Guran Lunar Tables and Programs from B. The accuracy of the longitude in degrees, for each kind of precision, for a date in ephemeris time for various time spans for Lunar Tables and Programs from B. I cannot suppose that anyone will seek to better the book for a generation or more. The second set of tables provide expansions of the semimajor axis, eccentricity, sine of half the inclination, longitude of perigee, longitude of node, and mean longitude, referred to the mean ecliptic and equinox date.
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Bretagnon and G. Francou  at the Bureau des Longitudes, Paris. This theory gives the ecliptic longitude and latitude of the planets, and their radius vector, as sums of periodic terms. In our calculations, we used the complete set of periodic terms of version D of VSOP87 this version provides the positions referred to the mean equinox of the date. Chapront-Touze and J. Chapront , again of the Bureau des Longitudes.
But many of these terms are very small: some have an amplitude of only 0. In our computer program, we neglected all periodic terms with coefficients smaller than 0. The center of figure of the Moon does not coincide exactly with its center of mass. To compensate for this property in their eclipse predictions, many of the national institutes employ an empirical correction to the center of mass position of the Moon.
Unfortunately, the large variation in lunar libration from one eclipse to the next minimizes the effectiveness of the empirical correction. In any case, it has no practical impact on the present work. The information above was previously published in:.
Ephemeride Lunaire Parisienne
Method[ edit ] 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 integrations known as the Jet Propulsion Laboratory Development Ephemeris which includes the Lunar Ephemerides , that in their turn have been fitted to actual astronomical observations. Advantages[ edit ] 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.
Solar and Lunar Coordinates
Lunar tables and programs from 4000 B.C. to A.D. 8000