Speed of satellite in geosynchronous orbit

[glennib]

Homework Statement

Derive an equation and 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.

• You should use your knowledge of forces and 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.

Homework Equations

I have arrived at a solution, but I suspect that I have used rotational kinematics. Can someone confirm or dismiss this?

The Attempt at a Solution

Here is a screenshot from my Maple work. It is relationship1 (1) and (2) that I am worried about.

Thanks in advance.

 

[majormaaz]

I have arrived at a solution, but I suspect that I have used rotational kinematics. Can someone confirm or dismiss this?

Here is a screenshot from my Maple work. It is relationship1 (1) and (2) that I am worried about.

If I recall, rotational kinematics is full of ω's, and such associated terms. Step 1 is the formula for a period, and step 2 is just the application of centripetal motion.

I think your work in regards to your rules/restrictions looks fine, but I strongly advise you not to take my word for it, and just double check that my suggestions are valid.

 

[majormaaz]

Actually, I just remembered that rotational velocity = v/r, and that rotational acceleration = a/r. So yeah, if that helps, use it.