Question

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.

Answer 1

Answer:

$5.0\cdot 10^{10}J$

Explanation:

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

$W=m(V_{\infty}-V)$

where

m is the mass of the object

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

$V_{\infty}=0$ 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

$V=-\frac{GM}{R}$

where

$G = 6.67\cdot 10^{-11} Nm^2/kg^2$ is the gravitational constant

$M=5.98\cdot 10^{24} kg$ is the mass of the Earth

$R=6.37\cdot 10^6 m$ is the Earth's radius

Substittuing into the initial equation, we find:

$W=-mV=\frac{GMm}{r}=\frac{(6.67\cdot 10^{-11})(5.98\cdot 10^{24})(800)}{6.37\cdot 10^6}=5.0\cdot 10^{10}J$