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

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

Gravitational force exerted by sun on Earth is

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

Thus, ratio of F_s to F_m is,

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

F_s / F_m = 2.7 * 10⁷ / 1.6 * 10⁵

F_s / F_m = 168.75

F_s = 168.75 F_m

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 1 year ago

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