Yes, there is indeed a factor (1-e^2) missing. I had it originally, but later "corrected" it away. I'll amend the answer soon. The factor [a] must be an error on your part, already because otherwise the physical dimension would be wrong.

On the physical dimension factors (using the notation whereby [.] denotes physical dimension): [h^2 v_r R / r^4] = [vc^2 a^2 vc a / a^4] = [vc^3 / a] = [Omega vc^2] since Omega=vc/a; and [v_r^2 V_t / r] = [vc^2 vc / a] = [vc^3 / a] = [Omega vc^2].

But you're correct regarding the values of the integrals. So, finally, we arrive at a formula that agrees with Einsteins (for K=3). I wonder whether there wasn't a simpler way to get there ...

Yes you are right about [a] I made an error. I realize you previously had the right (1-e^2) factor. This is a very pleasing result. Is it possible to indicate (from the analysis) the direction of periapse rotation? e.g. in same sense as planet motion or in opposite sense.

I'm not sure what you mean by "a simpler way to get there" do you mean a different form of peturbation analysis? For me the "simplest" way is by plugging the force into an orbital simulator but there is the difficulty of proving that particular results are not caused by artefacts of the simulation method.

I would like to refer to your analysis at some time in future. Would you consider publishing it in some form?

By simpler way to get there, I meant a simpler way to do the perturbation analysis. I would like to refer to your analysis at some time in future. In which context? In a publication?

The direction of periapse roation is in the sense of rotation (for K>0), since omega points in the direction of h.

Btw, I wouldn't mind if you finally accept my answer ...

Answer accepted - sorry I should have done that long before now.

"Simpler way" - OK, thanks for clarifying.

Direction of rotation. OK, thanks.

Re: "Refer to your analysis". In longer term I hope to publish my underlying model and ideally would like to refer to a published peer-reviewed form of your peturbation analysis. In short-term I need academic support in getting my model fit for publication and would like to refer (in correspondence or speech) to your analysis to help convince potential supporters that my model is worth consideration.