Introduction

The orbital motion of the planets around the Sun is fairly accurately described by Kepler's laws. (See Chapter 3.) Similarly, to a first approximation, the orbital motion of the Moon around the Earth can also be accounted for via these laws. However, unlike the planetary orbits, the deviations of the lunar orbit from a Keplerian ellipse are sufficiently large that they are easily apparent to the naked eye. Indeed, the largest of these deviations, which is generally known as evection, was discovered in ancient times by the Alexandrian astronomer Claudius Ptolemy (90 BCE–168 CE) (Pannekoek 2011). Moreover, the next largest deviation, which is called variation, was first observed by Tycho Brahe (1546–1601) without the aid of a telescope (Godfray 1853). Another non-Keplerian feature of the lunar orbit, which is sufficiently obvious that it was known to the ancient Greeks, is the fact that the lunar perigee (i.e., the point of closest approach to the Earth) precesses (i.e., orbits about the Earth in the same direction as the Moon) at such a rate that, on average, it completes a full circuit every 8.85 years. The ancient Greeks also noticed that the lunar ascending node (i.e., the point at which the Moon passes through the fixed plane of the Earth's orbit around the Sun from south to north) regresses (i.e., orbits about the Earth in the opposite direction to the Moon) at such a rate that, on average, it completes a full circuit every 18.6 years (Pannekoek 2011).