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In: Physics

The sun's mass is about 2.7 x 10^7 times greater than the moon's mass. The sun...

The sun's mass is about 2.7 x 10^7 times greater than the moon's mass. The sun is about 400 times farther from Earth than the moon. How does the gravitational force exerted on Earth by the sun compare with the gravitational force exerted on Earth by the moon? Use complete sentences.

Solutions

Expert Solution

Let the mass of the moon m. Mass of the sun is 2.7 * 107 times greater than mass of the moon, that is, mass of the sun is [2.7 * 107 * m].

Let distance between Earth and the moon be d. Distance between Earth and the sun is 400 times greater, that is, [400 * d].

Let M be the mass of the Earth.

Gravitational force exerted by moon on Earth is

Fm = G m M / d2              Equation (1)      where G is the universal gravitational constant

Gravitational force exerted by sun on Earth is

Fs = G 2.7 * 107 *m M / (400* d)2              Equation (2)

Thus, ratio of Fs to Fm is,

Fs / Fm = [G 2.7 * 107 * m M / (400* d)2] * [d2 / G m M]

Fs / Fm = 2.7 * 107 / 1.6 * 105

Fs / Fm = 168.75

Fs = 168.75 Fm

The equation shows that gravitational force exerted on Earth by sun is 168.75 times greater than the gravitational force exerted on Earth by the moon.

genius_generous answered 2 years ago
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