Many thanks,numerical integration of Eq.(25)succeeds in solving the problem, so congratulations! Eq. (27) comes from the apsidal method of note 403(6), Eq. (47), which you checked to be correct some days ago. I used the value of r at the perihelion. It may be better to compare the result of the direct integration with Eq. (42) of Note 403(6). In any case i will go through the note again.
Date: Sun, Mar 18, 2018 at 10:59 AM
Subject: Re: 403(8): Final Version of Note 403(7)
To: Myron Evans <myronevans123>
Numerical integration of (24) for a model system with alpha=1, epsilon=0.3 gives
Delta phi = 0.0119 * <drdr>.
From eq. (27), which is the near-curcular approximation, I obtain
Delta phi = 0.6533 * <drdr>
which is quite different. For epsilon=0 the integral gives Delta phi=0 as expected while (27) does not. I do not see that (27) is a meaningful approximation.
BTW, (26) is not the minimal but maximal u. In (27) there should be a minus sign in front of epsilon.
It is possible to construct a graph delta_phi/<drdr> in dependence of epsilon which could be interesting.
Horst
Am 16.03.2018 um 14:33 schrieb Myron Evans:
This leads to the integral (25), which has no analytical solution, but at the perihelion for nearly circular orbits leads to the result (27). It is seen that teh precesion at the perihelion is due to vacuum fluctuations. The result (25) is a small correction to an ellipse, and this correction is a precession.