1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Energy of orbits

  1. Jan 28, 2010 #1
    1. The problem statement, all variables and given/known data
    Show the the total energy of a parabolic is zero.
    Show that the energy of a hyperbolic orbit is positive.


    2. Relevant equations
    [tex]r=\frac{L^2}{GM\mu^2*(1+e cos\theta)}[/tex]
    [tex]v^2=GM \left (\frac{2}{r}-\frac{1}{a} \right )[/tex]


    3. The attempt at a solution
    [tex]E=T+U=\frac{1}{2}\mu v^2 -\frac{GM\mu}{r}[/tex]
    [tex]=\frac{1}{2}\mu GM \left (\frac{2}{r}-\frac{1}{a} \right ) -\frac{GM\mu}{r}[/tex]
    [tex]= \frac{\mu GM}{r}-\frac{\mu GM}{2a} -\frac{GM\mu}{r}[/tex]
    [tex]=-\frac{\mu GM}{2a} [/tex]
    So somehow I have to show that a, the semi-major axis is infinity for a parabola and a is negative for a hyperbola. But what is "a" for a parabola and hyperbola? How can I define them?
     
  2. jcsd
  3. Jan 28, 2010 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi E92M3! :smile:
    For an ellipse, the semi-major and semi-minor axes are a and b, with x2/a2 + y2/b2 = 1.

    For a hyperbola, x2/a2 - y2/b2 = 1, and a is still the semi-major axis (and there is no semi-minor axis).

    For a parabola, a is infinite (a bit obvious, since one focus is at infinity anyway :wink:)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Energy of orbits
  1. Energy for orbits (Replies: 4)

  2. Orbital Energy (Replies: 5)

  3. Orbital Energy (Replies: 1)

  4. Orbits and Energy (Replies: 7)

  5. Orbit and Energy (Replies: 20)

Loading...