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Constant energy in an elliptical orbit

  1. Nov 15, 2013 #1
    1. The problem statement, all variables and given/known data

    There's no specific question, but mostly a theory I wanted clarified. According to my textbook, the measurement of the total mechanical energy E of a mass orbiting a much larger mass in an ellipse is:

    E = radial (change in radius) kinetic energy + rotational kinetic energy + potential energy

    Or in other words,

    E = (1/2)μ(dr/dt)2 + (1/2)(angular momentum)^2 / μr2 - GMm/r

    But consider this: At both the apogee and perigee of the orbit the total energy should be constant and radial kinetic energy should be zero. Yet at these points the r is different and everything else is the same. How can energy be constant?

    2. Relevant equations

    r is the radius between the focus of the ellipse where the larger mass is and the smaller mass
    μ is the reduced mass 1/(1/m + 1/M)

    3. The attempt at a solution

    None so far. It seems like a rather fundamental issue with a hopefully fundamental fix.
     
    Last edited: Nov 15, 2013
  2. jcsd
  3. Nov 15, 2013 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Hello, sleepycoaster.

    Yes.

    Note that r occurs in the denominator of two terms and the two terms have opposite signs.
     
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