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Jet Propulsion Laboratory Developmental Ephemeris

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Jet Propulsion Laboratory Developmental Ephemeris

The name Jet Propulsion Laboratory Development Ephemeris (followed by a number), the abbreviation JPL DE(number), or just DE(number) designates one of a series of models of the Solar System produced at the Jet Propulsion Laboratory in Pasadena, California, primarily for purposes of spacecraft navigation and astronomy. The models consist of computer representations of positions, velocities and accelerations of major Solar System bodies, tabulated at equally spaced intervals of time, covering a specified span of years. Barycentric rectangular coordinates of the Sun, eight major planets and Pluto, and geocentric coordinates of the Moon are tabulated.


There have been many versions of the JPL DE, from the 1960s through the present,[1] in support of both robotic and manned[2] spacecraft missions. Available documentation is sketchy, but we know DE69 was announced in 1969 to be the third release of the JPL Ephemeris Tapes, and was a special purpose, short-duration ephemeris. The then-current JPL Export Ephemeris was DE19. These early releases were distributed on magnetic tape.

In the days before personal computers, computers were large and expensive, and numerical integrations such as these were run by large organizations with ample resources. The JPL ephemerides prior to DE405 were integrated on a Univac mainframe in double precision. For instance, DE102, which was created in 1977, took six million steps and ran for nine days on a Univac 1100/81.[3] DE405 was integrated on a DEC Alpha in quadruple precision.[4]

In the 1970s and early 1980s, much work was done in the astronomical community to update the astronomical almanacs from the theoretical work of the 1890s to modern, relativistic theory. From 1975 through 1982, six ephemerides were produced at JPL using the modern techniques of least-squares adjustment of numerically-integrated output to high precision data: DE96 in Nov. 1975, DE102 in Sep. 1977, DE111 in May 1980, DE118 in Sep. 1981, and DE200 in 1982.[5] DE102 was the first numerically integrated so-called Long Ephemeris, covering much of history for which useful astronomical observations were available: 1141 BC to AD 3001. DE200, a version of DE118 rotated to the J2000.0 reference frame, was adopted as the fundamental ephemeris for the new almanacs starting in 1984. The JPL ephemerides have remained the basis of the Astronomical Almanac to the present; the current Almanac is derived from DE405.[6]


Each such ephemeris was produced by numerical integration of the equations of motion, starting from a set of initial conditions. Due to the precision of modern observational data, the analytical method of general perturbations could no longer be applied to a high enough accuracy to adequately reproduce the observations. The method of special perturbations was applied, using numerical integration to solve the n-body problem, in effect putting the entire Solar System into motion in the computer's memory, accounting for all relevant physical laws. The initial conditions were both constants such as planetary masses, from outside sources, and parameters such as initial positions and velocities, adjusted to produce output which was a "best fit" to a large set of observations. A least-squares technique was used to perform the fitting.[3]

The physics modeled included the mutual Newtonian gravitational accelerations and their relativistic corrections (a modified form of the Einstein-Infeld-Hoffmann equation), the accelerations caused by the tidal distortion of the Earth, the accelerations caused by the figure of the Earth and Moon, and a model of the lunar librations.[3]

The observational data in the fits has been an evolving set, including: ranges (distances) to planets measured by radio signals from spacecraft,[7] direct radar-ranging of planets, two-dimensional position fixes (on the plane of the sky) by VLBI of spacecraft, transit and CCD telescopic observations of planets and small bodies, and laser-ranging of retroreflectors on the Moon, among others. DE102, for instance, was fit to 48,479 observations.

The time argument of the integrated ephemerides is a relativistic coordinate time scale called Teph,[8] necessary in precise work to account for the small relativistic effects of time dilation and simultaneity. In later ephemerides, Teph is essentially equivalent to the IAU definition of TCB.


