How much energy would be required to move the Moon from its present orbit around

Question

How much energy would be required to move the Moon from its present orbit around Earth to a location that is four times as far away? Assume the Moon's orbit around Earth is nearly circular and has a radius of 3.84 times 10^8 m, and that the Moon's orbital period is 27.3 days. 9.33E27 J The nonconservative work required to move the Moon from its present orbit to a location four times as far away is equal to the change in the Moon's mechanical energy. We need to determine the initial and final speeds of the Moon in order to calculate the change in the kinetic energy. We can relate the initial speed of the moon to its orbital period (T_0 = 27.3 days). The final orbital period can be found in terms of the original orbital period through Newton's second law. The net force acting on the Moon is the gravitational force due to the Earth: this net force causes the Moon to undergo centripetal motion. The mass of the Earth is 5.98 times 10^24 kg, the mass of the Moon is 7.35 times 10^22 kg, and the initial distance from the center of the Moon to the center of the Earth is 3.84 times 10^8 m.

Explanation / Answer

Given that

new distance d=4*3.84*10^8 m=15.36*10^8 m

mass of earth M=5.98*10^24 kg

mass of moon m=7.35*10^22 kg

basing on the concept of the gravitation

now we find the energy required to move

energy E=GMm/d

=6.67*10^-11*5.98*10^24*7.35*10^22/15.36*10^8

=19.1*10^27 J

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