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simple math question about orbital motion
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]] |
#2
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simple math question about orbital motion
On 2018-04-11, 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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