Speed of satellite in geosynchronous orbit

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SUMMARY

The discussion focuses on deriving the speed of a satellite in geosynchronous orbit without using altitude or radius values. Participants emphasize the importance of applying forces and uniform circular motion principles while avoiding rotational kinematics and Kepler's Laws. A user expresses concern about potentially using rotational kinematics in their solution, specifically referencing the use of angular velocity and acceleration terms. The consensus is to rely on centripetal motion and verify the validity of the suggested methods.

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glennib
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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.
jk7lT4o.jpg


Thanks in advance.
 
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glennib said:
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.
 
Actually, I just remembered that rotational velocity = v/r, and that rotational acceleration = a/r. So yeah, if that helps, use it.
 

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