Question

# (a) Find the magnitude of the gravitational force (in N) between a planet with mass 8.50...

(a)

Find the magnitude of the gravitational force (in N) between a planet with mass 8.50 ✕ 1024 kg and its moon, with mass 2.40 ✕ 1022 kg, if the average distance between their centers is 2.70 ✕ 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

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

Mass of the planet = M = 8.5 x 1024 kg

Mass of the moon = m = 2.4 x 1022 kg

Distance between the centers of the planet and the moon = R = 2.7 x 108 m

Gravitational force between the planet and the moon = F

F = 1.866 x 1020 N

Acceleration of the moon towards the planet = a1

ma1 = F

(2.4x1022)a1 = 1.866x1020

a1 = 7.775 x 10-3 m/s2

Acceleration of the planet towards the moon = a2

Ma2 = F

(8.5x1024)a2 = 1.866x1020

a2 = 2.195 x 10-5 m/s2

a) Magnitude of gravitational force between the planet and the moon = 1.866 x 1020 N

b) Acceleration of the moon towards the planet = 7.775 x 10-3 m/s2

c) Acceleration of the planet towards the moon = 2.195 x 10-5 m/s2

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