m earth = 5.9742 x 10 24 kg r earth = 6.3781 x 10 6 m m moon = 7.36 x 10 22 kg r

Question

mearth = 5.9742 x 1024 kg
rearth = 6.3781 x 106 m
mmoon = 7.36 x 1022 kg
rmoon = 1.7374 x 106 m
dearth to moon = 3.844 x 108 m (center to center)
G = 6.67428 x 10-11 N-m2/kg2

A 1800 kg satellite is orbitting the earth in a circular orbit with an altitude of 1700 km.

1How much energy does it take just to get it to this altitude?

2)How much kinetic energy does it have once it has reached this altitude?

3)What is the ratio of the this change in potential energy to the change in kinetic energy? (i.e. what is (a)/(b)?)

4)What would this ratio be if the final altitude of the satellite were 4900 km?

5)What would this ratio be if the final altitude of the satellite were 3185 km?

Explanation / Answer

The total energy required to put a satellite into an orbit of radius r around a planet of mass M and radius R is therefore the sum of the gravitational potential energy (GMm[1/R-1/r]) and the kinetic energy of the satellite (

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