# The acceleration due to gravity on the Moon is 1.6 m / s ^ 2. The mass of the

The acceleration due to gravity on the Moon is 1.6 m / s ^ 2. The mass of the Moon is 81 times less than the mass of the Earth. What is the radius of the Moon if the radius of our planet is 6370 km?

To determine the value of the radius of the Moon, we will use the equality: Ml / gl * Rl ^ 2 = G (gravitational constant) = Mz / gz * Rz2, whence we express: Rl = √ (Ml * gz * Rz ^ 2 / (gl * Mz)).

The values of the constants: Mz (Earth’s mass) = 81Ml (Moon’s mass); gz – acceleration of gravity on Earth (gz = 9.81 m / s2); Rz is the radius of the Earth (according to the condition Rz = 6370 km = 6370 * 10 ^ 3 m); gл – acceleration of gravity on the Moon (by condition gл = 1.6 m / s2).

Calculation: Rl = √ (Ml * gz * Rz2 / (gl * Mz)) = √ (Ml * 9.81 * (6370 * 10 ^ 3) ^ 2 / (1.6 * 81Ml)) = 1752.6 * 10 ^ 3 m = 1752.6 km.

Answer: The radius of the moon, according to the calculation, is 1752.6 km.

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