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Orbital energy of ellipse and hyperbolic trajectory

  1. Dec 12, 2009 #1
    Please tell me how to find the orbital energy of ellipse and hyperbolic trajectory.
    Thank you.
     
  2. jcsd
  3. Dec 12, 2009 #2

    Janus

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    In both cases, it is the sum of the kinetic energy and gravitational potential at any point of the trajectory.

    Alternatively, if you know the semi-major axis(a), it can be found by:

    [tex]-\frac{GM}{2a}[/tex]
    for an ellipse

    and

    [tex]\frac{GM}{2a}[/tex] for a hyperbola.
     
  4. Dec 12, 2009 #3
    Please show me how to prove it.
     
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