Question

how did the ancient greek astronomer aristarchus of samos determine that the moon’s diameter was about 1/3 that of earth?
a. by measuring the relative durations of lunar and solar eclipses
b. by measuring the time it takes the moon to move through earth’s shadow during a lunar eclipse
c. by measuring the time it takes the moon to pass in front of a background star
d. by measuring the time it takes the moon to cross the face of the sun during a solar eclipse

Explanation:

Aristarchus determined the Moon’s diameter relative to Earth’s by measuring the time the Moon takes to move through Earth’s shadow during a lunar eclipse. This method involves using the duration of the lunar eclipse (when the Moon passes through Earth’s umbra) to calculate the angular size and thus the relative diameter. Option a is about eclipse durations but not the right method for this; option c is about passing in front of a star (used for other measurements); option d is about solar eclipse (Moon crossing Sun, not for Moon - Earth diameter ratio). So the correct option is b.

Answer:

b. by measuring the time it takes the Moon to move through Earth's shadow during a lunar eclipse