Can a New Gravity Theory Rival Einstein's Predictions?

[Crosson]

We all know that Einsteins GTR accounts for observations that Newtonian gravitation cannot account for. I have "created" a theory of gravity (I put created in quotes becase it feels more like I found it) that makes corrections to Newtonian gravity in the same extreme relativistic cases. (this theory is compatible with STR) . For the purposes of math, I am talking about a force that is a function of radial distance: F(r).

The point of bothering you all with this, is that I would like to test my theory of gravity against experimental observations. I have thought about the classic test: the precession of the perihelion of mercury, but I have no idea how to undertake this calculation (I have studied the classical two body problem, but I don't know how to account for the perturbations caused by the other planets that cause the precession in the first place). I have tried looking for books, but I cannot find any that treat this problem in detail.

If anyone can suggest another test of GTR (besides gravitational lensing) that I could test my theory with, I would be very grateful. If anyone can tell me anything about the precession of the perihelion of mercury, I would be very grateful. I have heard that every testable prediction of GTR is based on the Schwarzschild metric, is this true?

 

[Nereid]

Hi Crosson,

The best place to start is http://relativity.livingreviews.org/Articles/lrr-2001-4/ - not only is there a very long list of tests of GR, but also literally hundreds of references.

I'm also moving this to the SR&GR section; you'll likely get a more focused set of replies here.

 

[pervect]

There is some limited information in Goldstein's "Classical mechanics", in the chapter on canoincal pertubatio theory, pg 511-512. However, the pertubation of the other planets isn't really addressed, only the pertubation due to GR, which is idealized as a small 1/r^3 "pertubation term" in the gravitational potential.

 

[dextercioby]

How about corrections to the Lorentz gamma factor ? As the influention of gravity fields on time dilation,length contraction,relativistic mass...

Daniel.

 

[pervect]

Here's what Goldstein has to say

In other words, the pertubation potential is a function of the dynamical variables only through r; it is not to be construed as velocity dependent.

Goldstein notes that you can derive the 1/r^3 potential correction from the 1-d energy equation on pg 688 of MTW's gravitation.

 

[HackaB]

Crosson:

What is your theory?

 

[Crosson]

Thanks for the information everyone, its funny how tough it is to dig up the nitty gritty details of these results that we hear quoted so often. So far, I am leaning towards the problem of the perihelion of mercury because it seems to be the easiest.

I had envisioned numerically solving differential equations to check the shift in perihelion by brute force. I am beginning to get the impression that the reason I have not seen this done in the literature is that it hasn't been done, because perturbation theory allows for a better way.

I have worked with perturbations before, but not in the context of celestial mechanics. Given that I will investigate the resources you have recommended, I would be grateful if you could answer this question: Would it be as simple as solving the two body problem, and then perturbing the angle theta to see how the perturbation grows in time? Alternatively (but just as simplemindedly), should I perturb the force and then solve the two body problem?

 

[pervect]

It's not quite that simple :-(. If you've done Hamilton-Jacobi theory and "action-angle" variables, or you've heard of Delaunay variables, Goldstein's approach will look pretty attractive. Otherwise, it might not.