Lunar Tables

The lack of accurate clocks up to date early 18th century necessitated the need for finding longitude using the moon. Lunar tables were thus required which were accurate enough, about 1 minute of arc (the moon subtends an angle of approximately 32 minutes), to enable ships to navigate at sea. The first lunar tables to achieve this accuracy were calculated by Mayer in 1753. These calculations were based on coefficients estimated from observation. Mayer's tables were later superseded by tables calculated using analytic and analytic-numerical approaches with accuracies of a few seconds of arc.

The theory which is in use today prepare the lunar ephemeris is that of Brown's (1919). His theory includes 1500 separate terms in which the variation, the evection and the equation of centre are the main parameters.

Recently a computer-produced andalytical lunar ephemeris has been made available by Deprit (1971) which is more accurate than Brown's. The number of trigonometric arguments used in the calculation for the moon's longitude alone exceeds 2000. A further merit point for this analytical method is that it is a routine task to differentially correct and improve the lunar tables everytime soshisticated instrumentation and highly accurate measurements force a significant revision of the astronomical constants involved.