Ephemeride Lunaire Parisienne
Encyclopedia
Éphéméride Lunaire Parisienne is a lunar theory
developed by Jean Chapront, Michelle Chapront-Touzé, and others at the Bureau des Longitudes
in the 1970s to 1990s.
ELP gives a series expansion
of the orbital elements
and the coordinates of the Moon
. The authors refer to it as a ´´semi-analytical´´ theory because they developed their expressions not purely symbolically, but introduced numerical values for orbital constants from the outset; but they also constructed partial derivatives of all terms with respect to these constants, so they could make corrections afterwards to reach the final solution.
ELP has been fitted not directly to observations, but to the numerical integration
s known as the Jet Propulsion Laboratory Development Ephemeris (which includes the Lunar Ephemerides), that in their turn have been fitted to actual astronomical observations. ELP was fitted initially to the DE200, but improved parameters have been published up to DE405.
Even though ELP contains more than periodic terms, it is not sufficiently accurate to predict the Moon's position to the centimeter accuracy with which that can be measured by LLR
. An attempt was made to improve the planetary terms with the ELP/MPP02 lunar theory, but heuristic corrections remained necessary.
A theory like the ELP has two advantages over numerical integration:
Upon popular demand, the Chapronts also published ELP2000-85 and a book, "Lunar programs and Tables" with a truncated version of their theory and with programs, that could be used by historians and amateur astronomers to compute the position of the Moon themselves. Jean Meeus
also used the ELP in his popular "Astronomical Algorithms".
Finally, the ELP has also been used e.g. to compute NASA´s 5000-year canon of eclipses.
Lunar theory
Lunar theory attempts to account for the motions of the Moon. There are many irregularities in the Moon's motion, and many attempts have been made over a long history to account for them. After centuries of being heavily problematic, the lunar motions are nowadays modelled to a very high degree...
developed by Jean Chapront, Michelle Chapront-Touzé, and others at the Bureau des Longitudes
Bureau des Longitudes
The Bureau des Longitudes is a French scientific institution, founded by decree of 25 June 1795 and charged with the improvement of nautical navigation, standardisation of time-keeping, geodesy and astronomical observation. During the 19th century, it was responsible for synchronizing clocks...
in the 1970s to 1990s.
ELP gives a series expansion
Series expansion
In mathematics, a series expansion is a method for calculating a function that cannot be expressed by just elementary operators . The resulting so-called series often can be limited to a finite number of terms, thus yielding an approximation of the function...
of the orbital elements
Orbital elements
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are generally considered in classical two-body systems, where a Kepler orbit is used...
and the coordinates of the Moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
. The authors refer to it as a ´´semi-analytical´´ theory because they developed their expressions not purely symbolically, but introduced numerical values for orbital constants from the outset; but they also constructed partial derivatives of all terms with respect to these constants, so they could make corrections afterwards to reach the final solution.
ELP has been fitted not directly to observations, but to the numerical integration
Numerical integration
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of...
s known as the Jet Propulsion Laboratory Development Ephemeris (which includes the Lunar Ephemerides), that in their turn have been fitted to actual astronomical observations. ELP was fitted initially to the DE200, but improved parameters have been published up to DE405.
Even though ELP contains more than periodic terms, it is not sufficiently accurate to predict the Moon's position to the centimeter accuracy with which that can be measured by LLR
Lunar laser ranging experiment
The ongoing Lunar Laser Ranging Experiment measures the distance between the Earth and the Moon using laser ranging. Lasers on Earth are aimed at retroreflectors planted on the moon during the Apollo program, and the time for the reflected light to return is determined...
. An attempt was made to improve the planetary terms with the ELP/MPP02 lunar theory, but heuristic corrections remained necessary.
A theory like the ELP has two advantages over numerical integration:
- it can be truncated to a lower level of accuracy for faster computation, which made it suitable for implementing in programs for micro computers.
- it can be evaluated for an unlimited period of time, unlike the results of a numerical integration which has specific moments of begin and end; however the accuracy deteriorates into the remote past or future, depending on the quality of the polynomials that model the so-called secular (long-term) changes in the orbital parameters. For the Moon, the main secular factor is tidal accelerationTidal accelerationTidal acceleration is an effect of the tidal forces between an orbiting natural satellite , and the primary planet that it orbits . The "acceleration" is usually negative, as it causes a gradual slowing and recession of a satellite in a prograde orbit away from the primary, and a corresponding...
: the magnitude of that effect has become better known after the initial version of the ELP was published, due to a longer base line of LLR observations.
Upon popular demand, the Chapronts also published ELP2000-85 and a book, "Lunar programs and Tables" with a truncated version of their theory and with programs, that could be used by historians and amateur astronomers to compute the position of the Moon themselves. Jean Meeus
Jean Meeus
Jean Meeus is a Belgian astronomer specializing in celestial mechanics. The asteroid 2213 Meeus is named after him.Jean Meeus studied mathematics at the University of Leuven in Belgium, where he received the Degree of Licentiate in 1953...
also used the ELP in his popular "Astronomical Algorithms".
Finally, the ELP has also been used e.g. to compute NASA´s 5000-year canon of eclipses.
Literature
- Lunar Tables and Programs from 4000 B.C. to A.D. 8000 (1991), ISBN 0943396336 , see Willmann Bell
- Astronomical Algorithms (1991), 1st ed, ISBN 0-943396-35-2
- Astronomical Algorithms (1998), 2nd ed, ISBN 0-943396-61-1, see Willmann Bell