Periodicities Cycles and Interrelationships

The periodicities in the motions of the planets were studied intently by astronomers from many cultures. Detailed records are available from Mesopotamia, India, China, and Mesoamerica. According to Neugebauer (1969, p. 127), the main interest of the Babylonian astronomers was the first and last visibility of the planets due to their motions and that of the Sun.38 The earliest observational records from Mesopotamia date from the middle of the second millenium b.c.; from China, they are slightly later. See ยงยง7.1.3 and 10.1.4 for further discussion of these sources.

There are two basic periods by which we characterize the motion of a planet in the sky: the sidereal and the synodic periods. The modern sidereal period is the time interval between successive passages of the planet through a line between a distant star and the Sun. The synodic period, on the other hand, is the (average) time interval between successive passages of the planet through a Sun-Earth line; it is therefore a relative period. These periods are analogous to the lunar sidereal and synodic months. The difference between the two types of period arises, in the case of an interior planet, from the time required for the interior planet to lap the earth as both revolve counterclockwise around the Sun. In the case of an exterior planet, the Earth moves faster, and the difference arises from the time required for earth to lap the exterior planet. Calculation39 of the relative rate of motion of a planet in terms of orbital motions of the planet and Earth gives the following expressions for the synodic periods (Psyn) of interior and exterior planets, respectively:

Interior:

Exterior:

Interior:

Exterior:

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