The Motions of the Moon

Chair: Robert A. Garfinkle, FRAS

In calculating the exact position of the Moon relative to the Earth and the Sun, over 133 geophysical parameters must be taken into account. Some of these parameters are constant, such as the masses, diameters, and shapes of the bodies. Many other parameters are variable, changing every second as the bodies move through space, such as the constantly changing distances between the Moon, Earth, and Sun, which cause variations in the Moon’s velocity and orbit. This is the result of the changing strength of the gravitational pull of the Sun and Earth upon the Moon as the relative distances among all 3 bodies changes. The effects of the weak gravitational pulls on the Earth-Moon system by the other Solar System bodies must also be integrated into the Lunar Theory equations. The Lunar Theory consists of the massive aggregation of equiations needed for the task of calculating the relative positions at any moment.

Topics include: The relative orientation of the equatorial planes of the Earth-Moon system; apogee and perigee; daily retardation of moonrise, regression of the nodes, the Moon’s changing declination (major and minor lunar standstills), Cassini’s 3 laws of lunar motion. Lunar time periods and cycles include: lunation, lunar synodic month, lunar sidereal month, lunar draconic month, lunar anomalistic month, lunar tropical month; lunar and lunisolar calendars, the saros cycle, and precession of the Moon’s poles. Affects on the Moon’s motion and the length of the month include evection, variation, annual equation, revolution of the line apsides, regression of the nodes, secular acceleration of the Moon’s mean motion, Hansen’s inequalities, and parallactic inequality. The history of the discovery of the various components runs from Greece through Greenwich. Tidal effects include Earth’s oceanic, atmospheric, and land tides.

References

Ernest W. Brown: An Introductory Treatise on the Lunar Theory (Dover 1960)

Brian G. Marsden and A. G. W. Cameron, editors: The Earth-Moon System (Plenum 1966)