Maximum distance in orbit from center of a planet

AI Thread Summary
The discussion focuses on calculating the initial speed (v0) required for a satellite to reach a maximum distance of 5R/3 from the center of a nonrotating planet. Participants reference the conservation of energy and angular momentum principles, noting the need to express the gravitational potential energy V(r) in terms of G, M, and R. The angular momentum is equated at the satellite's launch and its highest point in orbit. There is a mention of the gravitational acceleration formula a = GM/R^2, but its relevance is questioned. The conversation emphasizes the application of these physics concepts to solve the problem effectively.
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Homework Statement


Consider a spherical, nonrotating planet of mass M, and radius R, with no atmosphere. A satellite is fired from the surface of the planet with speed v0 at 45o from the local vertical. In its subsequent orbit the satellite reaches a maximum distance of 5R/3 from the centre of the planet. Use conservation of energy and angular momentum to find vo in terms of G, M, R.


Homework Equations



E=\frac{1}{2}mvr2+L2/2mr2+V(r)



The Attempt at a Solution


so far all I have is a=GM/R^2, which I probably don't even need.
 
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Have you got a formula for V(r)?
Also need to work on momentum:
Angular momentum at start = angular momentum at apogee
 
Well, L=mrv or L=mbv0
and i guess V=-GmM/r but i don't know how to use these at this point..
 

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