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  • simple math question about orbital motion

    From alsor@interia.pl@21:1/5 to All on Wed Apr 11 11:15:17 2018
    An acceleration of an orbiting body, in a central force, is defined as:

    a(r,v) = -k/r^2(1 + v^2/c^2)

    k = GM = const, v = dr/dt = r'

    what is the precession of perihelion,
    or the apsidal angle in this case?

    [[Mod. note -- This appears to be a homework exercise; our usual
    policy in the newsgroup is to not provide an answer but rather to
    try to explain appropriate methods for the student to obtain the
    answer themself.
    -- jt]]

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  • From Bruce Scott@21:1/5 to alsor@interia.pl on Fri Aug 24 16:40:36 2018
    On 2018-04-11, <alsor@interia.pl> <alsor@interia.pl> wrote:
    An acceleration of an orbiting body, in a central force, is defined as:

    a(r,v) = -k/r^2(1 + v^2/c^2)

    k = GM = const, v = dr/dt = r'

    what is the precession of perihelion,
    or the apsidal angle in this case?

    Basically, solve it without the v/c correction (ellipse) and then
    treat the extra term as a perturbation. The orbit will close slightly
    slower given the sign of the correction. Use this to find the extra shift
    of the closure angle (ie, where r dot is minimum). There is a trick to simplify it but I have forgotten it :-)

    (IIRC it is well described in Ohanian's text on General Relativity)

    --
    ciao, Bruce

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