Question

The mass of the Earth is 81 times the mass of the Moon, and the radius of the Earth is 3.7 times of the Moon. If the acceleration of free fall on the Earth is 9.81 ms, without using the actual mass and radius of Earth and Moon, determine the acceleration on the Moon? ​

Answer 1

Fe = m ge = G Me m / Re^2 force exerted on m by earth

ge = G Me / Re^2

gm = G Mm / Rm^2 same for measuring g on moon

ge / gm = (Me / Mm) * (Rm / Re)^2 ratio of g

ge / gm = 81 * (1 / 3.7)^2 = 81 / 13.7 = 5.92 acceleration of earth to moon