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College Physics

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A satellite in an elliptical orbit has a speed of 9.00km/s when it is at its closes approach to the Earth(perigee). The satellite is 7.00x10^6 m from the center of the Earth at this time. When the satellite is at its greatest distance from the center of the Earth (apogee), its speed is 3.66km/s. Find the distance from the satellite to the center of the Earth at apogee. (assume any energy losses are negligible.)

  • College Physics -

    Post your work thus far and I'll continue/correct/guide

  • College Physics -

    Kfinal + Ugravfinal = Kinitial + Ugravinitial
    which i ended up with
    Vfinal^2 + [2GM/r] = Vinitial^2 + [2GM/r]

    I believe I need to solve for r but this is where I got stuck.

  • College Physics -

    Well since it's an elliptical orbit you can set them the distances as functions of Kvff^3


    Tell me what you get

  • College Physics -

    Quick explanation because I have to go;
    Rearrange values so that kf^3=vf%
    vf% is of 6.76 because of orbit while 3.33 is the continual. Solve for d%
    d% the continual converted to elliptical motion is going to be roughly 4.1882 (4.188? I believe it's two, but shouldn't matter)
    By Ugravinitial
    and you have d when you apply the standard orbital motion functions.

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