# 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 10^{22} kg, the radius of the Moon is 1.7 x 10^{6} m, universal constant is 6.67 x 10^{-11} N m^{2} / kg^{2}

Solution

The formula of Newton’s second law of motion :

The formula of Newton’s law of universal gravitation :

*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 :

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

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

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

At R above Earth’s surface, the acceleration due to gravity = ¼ g. If g = 9.8 m/s^{2}, at R above Earth’s surface, acceleration due to gravity = 2.45 m/s^{2}.

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