Planet Observer's Ephemerides Page
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This is Erik De Sonville's "Planet Observer's Ephemerides Page" --- still Work In Process.

Discussion of planet ephemerides as most useful to the amateur astronomer, including links to the world's very best web resources on the subject.

Outline of stuff to be discussed

Imagine looking at a rotating world globe in a mostly dark room illuminated by a candle.

The visual appearance of "the planet" (globe) illuminated by "the Sun" (candle) as seen by "the earthly observer" (you) obviously depends upon the relative distances, positions and orientations of the planet, the Sun and the observer. One can also remember the various aspects of planet ephemerides from the acronym "TPMDIAR":

  • Time
  • Position
  • Magnitude
  • Disk diameter
  • Illumination
  • Axis orientation
  • Rotation
Time

Observation reports should include time of observation with unambiguous indication of time zone (e.g. MEST for Middle European Summer Time, UT+02). It is best to indicate time in UT (or UTC) as well. Though most ephemeris elements (P, M, D, I, A) for most planets change relatively little from day to day, correct time registration is particularly important for the "rotation" aspect (R).

Position

Position is usually indicated in right ascension and declination, which allows to position to planet on star charts. Another interesting xxx is elongation i.e. the angle xxx (+ ecliptic -> twilight).

Magnitude
Disk diameter

The (apparent) disk diameter for the outer planets is fairly constant, but varies (significantly) for the inner planets depending on the relative positions of planet and Earth in their orbits around the Sun.

Illumination

Because of their large distances, the outer planets always appear as fully illuminated. For the inner planets, a varying fraction of the visible disk is illuminated, depending on the angles formed in the Sun-Earth-planet triangle. Note that the illuminated part is (roughly) symmetrical to the ecliptic (since the inner planets roughly move within the plane of the ecliptic), such that the orientation of the celestial pole can be found from the terminator.

Axis orientation
Rotation

For earth-based amateur observation, not all aspects are applicable to every planet. Overview:

  • Mercury: TPMSI
  • Venus: TPMSI
  • Mars: TPMSIAR
  • Jupiter: TPMSAR + something on moons
  • Saturn: TPMSAR
  • Uranus: TPMS (A???)
  • Neptune: TPM (S???)

Rate of change and interpolation. Ephemeris data relating to P, M, S, I, A are slowly changing (i.e. with little change from day to day). Data relating to R are rapidly changing (in a matter of minutes to hours), require interpolation from the tables, and require correct registration of observation time.

Position: today's "bifurcation" between visual work (often dobsons - only finder charts are useful, RA/dec are no good) and CCD work (often computerized goto mounts with integrated search 'n' track functionality).

Equinox (J2000.0 vs. mean equinox of date). Accuracy. Planetary models. Links to JPL, SETI and other. Add links to finder-chart stuff (online planetarium pgms, Cartes du Ciel etc).

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Web resources

Online solar-system ephemeris resources
  • JPL Solar System Dynamics (2 synonymous urls): Generated with JPL's HORIZONS s/w.
  • IMCCE (Institut de Mécanique Céleste et de Calcul des Ephémérides): [f] www.imcce.fr/page.php?nav=fr/ephemerides/formulaire/form_ephepos.php
    Provides ephemerides for the Sun, the Moon, the planets, their moons, asteroids, comets. The user can specify time (UTC or TT); planetary model (VSOP82/ELP2000-82, VSOP87/ELP2000-82B, DE200/LE200, DE403/LE403, DE405/LE405, DE406/LE406); ephemeris type (astrometric J2000, mean J2000, apparent, mean equinox of date), and more.
  • U.S. Naval Observatory, Astronomical Applications Department, Data Services: [e] aa.usno.navy.mil/data/
    For planet ephemerides, follow the link "Web Version of MICA" - Multi-Year Interactive Computer Almanac. Remark: this web version is not a full MICA implementation; the dates for which data will be provided run from 1 January of the previous year through 30 days beyond the current date.
  • SETI (Mark Showalter): [e] pds-rings.seti.org/tools/tools.html
    Generated from various JPL ephemeris models.
Mars-specific ephemerides
Home Pages of the referenced organisations
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Theoretical background

Ephemeris models

There are essentially two ways to calculate ephemerides: (1) using analytical formulae, and (2) by numerical integration.

(1a) Ever since the days of Kepler and Newton (or even Ptolemy before them), various analytical models have been developed, based on "planetary theories". These models started from the unperturbed Keplerian motion of each planet, with a series of corrections to take into account the gravitational effects (perturbations) by the other planets. At the end of the 19th century, this culminated in the planetary theory of Simon Newcomb, then Director of the American Nautical Almanac Office. Accuracies (with many thousands of correction terms) are up to the order of 0.02 arcsec.

