Acceleration due to gravity – problems and solutions

1. What is the acceleration due to gravity at the Moon’s surface? Moon’s mass = 7.35 x 1022 kg, the radius of the Moon is 1.7 x 106 m, universal constant is 6.67 x 10-11 N m2 / kg2

Solution

The formula of Newton’s second law of motion :

Acceleration due to gravity – problems and solutions 1

The formula of Newton’s law of universal gravitation :

Acceleration due to gravity – problems and solutions 2

G = universal constant, M = Earth’s mass, m = object’s mass, r = the distance between Earth’s center and object. If the object is at Earth’s surface, r = Earth’s radius

Substitute F in equation 1 with F in equation 2 :

Acceleration due to gravity – problems and solutions 3

What is the acceleration due to gravity at the Moon’s surface?

Acceleration due to gravity – problems and solutions 4

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2. Acceleration due to gravity at Earth’s surface is g. At R (R is Earth’s surface), the acceleration due to gravity is…

Solution

Acceleration due to gravity – problems and solutions 5

R = Earth’s radius. At R above Earth’s surface = at 2R above Earth’s center.

Acceleration due to gravity – problems and solutions 6

At R above Earth’s surface, the acceleration due to gravity = ¼ g. If g = 9.8 m/s2, at R above Earth’s surface, acceleration due to gravity = 2.45 m/s2.

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