Question

In this age of Information, it is imperative that we be able to maintain constant communications with different parts of the world. In order to do this, we use satellites placed in orbit with a broad range of areas over which they can transmit and receive signals.

As satellites orbit the Earth they are in constant motion. To ensure that we never lose contact with some of our satellites they are placed in a Geosynchronous orbit.

There is a delicate balance between the pull of gravity and the uniform circular motion of the satellites. As it turns out there is only ONE possible combination of Altitude and Speed for a Geosynchronous satellite that will work. Your job is to calculate each one using the knowledge you have gained from the class. You may have to look up a few values and/or definitions.

a) DERIVE an equation & Solve for the Speed of a satellite in Geosynchronous orbit.

       (You may NOT use the value of the satellite’s Altitude or Radius in your calculations, if you do, you will receive no credit.)

b) DERIVE an equation & Solve for the Altitude of a satellite in Geosynchronous orbit.

      (You may NOT use the value of the satellite’s Speed in your calculations, if you do, you will receive no credit)

c) PRODUCE a general solution for the amount of work done on the satellite during one        

      complete orbit.

NOTE:

• You should use your knowledge of the Forces & Uniform Circular Motion for this assignment.
• DO NOT use the rotational kinematics from chapter 10. If you do you will receive NO credit.
• DO NOT attempt to apply Kepler’s Laws. If you do you will receive NO credit.
• To make life easy on you & me, ASSUME the orbit of the satellite to be CIRCULAR!
• Use Newton’s Universal Law of Gravity to help:

Fg=Gm1m2/R^2

-where G is the gravitation constant of the universe, m1 & m2 are the two masses involved and R is the center-to-center separation distance between the masses. You will need to lookup values for G and mass of Earth.

If possible make the parts A,B,C clear to tell which is which

Answer 1