Question

Mass of an imaginary planet is double earth's mass and radius is 1.5 times earth's radius. Using mass and radius, calculate the acceleration of gravity for the imaginary planet

Answer 1

Use g = GM/R^2. For the imaginary planet M' = 2M⊕ and R' = 1.5R⊕, so

g' = G(2M⊕)/(1.5R⊕)^2 = 2/(1.5^2) · (GM⊕/R⊕^2) = (2/2.25) g⊕ ≈ 0.8889 g⊕

Using g⊕ ≈ 9.81 m/s^2 gives g' ≈ 8.72 m/s^2 (more precisely ≈ 8.72 m/s^2 if g⊕ = 9.80665 m/s^2).

So surface gravity ≈ 8.72 m/s^2 (≈ 88.9% of Earth's).