1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Deriving Mechanics Equations for the Moon

  1. Jan 27, 2010 #1
    Alright, so I have a few questions.
    a) Consider a moon of mass m orbiting a planet of mass M in an elliptical orbit. The equation for the radius of an elliptical orbit is r=a(1-e2) / (1+ecos[tex]\vartheta[/tex]). Derive equations for the orbital radius of the moon when it closest to and farthest from the planet.
    My answer turns out to be periapse: r=a(1-e)
    and for apoapse: r=a(1+e) a is the semi major axis of the ellipse and e is the eccentricity

    b) Combing your result from a with angular momentum (L=mvr), derive an equations for the ratio of the moon's speed at periapse and apoapse in terms of eccentricty, that is vp/va.
    I ended up getting vp/va=(1+e) / (1-e)​

    c) Write down the equation which equates the total energy of the moon at apoapse with its total energy at periapse using the equation Ep=-GMm / r
    Im getting confused with this one. So the total energy would be the gravitational potential energy plus the kinetic energy right? So for the energy at periapse would look like
    E=(-GMm / r) + 1/2mv2
    the velocity being the one derived earlier.
    then using the equations derived in the first couple parts I end up getting
    E=(-2GMm + mv(1-e)) / (2a(1-e)​
    And somehow I think that is wrong. The next part asks me to show that at periapse
    v2=(GM / a)[(1+e)/(1-e)] ​
    but I may be over complicating things for part c and trying to solve d at the same time im not sure. Anyone have any ideas if I made a mistake earlier or if they can offer some advice in solving it?
  2. jcsd
  3. Jan 28, 2010 #2
    nevermind I figured it out
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook