A satellite in a circular orbit around the earth with a radius 1.021 times the m

Question

A satellite in a circular orbit around the earth with a radius 1.021 times the mean radius of the earth is hit by an incoming meteorite. A large fragment M = 77.0 kg is ejected in the backwards direction so that it is stationary with respect to the earth and falls directly to the ground. Its speed just before it hits the ground is 365.0 m/s. Find the total work done by gravity on the satellite fragment. The radius of the Earth = 6.37 times 103 km; The mass of the Earth = 5.98 times 1024 kg. Calculate the amount of that work that is converted in to heat.

Explanation / Answer

using work energy principle:

initial potential energy of the large fragment + work done by gravity=final kinetic energy of the fragment

==>(-G*mass of earth*mass of fragment/distance)+work done=0.5*mass of fragment*speed^2

==>(-6.67*10^(-11)*5.98*10^24*77/(1.021*6.37*10^3*1000 ))+work done=0.5*77*365^2

==>work done=4.73*10^9 J

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