Question

Explain whether the acceleration of the moon is higher than,less or equal to that on the earth

Answer 1

Answer:

If we know that $m < M$, then acceleration of the Moon is less to that on the Earth.

Explanation:

From Newton's Law of Gravitation we know that gravitational force between Earth and Moon ($F$), measured in newtons, is expressed by this formula:

$F = G\cdot \frac{M\cdot m}{r^{2}}$ (1)

Where:

$G$ - Gravitational constant, measured in cubic meters per kilogram-square second.

$M$ - Mass of the Earth, measured in kilograms.

$m$ - Mass of the Moon, measured in kilograms.

$r$ - Distance between centers, measured in meters.

By comparing (1) with definition of Weight, we see that gravitational acceleration experimented by Earth ($g$), measured in meters per square second, is:

$g = \frac{G\cdot m}{r^{2}}$ (2)

If we know that $m < M$, then acceleration of the Moon is less to that on the Earth.