The Moon’s precise equatorial diameter is 3476 km, and its orbital distance from

Question

The Moon’s precise equatorial diameter is 3476 km, and its orbital
distance from Earth varies between 356,400 km and 406,700 km. The Sun’s diameter is
1,390,000 km, and its distance from Earth ranges between 147.5 and 152.6 million km.
a. Find the Moon’s angular size at its minimum and maximum distances from Earth.
b. Find the Sun’s angular size at its minimum and maximum distances from Earth.
c. Based on your answers to (a) and (b), is it possible to have a total solar eclipse when
the Moon and Sun are both at their maximum distances? Explain.

Explanation / Answer

(a)

moon maximum: 3476/406700 = 0.008547 radians

moon minimum: 3476/356400 = 0.009753 radians

(b)

sun maximum: 1.39/152.6 = 0.009109 radians

sun minimum: 1.39/147.5 = 0.009424 radians

(c) no, when both are at maximum distance the moon's angular size is smaller than the sun's so it will not cover it completely

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