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Maximum distance in orbit from center of a planet

  1. Oct 21, 2009 #1
    1. The problem statement, all variables and given/known data
    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.


    2. Relevant equations

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



    3. The attempt at a solution
    so far all I have is a=GM/R^2, which I probably don't even need.
     
  2. jcsd
  3. Oct 21, 2009 #2

    Delphi51

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    Homework Helper

    Have you got a formula for V(r)?
    Also need to work on momentum:
    Angular momentum at start = angular momentum at apogee
     
  4. Oct 22, 2009 #3
    Well, L=mrv or L=mbv0
    and i guess V=-GmM/r but i dont know how to use these at this point..
     
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