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Elliptical Orbits velocity and distance

  1. Oct 11, 2009 #1
    This question is of an elliptical orbit with v1 ant its distance r1 and a second v2 with distance r2 located a different point in the elliptical orbit
    Which general relation connects the speed
    vi of the satellite and its distance ri from
    the center of mass of the planet at any two
    arbitrary points on the orbit?

    I thought it was r1 v1 = r2 v2 based on Keplers 2 law
    but that is not the answer, and im confused between these two i know it might be a because
    that is the equation of total energy, but what confuse me is that its multiplied by 2

    a)v^2−(2GM/r1)= v^2−(2GM/r2)

    b)v^2/r1=v^2/r2

    I hope you all can clear my confusion thank you
     
  2. jcsd
  3. Oct 12, 2009 #2

    D H

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    One way to express Kepler's 2nd law is that [itex]r v_{\perp} = \text{constant}[/itex], where [itex]r v_{\perp}[/itex] is the component of the velocity perpendicular to the line connecting the center of the planet and the satellite.

    The total energy of the satellite doesn't change; it is a constant of the orbit. If you multiply a constant by 2 (or by any other constant) you still have a constant.

    One of those equations is indeed just the total energy times some constant. The other one is wrong.
     
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