Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Speed at perihelion and aphelion?

  1. Jan 16, 2009 #1
    SO the equations for the speed at the aphelion and perihelion are, respectively:

    v=SQRT[GM( (2/r_p) -(1/a) )]

    v=SQRT[GM( (2/r_a) - (1/a) )]

    where M is mass of sun, r_a & r_p are distances from sun at aphelion and perihelion , and a is length of semi major axis.

    How do you derive them? I am having trouble seeing where they come from, and a quick Google turns up NOTHING on them unfortunately.

    ANy help?
  2. jcsd
  3. Jan 16, 2009 #2

    D H

    Staff: Mentor

    Those equations result simply from inserting the perifocal and apofocal distances into the vis-viva equation,

    [tex]v^2 = GM\left(\frac 2 r - \frac 1 a\right)[/tex]

    This equation follows directly from conservation of energy. The total energy (kinetic plus potential) of a point mass m separated by a distance r from some other point mass M and moving with a velocity v relative to that other point is

    [tex]E = \frac 1 2 m v^2 - \frac {G M m}{r}[/tex]

    The total energy of a point mass in an elliptical orbit is also given (see any intermediate-level classical mechanics text) by

    [tex]E = - \frac {G M m}{2a}[/tex]

    Equating the two expressions leads directly to the vis-viva equation.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Speed at perihelion and aphelion?
  1. Mechanics. Speed. (Replies: 2)

  2. Speed of EMW (Replies: 1)

  3. Speed of sound (Replies: 2)

  4. Speed of shockwaves (Replies: 8)