The mass of the Moon is 80 times less than the mass of the Earth, and its radius is 3.6 times less

The mass of the Moon is 80 times less than the mass of the Earth, and its radius is 3.6 times less than the radius of the Earth. Determine the acceleration due to gravity on the moon. Consider the acceleration of gravity on Earth as 10 m / s2.

Given:

Mz = Ml * 80 – the mass of the Moon is 80 times less than the mass of the Earth;

Rz = Rl * 3.6 – the radius of the Moon is 3.6 times less than the radius of the Earth;

g = 10 m / s ^ 2 – acceleration of gravity on Earth;

G is the gravitational constant.

It is required to determine g1 (m / s ^ 2) – the acceleration of gravity on the Moon.

Free fall acceleration on Earth is found by the formula:

g = G * Mz / Rz ^ 2, hence: G = g * Rz ^ 2 / Mz.

Free fall acceleration on the Moon is found by the formula:

g1 = G * Ml / Rl ^ 2, hence: G = g1 * Rl ^ 2 / Ml.

g * Rz ^ 2 / Mz = g1 * Rl ^ 2 / Ml, hence:

g1 = g * Rz ^ 2 * Ml / (Mz * Rl ^ 2) = g * Rl ^ 2 * 3.6 ^ 2 * Ml / (Ml * 80 * Rl ^ 2) =

= g * 3.6 ^ 2/80 = 10 * 3.6 ^ 2/80 = 10 * 12.96 / 80 = 129.6 / 80 = 1.62 m / s ^ 2.

Answer: the acceleration of gravity on the moon is 1.62 m / s ^ 2.