Solar Eclipse Predictions with JPL DE406

Fred Espenak

The coordinates of the Sun used in these eclipse predictions have been calculated on the basis of the JPL DE406 solar system ephemeris. This ephemeris consists of computer representations of the positions, velocities and accelerations of major Solar System bodies, tabulated at equally spaced intervals of time, covering the span -3001 Feb 04 to +3000 May 06. DE406 is a slightly less accurate version of the DE405 but it covers a much longer time span. The interpolating accuracy of the DE406 is no worse than 25 meters for any planet and no worse than 1 meter for the Moon. See Jet Propulsion Laboratory Developmental Ephemeris for more information of these ephemerides.

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. This correction is typically +0.50" in longitude and -0.25" in latitude. Unfortunately, the large variation in lunar libration from one eclipse to the next minimizes the effectiveness of the empirical correction. We choose to ignore this convention and have performed all calculations using the Moon's center of mass position. In any case, it has no practical impact on the present work.

The predictions use a smaller value for the Moon's radius k (=0.272281) than the one adopted by the 1982 IAU General Assembly (k=0.2725076). The smaller k is a better approximation of the Moon's minimum diameter and results in a slightly shorter total or longer annular eclipse when compared with calculations using the IAU value. No correction has been made between the Moon's center of mass and center of figure. The difference is small and of consequence only where careful timings are needed or for observations near the northern or southern path limits. In such cases, a more detailed predictions are required which include the effects of the Moon's limb profile.