The true angle between Sun and Moon at the time of quarter Moon is less than 90 degrees by only 9 minutes of arc-a quantity impossible to measure in antiquity. (In a later publication, Aristarchus gave the angular size of the Moon as half a degree, which is about right, but he apparently did not modify his earlier work.) Premise 3 was probably not based on measurement but rather on an estimate it is equivalent to assuming that the time from first quarter Moon to third quarter Moon is one day longer than the time from third quarter to first quarter. Located in Western Queensland, the lights are described as airborne fiery orbs with a tendency to follow rather than to lead. Premise 2 overestimates the Moon’s angular diameter by a factor of four, which is puzzling, since this is an easy measurement to make. In Aristarchus’s day the geometric method was considered more important than numerical measurements. (The diameters of the Moon and the Sun compared with that of Earth are actually 0.27 and 109, respectively.) 'Fascinatingly exciting, said project scientist Nour Raouafi of Johns Hopkins University. Scientists said it took a few months to get the data back and then several more months to confirm. He found the Moon’s diameter to be between 0.32 and 0.40 times the diameter of Earth and the Sun’s diameter to be between 6.3 and 7.2 times the diameter of Earth. The Parker Solar Probe actually flew through the corona in April during the spacecraft’s eighth close approach to the sun. (The actual ratio is about 390.) Using this result and premises 1 and 2 in a clever geometric construction based on lunar eclipses, he obtained values for the sizes of the Sun and Moon. Using premise 3, Aristarchus showed that the Sun is between 18 and 20 times farther away from Earth than the Moon is. (3) at the time of quarter Moon, the angular distance between the Moon and the Sun is 87 degrees.
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