Hipparchus compared observations of a solar eclipse in Syene and in Alexandria to determine the distance from the Earth to the Moon.
Hipparchus measured the distance from the Earth to the Moon during a solar eclipse that was a total eclipse at Syene and a partial eclipse at Alexandria. At the same time that an observer at Syene saw the entire Sun blocked by the Moon, one at Alexandria saw 1/5th of the Sun's disk, that is 1/5th of 30 arcminutes of the Sun's disk was visible (The Sun's angular diameter is 30 arcminutes or 1/2 degree). The angular size of the visible Sun seen at Alexandria therefore is 1/10th of a degree (0.1 degree) and this angle, expressed in radians and applying the small angle approximation gives the ratio of the Syene-Alexandria distance to the Earth-Moon distance.
Hipparchus also measured the precession of the Earth's rotation axis. Today we know that the precession period is about 26,000 years. While the North Celestial Pole today is near the star Polaris, in 3000 B.C., it was near the star Thuban in the constellation Draco, and in 14,000 A.D. , it will be found near the star Vega in the constellation Lyra.
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