Hill on the Motion of the Lunar Perigee

Abstract

Of Hill’s two innovative papers on the lunar theory, the first, “On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon” (Cambridge, MA: JohnWilson, 1877, 28pp; reprinted in Acta Mathematica 8 (1886), pp. 1–36) was by far the most esoteric in its subject matter and hyper-refined in the methods it employed. The second paper introduces the new lunar theory in a more pedestrian and reader-friendly way, as the reader will discover in our later section on “Hill’s Variation Curve.” The first paper must have made a stunning impression on those readers who were prepared to appreciate it; it is a blockbuster of a paper, astonishing in what and how it achieves.We shall attempt to make its essential steps understandable for readers with a moderate amount of training in algebra and the calculus.