# Correction term to Newtons gravitation law

1. May 8, 2010

### 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 cant 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?

2. May 8, 2010

### 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.

Last edited: May 8, 2010
3. May 8, 2010

### 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 dont know the real formula for it/dont know any general relativity...

4. May 8, 2010

### 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.

5. May 8, 2010

### 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.

6. May 8, 2010

### Phrak

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? :uhh:

7. May 8, 2010

### Kurret

Cool, i will check my library. You dont happen to have an internet source?

that woudl be great :|
altough i dont really need the explanation, just the final expression for force interaction between two bodies...

8. May 8, 2010

### Phrak

Can you describe your intended experimental setup?

9. May 8, 2010

### Kurret

10. May 8, 2010

### Phrak

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

11. May 8, 2010

### Kurret

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.

12. May 8, 2010

### D H

Staff Emeritus
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 [Broken]

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

Last edited by a moderator: May 4, 2017