Question

(a) Find the magnitude of the gravitational force (in N) between a planet with mass 8.00 ✕ 1024 kg and its moon, with mass 2.65 ✕ 1022 kg, if the average distance between their centers is 2.90 ✕ 108 m.

N

(b) What is the moon's acceleration (in m/s2) toward the planet? (Enter the magnitude.)

m/s2

(c) What is the planet's acceleration (in m/s2) toward the moon? (Enter the magnitude.)

m/s2

Answer 1

Gravitational constant = G = 6.67 x 10^-11 N.m²/kg²

Mass of the planet = M = 8 x 10²⁴ kg

Mass of the moon = m = 2.65 x 10²² kg

Average distance between the centers of the planet and the moon = R = 2.9 x 10⁸ m

Magnitude of gravitational force between the planet and the moon = F

F = 1.68 x 10²⁰ N

Magnitude of the moon;s acceleration = a₁

a₁ = 6.34 x 10^-3 m/s²

Magnitude of the planet's acceleration = a₂

a₂ = 2.1 x 10^-5 m/s²

a) Magnitude of the gravitational force between the planet and the moon = 1.68 x 10²⁰ N

b) Magnitude of the moon's acceleration towards the planet = 6.34 x 10^-3 m/s²

c) Magnitude of the planet's acceleration towards the moon = 2.1 x 10^-5 m/s²