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

Aug 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010amjph..78..834k&link_type=abstract

American Journal of Physics, Volume 78, Issue 8, pp. 834-838 (2010).

Astronomy and Astrophysics

Astrophysics

1

Angular Measurement, Celestial Mechanics, Measurement Uncertainty, Moon, Physics Education, Student Experiments, Fundamental Astronomy And Astrophysics, Instrumentation, Techniques, And Astronomical Observations

Scientific paper

Prior to the invention of the telescope many astronomers worked out models of the motion of the Moon to predict the position of the Moon in the sky. These geometrical models implied a certain range of distances of the Moon from Earth. Ptolemy's most quoted model predicted that the Moon was nearly twice as far away at apogee than at perigee. Measurements of the angular size of the Moon were within the capabilities of pretelescopic astronomers. Such measurements could have helped refine the models of the motion of the Moon, but hardly anyone seems to have made any measurements that have come down to us. We use a piece of cardboard with a small hole in it which slides up and down a yardstick to show that it is possible to determine the eccentricity ɛ~0.039+/-0.006 of the Moon's orbit. A typical measurement uncertainty of the Moon's angular size is +/-0.8 arc min. Because the Moon's angular size ranges from 29.4 to 33.5 arc min, carefully taken naked eye data are accurate enough to demonstrate periodic variations of the Moon's angular size.

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