Determining the Eccentricity of the Moon's Orbit without a Telescope

Details Determining the Eccentricity of the Moon's Orbit without a Telescope Determining the Eccentricity of the Moon's Orbit without a Telescope

Jan 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010aas...21533102k&link_type=abstract

American Astronomical Society, AAS Meeting #215, #331.02; Bulletin of the American Astronomical Society, Vol. 42, p.429

Astronomy and Astrophysics

Astronomy

Scientific paper

Ancient Greek astronomers knew that Moon's distance from the Earth was not constant. Ptolemy's model of the Moon's motion implied that the Moon ranged in distance from 33 to 64 Earth radii. This implied that its angular size ranged nearly a factor of two. Tycho Brahe's model of the Moon's motion implied a smaller distance range, some ±3 percent at syzygy. However, the ancient and Renaissance astronomers are notably silent on the subject of measuring the angular size of the Moon as a check on the implied range of distance from their models of the position of the Moon. Using a quarter-inch hole in a piece of cardboard that slides along a yardstick, we show that pre-telescopic astronomers could have measured an accurate mean value of the angular size of the Moon, and that they could have determined a reasonably accurate value of the eccentricity of the Moon's orbit. The principal calibration for each observer is to measure the apparent angular diameter of a 91 mm disk viewed at a distance of 10 meters, giving a true angular size of 31.3 arcmin (the Moon's mean angular size). Because the sighting hole is not much bigger than the size of one's pupil, each observer obtains a personal correction factor with which to scale the raw measures. If one takes data over the course of 7 lunations (7.5 anomalistic months), any systematic errors which are a function of phase should even out over the course of the observations. We find that the random error of an individual observation of ±0.8 arcmin can be achieved.

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