Testing a Theory of Gravity

In summary, Daniel has created a theory of gravity that makes corrections to Newtonian gravity in the same extreme relativistic cases. He is interested in testing his theory against experimental observations, but does not know how to calculate the precession of the perihelion of mercury. If anyone can suggest another test of GTR (besides gravitational lensing), he would be grateful.
  • #1
Crosson
1,259
4
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?
 
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  • #2
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.
 
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  • #3
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.
 
  • #4
How about corrections to the Lorentz gamma factor ? As the influention of gravity fields on time dilation,length contraction,relativistic mass...

Daniel.
 
  • #5
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.
 
  • #6
Crosson:

What is your theory?
 
  • #7
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?
 
  • #8
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.
 

What is a theory of gravity?

A theory of gravity is a scientific explanation that describes the force of gravity and how it affects objects in the universe.

Why is it important to test a theory of gravity?

Testing a theory of gravity allows scientists to gather evidence and determine if the theory accurately explains the phenomenon of gravity. It also helps to refine and improve the theory, leading to a better understanding of the natural world.

How do scientists test a theory of gravity?

Scientists can test a theory of gravity through various methods, such as conducting experiments, making observations, and using mathematical models. These tests can provide evidence to support or refute the theory.

What are some potential outcomes of testing a theory of gravity?

The results of testing a theory of gravity can lead to three potential outcomes: confirmation, refinement, or rejection. If the evidence supports the theory, it is confirmed. If the evidence suggests changes or improvements to the theory, it is refined. If the evidence contradicts the theory, it is rejected.

What are some real-life applications of a theory of gravity?

A theory of gravity has many practical applications in fields such as astronomy, space exploration, and engineering. It helps explain the motion of celestial bodies, enables the prediction of astronomical events, and is essential for the design and operation of spacecraft and satellites.

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