Proof of angular speed of satellite

AI Thread Summary
The discussion focuses on proving the orbital angular momentum of a geostationary satellite, specifically that ω² = G(M/R³), where G is the gravitational constant, M is Earth's mass, and R is the orbital radius. Participants suggest using Newton's 2nd Law to equate the gravitational force acting on the satellite with the centripetal acceleration required for circular motion. The importance of understanding circular motion and centripetal acceleration is emphasized in the context of the proof. The thread highlights the need for a clear mathematical approach to derive the equation. Overall, the conversation centers on the principles of physics necessary to validate the relationship for satellite motion.
Miklagaard
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What do you know about circular motion? In particular, about centripetal acceleration?
 
Miklagaard said:

Homework Statement


http://img577.imageshack.us/img577/5457/gmblrekp.th.jpg
The problem is to show that the orbital angular momentum of a geostationary satellite is given by \omega^2=G{{M}\over{R^{\,3}}}\,, where G is the gravitational constant, M is the mass of the earth, and R is the radius of the orbit.

Miklagaard said:

Homework Equations





The Attempt at a Solution



Proof was asked from me. How do i proof it.

In "w^2 sub. uydu", uydu means satellite.

Use Newton's 2nd Law. Equate the gravitational force on the satellite to the product of the satellite's mass times its centripetal acceleration.
 
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