Correction term to Newtons gravitation law

[Kurret]

Hey!
My teacher told me that there is a correction term to Newtons law of gravitation when you take general relativity into account, somthing lik:

$F=G\frac{M_1M_2}{r^2}+F_{correction}$
I been searching like mad but can't find it on the internet anywhere. The only things I found was a set of insane differential equations and a lot of tensor notation, which is too advanced for me to convert to a force equation. Anyone know what my teacher means?

thanks in advance!

 

[Phrak]

I'm sure one could come up with a one of limited applicability--call it a 'perturbation force', for small masses and correct for orbital precession such as the Sun acting on the orbit of Mercury.

If you had such a corrective force in hand, it would fail to account for the deflection of light by gravity and fail to model black holes.

 

[Kurret]

Yea, I only need to approximate the correction terms magnitude to see if if an experiment i will do is good enough to measure it (i guess not), but it gets kind of hard when I don't know the real formula for it/dont know any general relativity...

 

[haushofer]

In every textbook you can find the non-relativistic limit of the Einstein equations. It's just a matter of taking into account second order effects, I would say. But I can't remember where these kind of calculations are done in detail.

 

[meopemuk]

This is called the Einstein-Infeld-Hoffmann Hamiltonian. The original paper is

A. Einstein, L. Infeld, B. Hoffmann, "The Gravitational Equations and the Problem of Motion",
Ann. Math., 39 (1938), 65.

You can also find it in section 106 of

L. Landau, E. Lifgarbagez, "Course of theoretical physics, Volume 2, Field theory"

Eugene.

 

[Phrak]

In every textbook you can find the non-relativistic limit of the Einstein equations. It's just a matter of taking into account second order effects, I would say. But I can't remember where these kind of calculations are done in detail.

I think you're right, if you mean second order terms in the pertubation of the Minkowski metric. Now, can you explain this to Kurret without using tensor calculus?

 

[Kurret]

This is called the Einstein-Infeld-Hoffmann Hamiltonian. The original paper is

A. Einstein, L. Infeld, B. Hoffmann, "The Gravitational Equations and the Problem of Motion",
Ann. Math., 39 (1938), 65.

You can also find it in section 106 of

L. Landau, E. Lifgarbagez, "Course of theoretical physics, Volume 2, Field theory"

Eugene.

Cool, i will check my library. You don't happen to have an internet source?

I think you're right, if you mean second order terms in the pertubation of the Minkowski metric. Now, can you explain this to Kurret without using tensor calculus?

that woudl be great :|
altough i don't really need the explanation, just the final expression for force interaction between two bodies...

 

[Phrak]

...although i don't really need the explanation, just the final expression for force interaction between two bodies...

Can you describe your intended experimental setup?

 

[Kurret]

Can you describe your intended experimental setup?

It is the Cavendish experiment, with lead balls of 2.5 and 0.0025 kg if I remember correctly.
http://en.wikipedia.org/wiki/Cavendish_experiment

 

[Phrak]

OK then. Your first challenge is to get Netwon. Worry about Einstein much later.

 

[Kurret]

OK then. Your first challenge is to get Netwon. Worry about Einstein much later.

Yea I know, i doubt my teacher really meant that I should try to measure that term, since he said that a value of G differing with maybe 20% should be considered a success. I think he just wanted me to think through if it was possible to measure that therm with the equipment available, and I believe the answer will be no but I still have to motivate it.

 

[D H]

The concept is summarized (but not derived) in section 10.2 of IERS Technical Note #32 entitled "Equations of Motion for an Artificial Earth Satellite." Here is a link to chapter 10 of that note:
http://www.iers.org/nn_11216/SharedDocs/Publikationen/EN/IERS/Publications/tn/TechnNote32/tn32__104,templateId=raw,property=publicationFile.pdf/tn32_104.pdf

For more on the topic (a whole lot more; 121 pages) see http://arxiv.org/abs/gr-qc/0403068.