Question

(a)

Find the magnitude of the gravitational force (in N) between a
planet with mass 8.50 ✕ 10^{24} kg and its moon, with mass
2.40 ✕ 10^{22} kg, if the average distance between their
centers is 2.70 ✕ 10^{8} m.

N

(b)

What is the moon's acceleration (in m/s^{2}) toward the
planet? (Enter the magnitude.)

m/s^{2}

(c)

What is the planet's acceleration (in m/s^{2}) toward
the moon? (Enter the magnitude.)

m/s^{2}

Answer #1

Gravitational constant = G = 6.67 x 10^{-11}
N.m^{2}/kg^{2}

Mass of the planet = M = 8.5 x 10^{24} kg

Mass of the moon = m = 2.4 x 10^{22} kg

Distance between the centers of the planet and the moon = R =
2.7 x 10^{8} m

Gravitational force between the planet and the moon = F

F = 1.866 x 10^{20} N

Acceleration of the moon towards the planet = a_{1}

ma_{1} = F

(2.4x10^{22})a_{1} = 1.866x10^{20}

a_{1} = 7.775 x 10^{-3} m/s^{2}

Acceleration of the planet towards the moon = a_{2}

Ma_{2} = F

(8.5x10^{24})a_{2} = 1.866x10^{20}

a_{2} = 2.195 x 10^{-5} m/s^{2}

a) Magnitude of gravitational force between the planet and the
moon = 1.866 x 10^{20} N

b) Acceleration of the moon towards the planet = 7.775 x
10^{-3} m/s^{2}

c) Acceleration of the planet towards the moon = 2.195 x
10^{-5} m/s^{2}

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