides E5. Astronomy and Astrophysics Supplement Series. V. 129. P. 205-217. Oberti P. (1990) Lagrangian satellites of Tethys and Dione. II - Theory of motion. Astronomy and Astrophysics. V. 228. P. 275-283. Oberti P., Vienne A. (2003) An upgraded theory for Helene, Telesto, and Calypso Astronomy and Astrophysics. V. 397. P. 353-359. Pascu D., Rohde J.R., Seidelmann P.K., Wells E.N., Kowal C.T., Zellner B.H., Storrs A.D., Currie D.G., Dowling D.M. (1998) Hubble Space Telescope Astrometric Observations and Orbital Mean Motion Corrections for the Inner Uranian Satellites. The Astronomical Journal. V. 115. Issue 3. P. 1190-1194. Pascu D., Rohde J. R., Seidelmann P. K., Wells E. N., Hershey John L., Storrs A. D., Zellner B. H., Bosh A. S., Currie D. G., (2004) Hubble Space Telescope Astrometric Observations and Orbital Mean Motion Corrections for the Inner Satellites of Neptune. The Astronomical Journal. V. 127. N. 5. P. 2988-2996. Porco C. C., Baker E., Barbara J., Beurle K., Brahic A., Burns J. A., Charnoz S., Cooper N., Dawson D. D., Del Genio A. D., Denk T., Dones L., Dyudina U., Evans M. W., Giese B., Grazier K., Helfenstein P., Ingersoll A. P., Jacobson R. A., Johnson T. V., McEwen A., Murray C. D., Neukum G., Owen W. M., Perry J., Roatsch T., Spitale J., Squyres S., Thomas P., Tiscareno M., Turtle E., Vasavada A. R., Veverka J., Wagner R., West R. (2005) Cassini Imaging Science: Initial Results on Saturn's Rings and Small Satellites. Science. V. 307. Issue 5713. P. 1226-1236. Taylor D. B., Sinclair A. T., Message P. J. (1987) Corrections to the theory of the orbit of Saturn's satellite Hyperion. Astronomy and Astrophysics. V. 181. P. 383-390. Tholen D.J., Buie M.W., Grundy W.M., Elliott G.T. (2008) Masses of Nix and Hydra. Astronomical Journal. V. 135. P. 777-784. Vienne A., Duriez L. (1995) TASS1.6: Ephemerides of the major Saturnian satellites. Astronomy and Astrophysics. V. 297. P. 588. Zhang H. Y., Shen K. X., Dourneau G., Harper D., Qiao R. C., Xi X. J., Cheng X., Yan D., Li S. N., Wang S. H. (2014) An orbital determination of Triton with the use of a revised pole model. Mon. Not. R. Astron. Soc. 2014. V. 438. P. 1663-1668. Theories used for the planetary motion.. To calculate topocentric or geocentric satellite coordinates, heliocentric rectangular coordinates of the corresponding planet are necessary. It is not essential to use very accurate models of planetary motion to calculate relative coordinates of satellites (satellite / planet, satellite / satellite) but the result on the satellite positions, however, depends on the planetary model. Contrarily, to calculate the absolute coordinates of the satellites (right ascension and declination), the ephemeris used for the planet is very important because its accuracy will be reported on that of the satellite. There will be accumulated errors from both ephemeris (planet + satellite). Following planetary ephemerides made at IMCCE (France), at IAA RAS (Russia), and at JPL (USA) are proposed by our ephemerides server:  1. INPOP19a - IMCCE (Fienga et al., 2019)  2. INPOP17a - IMCCE (Viswanathan, Fienga, Gastineau, Laskar, 2017)  3. INPOP13C - IMCCE (Fienga, Manche, Laskar, Gastineau, Verma, 2014)  4. EPM2017 - IAA RAS http://iaaras.ru/en/dept/ephemeris/epm/2017/  5. DE431 - JPL {Folkner, Williams, Boggs, Park, Kuchynka, 2014)  6. DE441 - JPL {Park et al., 2021)  7. DE405 - JPL {Standish, 1998)  8. DE406 - JPL {Standish, 1998)  9. DE200 - JPL {Standish, 1990) 10. VSOP87 - IMCCE (Bretagnon and Francou, 1988) The user may select any of these planetary ephemerides. Ephemerides intervals when using planetary ephemerides: MJD MJD d m y d m y INPOP19a: -323399 - 426488 ( 0 h 10/06/ 973 - 0 h 25/07/3026) INPOP17a: -323431 - 426521 ( 0 h 09/05/ 973 - 0 h 27/08/3026) INPOP13C: -323431 - 426521 ( 0 h 09/05/ 973 - 0 h 27/08/3026) EPM2017: -26000 - 130000 ( 0 h 10/09/1787 - 0 h 22/10/2214) DE431: covering years -13,200 to +17,191 DE441: -94576 - 124624 ( 0 h 09/12/1599 - 0 h 22/10/2204) (Cropped version) DE405: 4048 - 69808 ( 0 h 17/12/1869 - 0 h 02/01/2050) DE406: 45 - 88068 ( 0 h 01/01/1859 - 0 h 31/01/2099) DE200: 33264 - 69808 ( 0 h 14/12/1949 - 0 h 02/01/2050) VSOP87: 45 - 88068 ( 0 h 01/01/1859 - 0 h 31/12/2099) References to the cited publications. Bretagnon P., Francou G. Planetary theories in rectangular and spherical variables. VSOP87 solutions. Astronomy and Astrophysics. 