Use Newton's Law of Gravitation to compute the work W required to propel a 800 kg satellite out of the earth's gravitational field. You may assume that the earth's mass is 5.98✕1024 kg and is concentrated at its center. Take the radius of the earth to be 6.37✕106 m and G = 6.67✕10-11 Nm2/kg2.

The work done in propelling an 800 kg satellite out of the earth's gravitational field is 5 ✕10^10 J.

The work done in propelling an 800 kg satellite out of the earth's gravitational field is given by the gravitational potential energy;

U = GMeM/re

U = gravitational potential energy

G = gravitational constant

Me = mass of the earth

M = mass of the body

re = radius of the earth

Substituting values;

U = 6.67✕10^-11 Nm2/kg2 ✕ 5.98✕10^24 kg ✕ 800 kg/6.37✕10^6

U = 5 ✕10^10 J

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Explanation:

The work W required to make an object escape from a gravitational field is given by

where

m is the mass of the object

V is the gravitational potential at the initial position of the object

is the potential at infinity

In this problem, we have:

m = 800 kg is the mass of the satellite

The gravitational potential at the Earth's surface is given by

where

is the gravitational constant

is the mass of the Earth

is the Earth's radius

Substittuing into the initial equation, we find:

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