Éphéméride Lunaire Parisienne is a
lunar theory Lunar theory attempts to account for the motions of the Moon. There are many small variations (or perturbations) in the Moon's motion, and many attempts have been made to account for them. After centuries of being problematic, lunar motion can now ...
developed by Jean Chapront, Michelle Chapront-Touzé, and others at the
Bureau des Longitudes
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in the 1970s to 1990s.
Method
ELP gives a
series expansion
In mathematics, a series expansion is an expansion of a function into a series, or infinite sum. It is a method for calculating a function that cannot be expressed by just elementary operators (addition, subtraction, multiplication and division) ...
of the
orbital elements
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler orbit. There are many different ways to mathematically describe the same ...
and the coordinates of the
Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
. 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
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Part ...
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
In analysis, numerical integration comprises 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 ...
s known as the
Jet Propulsion Laboratory Development Ephemeris Jet Propulsion Laboratory Development Ephemeris (abbreved JPL DE(number), or simply DE(number)) designates one of a series of mathematical models of the Solar System produced at the Jet Propulsion Laboratory in Pasadena, California, for use in space ...
(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 20,000 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.
Advantages
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 acceleration
Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite (e.g. the Moon) and the primary planet that it orbits (e.g. Earth). The acceleration causes a gradual recession of a satellite in a prograde orbit away from ...
: 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.
Availability and use
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 used the ELP in his popular book ''Astronomical Algorithms'' (1991, 1998).
The ELP was also used to compute NASA's 5000-year canon of eclipses.
See also
*
VSOP87
References
External links
*
*
*
* {{cite web , title=Improved ELP/MPP02 , url=ftp://cyrano-se.obspm.fr/pub/2_lunar_solutions/2_elpmpp02/ , format=FTP download
Effects of gravitation
Time in astronomy
Moon