1988. V. 202. P. 309. Fienga A., Laskar J., Morley T., Manche H., Kuchynka P., Le Poncin-Lafitte C., Budnik F., Gastineau M., Somenzi L. INPOP08, a 4-D planetary ephemeris: from asteroid and time-scale computations to ESA Mars Express and Venus Express contributions. Astronomy and Astrophysics. 2009. V. 507. P. 1675-1686. Fienga A., Laskar J., Kuchynka P., Manche H., Desvignes G., Gastineau M., Cognard, I.; Theureau, G. The INPOP10a planetary ephemeris and its applications in fundamental physics. Celestial Mechanics and Dynamical Astronomy. 2011. V. 111. Issue 3. P.363-385. Fienga A., Manche H., Laskar J., Gastineau M., Verma A. INPOP new release: INPOP13b. 05/2014. eprint arXiv:1405.0484. Fienga A., Deram P., Viswanathan V. , Di Ruscio A. , Bernus L., Durante D., Gastineau M. and Laskar J. INPOP19a planetary ephemerides, 2019. Folkner W.M., Williams J.G., Boggs D.H. The Planetary and Lunar Ephemeris DE421 JPL Interoffice Memorandum IOM 343.R-08-003, 2008. Folkner W.M., Williams J.G., Boggs D.H., Park R.S., Kuchynka P. The Planetary and Lunar Ephemerides DE430 and DE431. IPN Progress Report 42-196, 2014. Park R.S., et al. The JPL Planetary and Lunar Ephemerides DE440 and DE441. The Astronomical Journal, 161:105 (15pp), 2021 March. Pitjeva E.V. Updated IAA RAS Planetary Ephemerides-EPM2011 and Their Use in Scientific Research. Solar System Research. 2013. V. 47. No. 5. P. 386-402. Standish E.M. The observational basis for JPL's DE200, the planetary ephemerides of the Astronomical Almanac. Astronomy and Astrophysics. 1990. V. 233. P. 252. Standish E.M. JPL Planetary and Lunar Ephemerides, DE405/LE405. JPL Interoffice Memorandum 312.F-98-048, 1998. Viswanathan V., Fienga A., Gastineau M., Laskar J. INPOP17a planetary ephemerides. Notes Scientifiques et Techniques de l'Institut de mécanique céleste, (ISSN 1621-3823). N. 108, ISBN 2-910015-79-3. 2017. 39 pp.

The server MULTI-SAT: phenomena and configurations of the planetary satellites.

Information on methods used for calculate special ephemerides Phenomena of the natural planetary satellites The Galilean satellites of Jupiter, the main satellites of Saturn and Uranus. The software allows to calculate the phenomena for any period of time. It allows also to choose the ephemerides used for the calculation. These satellites present phenomena of eclipses and occultations by their planet, transits and shadows on the disk of the planet near every day for Jupiter, every 15 years for Saturn and every 42 years for Uranus (in 2006-2010). In the case of the Jovian systemn one time every six years, during one year, the satellites will occult and eclipse themselves by pairs: these are the mutual phenomena. For the major satellites of Saturn, mutual events occur also every 15 years during only one year. For the major satellites of Uranus, mutual events only every 42 years. Elongations of the satellites The dates of maximum elongation of the satellites are very interesting for programming observations, especially for those satellites too close to their bright planet polluting observations. Thus, the elongation moments are favorable for the observation of some satellites. The calculation software offers the choice of models as in the case of conventional ephemerides. Observations of the coorbital satellites of Saturn. The ephemerides of these satellites were calculated using our ephemerides built with the formulae published in the papers of Yoder et al. (1989) and Nicholson et al. (1992). References to the cited publications. Nicholson P.D., Hamilton D.P., Matthews K., Yoder C.F. New observations of Saturn's coorbital satellites. Icarus. 1992. V. 100. N. 2. P. 464-484. Yoder C.F., Synnott S.P., Salo H. Orbits and masses of Saturn's co-orbiting satellites, Janus and Epimetheus. Astronomical Journal. 1989. V. 98. P. 1875-1889.