Lunar theory
Lunar theory attempts to account for the motions of the Moon. There are many small variations (or perturbations) in the Moon's motion, and many attempts have been made to account for them. After centuries of being problematic, lunar motion can now be modeled to a very high degree of accuracy (see section Modern developments).
Lunar theory includes:
Lunar theory has a history of over 2000 years of investigation. Its more modern developments have been used over the last three centuries for fundamental scientific and technological purposes, and are still being used in that way.
Applications of lunar theory have included the following:
The Moon has been observed for millennia. Over these ages, various levels of care and precision have been possible, according to the techniques of observation available at any time. There is a correspondingly long history of lunar theories: it stretches from the times of the Babylonian and Greek astronomers, down to modern lunar laser ranging.
Among notable astronomers and mathematicians down the ages, whose names are associated with lunar theories, are:
Other notable mathematicians and mathematical astronomers also made significant contributions.
The history can be considered to fall into three parts: from ancient times to Newton; the period of classical (Newtonian) physics; and modern developments.
Ancient times to Newton[edit]
Babylon[edit]
Of Babylonian astronomy, practically nothing was known to historians of science before the 1880s.[3] Surviving ancient writings of Pliny had made bare mention of three astronomical schools in Mesopotamia – at Babylon, Uruk, and 'Hipparenum' (possibly 'Sippar').[4] But definite modern knowledge of any details only began when Joseph Epping deciphered cuneiform texts on clay tablets from a Babylonian archive: In these texts he identified an ephemeris of positions of the Moon.[5] Since then, knowledge of the subject, still fragmentary, has had to be built up by painstaking analysis of deciphered texts, mainly in numerical form, on tablets from Babylon and Uruk (no trace has yet been found of anything from the third school mentioned by Pliny).
To the Babylonian astronomer Kidinnu (in Greek or Latin, Kidenas or Cidenas) has been attributed the invention (5th or 4th century BC) of what is now called "System B" for predicting the position of the moon, taking account that the moon continually changes its speed along its path relative to the background of fixed stars. This system involved calculating daily stepwise changes of lunar speed, up or down, with a minimum and a maximum approximately each month.[6] The basis of these systems appears to have been arithmetical rather than geometrical, but they did approximately account for the main lunar inequality now known as the equation of the center.
The Babylonians kept very accurate records for hundreds of years of new moons and eclipses.[7] Some time between the years 500 BC and 400 BC they identified and began to use the 19 year cyclic relation between lunar months and solar years now known as the Metonic cycle.[8]
This helped them build a numerical theory of the main irregularities in the Moon's motion, reaching remarkably good estimates for the (different) periods of the three most prominent features of the Moon's motion:
the two eccentricities (, about 0.0549, and , about 0.01675) of the ellipses that approximate to the apparent orbits of the Moon and the Sun;
the angular direction of the perigees ( and ) (or their opposite points the apogees) of the two orbits; and
the angle of inclination (, mean value about 18523") between the planes of the two orbits, together with the direction () of the line of nodes in which those two planes intersect. The ascending node () is the node passed by the Moon when it is tending northwards relative to the ecliptic.
