Question

A satellite in a circular orbit around the earth with a radius 1.011 times the mean radius of the earth is hit by an incoming meteorite. A large fragment (m = 75.0 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 359.0 m/s.

Find the total work done by gravity on the satellite fragment. R_E 6.37

Answer 1

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A satellite in a circular orbit around the earth with a radius 1.011 times the mean radius of the earth is hit by an incoming meteorite. A large fragment (m = 79 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 371 m/s. Find the total work done by gravity on the satellite fragment. RE 6.37 x 103 km; Mass of the earth= ME 5.98 x 10^24 kg.

PEinitial + KEinitial = PEfinal +KEfinal - W

KEi = 0
PEf = 0

W = KEf - PEi

Work Done = (1/2 * (65) * (369)^2) - (-G*(5.98*10^24)*(65))/(1.021*6.37*10^3)
Work Done = 4425232.5 - (-3.9881408782 * 10^-9)
Work Done = 4425232.5 J