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I Trajectories of planets using reduced mass and CM frame

  1. Apr 9, 2016 #1
    In planetary motion, the reduced mass of a system [itex]\mu[/itex] is used in order to study the motion of the planet [itex]m[/itex] in the non-inertial frame of the star [itex]M[/itex]. Using [itex]\mu[/itex] the trajectory of [itex]m[/itex] turns out to be a conic. But this is the trajectory of the planet [itex]m[/itex] as seen from the star [itex]M[/itex], correct?

    I read that in the CM frame the trajectories are still conics (ellipses for istance) but that the focus is in the CM. Moreover the Sun (or the star) also follows a conic trajectory with focus in the CM of the system.

    Is the trajectory of the planet seen in CM frame different from the one calculated using [itex]\mu[/itex] (and so the one in the [itex]M[/itex] frame)?
     
  2. jcsd
  3. Apr 9, 2016 #2
    if you see the resources on the net detail plots are there of the orbits when the observer moves from centre of mass frame to one of the bodies.

    for example
    [PDF]The Two-Body Problem - KSU Math Home
    https://www.math.ksu.edu/~dbski/writings/twobody.pdf
     
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