Multisteps in Theoria Lunae

Abstract

In Chap. 5 we have studied Mayer’s lunar theory, and we have seen how Mayer had derived, from differential equations of motion and Newton’s law of gravitation, a mathematical formula expressing the true longitude of the moon in terms of its mean motion. His solution of the differential equations amounts to what we have termed a single-stepped one. In contrast, we have seen in Chap. 4 that his lunar tables implemented a multistepped procedure, using not only mean motion arguments: several tables had to be entered with arguments that had been modified in the course of calculation. Chapter 6 demonstrated that the multistep procedure is rooted in Newton’s Theory of the Moon’s Motion (NTM) and that Mayer is unlikely to have had a theoretical justification of it. Thus, a gap shows up between theory and tables.

Yet, Mayer compiled Theoria Lunae in order to satisfy Bradley’s interest in the theoretical background of the tables, and his declared intention with it was to show that from the Newtonian theory (i.e., the law of gravitation) no arguments against his tables could be drawn.¹ A gap between the singlestepped solution and the multistepped tables would certainly be regarded as such an argument. So the task awaited Mayer to reconcile the mathematical equation of the moon’s motion, as derived from the differential equations, with the astronomical equAtions represented by the tables.