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Angular Momentum and Orbits

  1. Mar 23, 2010 #1
    1. The problem statement, all variables and given/known data
    A planet has an eccentricity of 0.006800 and a semimajor axis of 0.7233 AU, find the ratio of ortibal speed at perihelion to that at aphelion.


    2. Relevant equations

    d=e x a
    L=mvrsin[tex]\theta[/tex]

    3. The attempt at a solution
    I plugged in and solved for the distance between the foci (0.004918)
    and then set the angular momentum constants equal to each other:
    m v(p) rmin sin[tex]\theta[/tex]=m v(a) rmax sin[tex]\theta[/tex]
    the masses and sin[tex]\theta[/tex] cancel out, so
    v(p) x r min = v(a) x r max
    and so the ratio is:
    v(p) / v(a) = r max / r min

    r max is the semimajor axis, and r min is the semimajor axis minus the d as found above:
    So, it should be .7233/.718382 which gives me 1.00685, but this was incorrect according to my online homework, could you tell me what I did wrong?
     
  2. jcsd
  3. Mar 24, 2010 #2

    Filip Larsen

    User Avatar
    Gold Member

    The relation vp/va = ra/rp is correct, but ra and rp are the aphelion and perihelion distances, respectively, and are given by ra = a(1+e) and rp = a(1-e).
     
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