• #### 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
-- 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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