(1b) The most recent analytical models, VSOP82 [5] and its successor VSOP87 [6], are essentially polynomial best-fits to the JPL DE200 numerical-integration model (that is now superseded by DE450). For the Moon, ELP2000-82 [7] and its successor ELP2000-82B [8] are semi-analytical models, i.e. analytical models with parameters fine-tuned from comparison with the JPL LE200 numerical-integration model.

(1c) There are also modern state-of-the-art analytical models for the moons of Mars [9], Jupiter [10], Saturn [11] and Uranus [12].

(2) Today's most accurate ephemerides (accuracy within a 50-year span of typ. 0.005 arcsec) are obtained by numerical integration using JPL's DE405 model, the successor to JPL's older DE200 [1] and DE403 [2] models. These three models cover the period from roughly 1600AD to 2200AD; the long-range variant, DE406, roughly covers the period between 3000BC and 3000AD. For the Moon, the DE models find their counterparts in LE200 [1], LE403 [2], LE405 and LE406. Also the Russian EPM98 and EPM2000 models (IAA, Institute of Applied Astronomy of the Russian Academy of Sciences) are numerical-integration models, based on the same observations as the DE/LE models, and essentially of the same accuracy as DE403/405.

References
  • [1] DE200/LE200: E.M. Standish. The observational basis for JPL's DE200, the planetary ephemerides of the Astronomical Almanac. Astron. Astrophys., 233:252, 1990.
  • [2] DE403/LE403: E.M. Standish, X.X. Newhall, J.G. Williams, W.F. Folkner. JPL planetary and lunar ephemerides, DE403/LE403. JPL IOM, 314:10, 1995.
  • [3] DE405/LE405: Standish, E. M. 1998, JPL planetary and lunar ephemerides, DE405/LE405, IOM 312, F-98-048, Publication Jet Propulsion Laboratory, Pasadena.
  • [4] DE406/LE406
  • [5] VSOP82: P. Bretagnon. Theory for the motion of all the planets - The VSOP82 solution. Astron. Astrophys., 114:278, 1982.
  • [6] VSOP87: P. Bretagnon, G. Francou. Planetary theories in rectangular and spherical variables. VSOP87 solutions. Astron. Astrophys., 202:309, 1988.
  • [7] ELP2000-82: M. Chapront-Touzé J. Chapront, The lunar ephemeris ELP 2000. Astron. Astrophys., 124:50, 1983.
  • [8] ELP2000-82B
  • [9] ESAPHO/ESADE (moons of Mars): M. Chapront-Touzé. Orbits of the Martian satellites from ESAPHO and ESADE theories. Astron. Astrophys., 240:159, 1990.
  • [10] G5 (moons of Jupiter): J.E. Arlot. New constants for Sampson-Lieske theory of the Galilean Satellites of Jupiter. Astron. Astrophys., 107:305, 1982.
  • [11] TASS 1.7 (moons of Saturn): A. Vienne, L. Duriez. TASS 1.6: Ephemerides of the major Saturnian satellites. Astron. Astrophys., 297:588, 1995.
  • [12] GUST86 (moons of Uranus): J. Laskar. GUST86 - An analytical ephemeris of the Uranian satellites. Astron. Astrophys., 188:212, 1987.
See also...
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Programmer's annex

Below are a few start-me-up hooks for the programmer whizkids who insist on calculating planet ephemerides and/or on developing ephemeris software by themselves. Which is an honorable hobby in its own right, but tends to steal night time from observing! With hints from and thanks to the A.L.P.O. Computing Section. [List below is subject to review]

Analytical models
  • The seminal books by Jean Meeus, publ. Willmann-Bell, Inc.
  • How to compute planetary positions, by Paul Schlyter, Stockholm, Sweden: [e] www.stjarnhimlen.se/comp/ppcomp.html
    Also see the related tutorial: [e] www.stjarnhimlen.se/comp/tutorial.html
    A comprehensive page about finding the positions of the Sun, Moon and planets to an accuracy of one or two minutes of arc using mean orbits with basic perturbation corrections, using adapted and simplified methods contained in a paper by T. van Flandern and K. Pulkkinen called "Low precision formulae for planetary positions", originally published in the Astrophysical Journal Supplement Series, 1980. Also includes an extensive list of links to other ephemeris resources.
  • vsop87 modules in c++ available (in source format) on the web under GNU General Public License, e.g. from Celestia: [e] celestia.teyssier.org/source-documentation/vsop87_8cpp.html
    The source of this vsop87 module has 17,676 lines, of which barely 2% "code" (the remainder are tables with numbers).
    Celestia, an open-source project, is the free space simulation that lets you explore our universe in three dimensions. Celestia runs on Windows, Linux, and Mac OS X. Homepage:     [e] shatters.net/celestia/
Numerical integration models and Almanacs

Content and layout © Erik De Sonville 2005.