The oscillation of the synodic period of the Moon: A ``beating'' phenomenon

Details The oscillation of the synodic period of the Moon: A ``beating'' phenomenon The oscillation of the synodic period of the Moon: A ``beating'' phenomenon

Sep 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989amjph..57..802r&link_type=abstract

American Journal of Physics, Volume 57, Issue 9, pp. 802-807 (1989).

Physics

2

Moon, Eclipses, Transits, And Occultations

Scientific paper

The synodic period of the Moon (the period of the phases or the time from, say, full moon to full moon) exhibits oscillations about its mean value of 29.530 59 days which immediately suggest a ``beating'' between at least two frequencies. A Fourier analysis can provide some insight into the causes of the oscillation without the complexity of rigorous lunar theories. Such a Fourier approach is quite appropriate for undergraduate students of physics and astronomy, but, of course, is no substitute for more rigorous lunar theory. Fourier analysis suggests the periods of the beating frequencies to be 411 and 366 days. The 411-day period arises since this is the time it takes the Sun to return to a similar orientation along the line of apsides (the major axis) of the lunar orbit. The 366-day period is about a year or the time it takes the Earth to orbit the Sun. Since the lunar phases occur because of the relative orientation of the Earth, Moon, and Sun, an annual period might also be anticipated. The beat period of 3293 days is half the saros eclipse cycle period of 6585.3 days. Alternating lunar and solar eclipses are separated by the beat period. Higher frequency effects are apparent from the data, but not from the elementary Fourier approach. Thus this procedure must be used with caution in analyzing complex periodic data in astronomy.

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