Answer:
[tex]5.0\cdot 10^{10}J[/tex]
Explanation:
The work W required to make an object escape from a gravitational field is given by
[tex]W=m(V_{\infty}-V)[/tex]
where
m is the mass of the object
V is the gravitational potential at the initial position of the object
[tex]V_{\infty}=0[/tex] 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
[tex]V=-\frac{GM}{R}[/tex]
where
[tex]G = 6.67\cdot 10^{-11} Nm^2/kg^2[/tex] is the gravitational constant
[tex]M=5.98\cdot 10^{24} kg[/tex] is the mass of the Earth
[tex]R=6.37\cdot 10^6 m[/tex] is the Earth's radius
Substittuing into the initial equation, we find:
[tex]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[/tex]
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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