An alternate solution would be to simply divide the circumference of the orbit, by velocity, to obtain time or in other words the period.
g) When calculating the work required to take an object from Earth's surface to some radial distance away, we need not concern ourselves with the kinetic energy of the object when on the planet's surface. It's value is rather insignificant when compared to the potential energy the object when on the planet's surface, due to the fact that the velocity on the Earth's surface is only 463 m/s, which translates into a relatively small initial kinetic energy. Note as well that the expression for kinetic energy as shown in part (f) is not valid at the Earth's surface since the satellite is not in orbit about the Earth initially, but only sitting on it.
h) In this case, the satellite is already in orbit, thus having both kinetic and potential energy values of significance and both orbital radii. Therefore, the work required is equal to the change in total energy.
Notice that the work required to move through a distance of one Earth radii, when the satellite is already in orbit, is approximately one-ninth of what it was to move the satellite that same distance off the Earth's surface.
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