Because the ephemeris is a tabulation at regularly-spaced time intervals, interpolation would be necessary if coordinates for non-tabulated times were desired. The ephemeris data are distributed in the form of a file of numerical coefficients for Chebyshev polynomials. The polynomials are curves fit to the tabulated coordinates over a range of dates; solving the polynomials allows recovery (calculation) of the positions, velocities and accelerations throughout the range of dates directly, interpolation occurring automatically with the use of the time argument. The file consists of coefficients covering a number of intervals of time, enough intervals to span the dates covered by the original numerical integration.[3] The ephemerides are now available via World Wide Web and FTP[9] in the form of data files containing the Chebyshev coefficients, along with source codes to recover positions and velocities.[10]

Evaluation of the Chebyshev polynomials can recover planetary and lunar coordinates to high precision relative to the original numerical integration. DE405 recovery for the inner planets is about 0.001 arcseconds (equivalent to about 1 km at the distance of Mars); for the outer planets it is generally about 0.1 arcseconds. The 'reduced accuracy' DE406 ephemeris gives an interpolating precision (relative to the full ephemeris values) no worse than 25 metres for any planet and no worse than 1 metre for the moon. Note that this precision says nothing about how well the ephemeris describes the actual motions of the planets, which is a function of the accuracy of the original observations and of the "goodness" of the least-squares fit.


  • JPL uses the ephemerides for navigation of spacecraft throughout the Solar System. Typically, a new ephemeris is computed including the latest available observations of the target planet(s), either for planning of the mission(s), or for final contact of the spacecraft with the target. See below, Recent ephemerides in the series.
  • The Astronomical Almanac for 1984 through 2002 were based on JPL ephemeris DE200, and from 2003 onwards the Astronomical Almanac has been based on JPL ephemeris DE405.[6]
  • The JPL ephemerides are widely used for planetary science; some examples are included in the Notes and References.
  • Software is available to use the JPL ephemerides for the production of apparent ephemerides for any location and time; these are widely used by professional and amateur astronomers for reducing planetary observations and producing very precise observing guides.[11]

Recent ephemerides in the series

The most recent members of the series, designated DE4xx, are expressed in coordinates referred to the International Celestial Reference Frame (ICRF).

DE402 was released in 1995, and was quickly superseded by DE403.

DE403[12] was released in 1995. For the first time, the JPL ephemeris was expressed in the coordinates of the International Earth Rotation Service (IERS) reference frame, essentially the ICRF. The data crunched by JPL to derive the ephemeris began to move away from limited-accuracy telescopic observations and more toward higher-accuracy radar-ranging of the planets, radio-ranging of spacecraft, and very-long-baseline-interferometric (VLBI) observations of spacecraft, especially for the four inner planets. Telescopic observations remained important for the outer planets because of their distance, hence the inability to bounce radar off of them, and the difficulty of parking a spacecraft near them. The perturbations of 300 asteroids were included, vs DE118/DE200 which included only the five asteroids determined to cause the largest perturbations. Better values of the planets' masses had been found since DE118/DE200, further refining the perturbations. Lunar Laser Ranging accuracy was improved, giving better positions of the Moon. DE403 covered the time span Apr 1599 to Jun 2199.[13]

DE404[14] was released in 1996. A so-called Long Ephemeris, this condensed version of DE403 covered 3000 BC to AD 3000. While both DE403 and DE404 were integrated over the same timespan, the interpolation of DE404 was somewhat reduced in accuracy and nutation of the Earth and libration of the Moon were not included.

DE405[15] was released in 1998. It added several years' extra data from telescopic, radar, spacecraft, and VLBI observations (of the Galileo spacecraft at Jupiter, in particular). The method of modeling the asteroids' perturbations was improved, although the same number of asteroids were modeled. The ephemeris was more accurately oriented onto the ICRF. DE405 covered 1600 to 2200 to full precision.

DE406 was released with DE405 in 1998. A Long Ephemeris, this was the condensed version of DE405, covering 3000 BC to AD 3000 with the same limitations as DE404.

DE407[16] was apparently unreleased. Details in readily-available sources are sketchy.

DE408[17] was an unreleased ephemeris, created in 2005 as a longer version of DE406, covering 20,000 years.

