Physics 12 - Quiz #4
Geosynchronous Orbits

Solution:

a) If the orbital period, T, is required to be 24 hours, we must first convert that value into seconds

b)

c)

 or

d)

e)

f)

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 (e) 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 at both orbital radii. Therefore, the work required is equal to the change in total energy.

Notice that the work required to move the satellite into a closer orbit is negative since the system does the work. No external force is required.

i)

 or using Kepler's Law

j) At the new radius of one-half the original we expect the kinetic energy to be greater and thus so to the velocity.

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