a 83.5 kg satellite has a perigee of 6.61 x 10^6m and a apogee of 7.33 x 10^6m. What is the difference in gravitational potential energy as it moves from perigee to apogee.
Homework Answers
In this case the gravitational PE is given by
U = -GMm/r
where r is the distance from the center of the earth
So
Ua = Uf = -GMm/Ra
Up = Ui = -GMm/Rp
so
Uf - Ui = -GMm(1/Ra - 1/Rp)
Rp,a must be in meteres
G = 6.67E-11
M = 5.98E24kg
m=83.5 kg
Uf - Ui = -GMm(1/Ra - 1/Rp) = -(6.67*10^-11*5.98*10^24*83.5)*[(1/7.33*10^6) - (1/6.61*10^6)]
= 494926326.43 J = 4.95*10^8 J
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