Physics-Gravitational Force

Question

Planet A has mass M kilograms and radius r meters. Planet B has mass 3.00 M kilograms and radius

1 2.00 r meters. If the acceleration due to gravity on planet A is 14.6 m/s2 then what is the acceleration due to gravity on planet B?

Answer 1

We can use the gravitational force equation to determine the factor by which the acceleration on planet B changes: F = GMm / r². M is the mass of the planet, m is the mass being accelerated, r is the distance between them (in this case the radius of the planet) and G is a constant.

Planet A exerts a force at its surface of F_A = GMm / r²

Planet B has force F_B = G3Mm / (2r)² = 3GMm / 4r²

Since acceleration is proportional to force, set up a proportion: a_B / 14.6 m/s² = 3GMm/4r² / GMm/r²

a_B = 14.6 x 3 / 4 = 11 m/s²