Shown below is a satellite (m = 1000 kg) in a geosynchronous orbit. Recall that a geosynchronous orbit allows the satellite to remain over a fixed point on the planet, thus having an orbital period of 24 hours.
a) What is the necessary radius, from Earth's center, for a geosynchronous orbit?
b) What is the gravitational force exerted on the satellite by Earth at this radius?
c) What is the orbital velocity for the satellite?
d) What is the gravitational potential energy of the satellite?
e) What is the kinetic energy of the satellite?
f) What is the total energy of the satellite?
g) How much work was required to put the satellite into this orbit?
h) How much work would be required to move the satellite from its present orbit to an orbit that is one-half the previous value?
i) What is the period of rotation at this new position?
j) What is the orbital velocity at this new position?
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