DE409[18] was released in 2003 for the MER spacecraft arrival at Mars and the Cassini arrival at Saturn. Further spacecraft ranging and VLBI (to the Mars Global Surveyor, Mars Pathfinder and the Mars Odyssey spacecraft) and telescopic data were included in the fit. The orbits of the Pioneer and Voyager spacecraft were reprocessed to give data points for Saturn. These resulted in improvements over DE405, especially to the predicted positions of Mars and Saturn. DE409 covered the years 1901 to 2019.

DE410[19] was also released in 2003 for the arrivals of the MER and Cassini spacecraft. It was different from DE409 only in that masses for the planets Venus, Mars, Jupiter, Saturn and the Earth-Moon system were updated to newer research. The masses had not yet been adopted by the IAU. DE410 covered the years 1901 to 2019.

DE411[20] was apparently unreleased, but was widely cited in the astronomical community.

DE412[21] was also unreleased, and was also widely referenced.

DE413[20] was released in 2004 for the sole purpose of providing an updated ephemeris of Pluto for the occultation of a star by its satellite Charon on 11 Jul 2005. DE413 was fit to new CCD telescopic observations of Pluto in order to give improved positions of the planet and its moon.

DE414[22] was created in 2005 and released in 2006. The numerical integration software was updated to use quadruple-precision for the Newtonian part of the equations of motion. Ranging data to the Mars Global Surveyor and Mars Odyssey spacecraft were extended to 2005, and further CCD observations of the five outer planets were included in the fit. Some data was accidentally left out of the fit, namely Magellan Venus data for 1992-94 and Galileo Jupiter data for 1996-97. Some ranging data to the NEAR Shoemaker spacecraft orbiting the asteroid Eros was used to derive the Earth/Moon mass ratio. DE414 covered the years 1599 to 2201.

DE418[23] was released in 2007 for planning the New Horizons mission to Pluto. New observations of Pluto, which took advantage of the new astrometric accuracy of the Hipparcos star catalog, were included in the fit. Mars spacecraft ranging and VLBI observations were updated through 2007. Asteroid masses were estimated differently. Lunar laser ranging data for the Moon was added for the first time since DE403, significantly improving the lunar orbit and librations. Estimated position data from the Cassini spacecraft was included in the fit, improving the orbit of Saturn, but rigorous analysis of the data was deferred to a later date. DE418 covered the years 1899 to 2051, and JPL recommended not using it outside of that range due to minor inconsistencies which remained in the planets' masses due to time constraints.

DE421[24] was released in 2008. It included additional ranging and VLBI measurements of Mars spacecraft, new ranging and VLBI of the Venus Express spacecraft, the latest estimates of planetary masses, additional lunar laser ranging, and two more months of CCD measurements of Pluto. DE421 covered the years 1900 to 2050.

DE422[25] was created in 2009 for the MESSENGER mission to Mercury. A Long Ephemeris, it was intended to replace DE406, covering 3000 BC to AD 3000.

DE423[26] was released in 2010. Position estimates of the MESSENGER spacecraft and additional range and VLBI data from the Venus Express spacecraft were fit. DE423 covered the years 1799 to 2200.

DE424[27] was created in 2011 to support the Mars Science Laboratory mission.

DE430[28] was released in 2013. It covers the dates 1550 Jan 01 to 2650 Jan 22 with the most accurate lunar ephemeris.

DE431[28] was released in 2013. It covers a longer time span than DE430 (13201 BC to AD 17191) with a less accurate lunar ephemeris than DE430.

See also

Notes and references

External links

  • Folkner's descriptions of most of JPL's DE series
  • NRAO description of the format and uses of the JPL ephemerides
  • IAU's Papers and Information Related to Ephemerides
  • JPL Solar System Dynamics
  • Information about JPL ephemerides and links to programs and source code
  • Java source code that implements JPL ephemerides and other theories
  • JPL FTP site with ephemerides (data files), source code (for access and basic processing of the data to recover positions and velocities), and documentation.
  • JPL Interoffice Memoranda describing features of the ephemerides.
  • US Naval Observatory (Naval Oceanography Portal), "History of the Astronomical Almanac" (accessed December 2009).


  • .
  • Standish and Williams, CHAPTER 8: Orbital Ephemerides of the Sun, Moon, and Planets, an unpublished, updated version of the above source.
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