Gravitational and electric fields

AI Thread Summary
The discussion focuses on deriving the relationship T^2 proportional to R^3 using centripetal force in planetary orbits. Participants reference Kepler's third law and attempt to manipulate equations related to orbital period and gravitational force. The key equations discussed include the circumference of the orbit and the expression for period P in terms of radius R and gravitational constants. There is confusion about the origins of certain expressions and the application of Newton's second law to find radial acceleration. The conversation emphasizes the need to clarify these equations to complete the derivation successfully.
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Homework Statement


By considering the centripetal force which acts on a planet in a circular orbit, show that T^2 is proportional to R~^3 where T is the time taken for one orbit around the sun and R is the radius of the orbit


Homework Equations


I'm thinking keplers third law?



The Attempt at a Solution


C=2piR

P=2piR/ sqrt*GMm/r

rearranged to give P = 2pi sqrt*R^3/GM

Lost now..
 
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confusedpilot said:

P=2piR/ sqrt*GMm/r


Where did that expression come from?


Find an expression for the radial acceleration in terms of the orbital speed and R.

Then use Newton's second law.
 

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