Experimental proof that gravity ~ 1/R^2 ?

Vanadium 50

Astronomically, there's no point in a test theory of Newtonian gravity, because we know that GR does a better job. There is something called the "PPN Formalism", which has a dozen or so inputs to calculate observable quantities; GR is consistent with observations.

Certainly 2 and 2 + ϵ can be distinguished. A change in ϵ by 1 unit will cause a perihelion advance of ~0.5 radian per orbit, which deviates from Newton by 43 million arc-seconds per century. So we have confirmed that |ϵ| < ~10^-6 or so astronomically.

In the lab, 2 + ϵ is one popular choice. Another is to multiply by an exp(-r/a) term and set limits on a.

TurtleMeister

It is my understanding that GR is no better at explaining the flat rotation curve of spiral galaxies than Newtonian gravity is, without using the unconfirmed existence of dark matter. So, as NSEFF has already stated, it seems that the law of 1/R^2 for gravity is merely a postulate at very long ranges.

NSEFF

CTHUGHA: Yes, MOND was what I had in mind, though it has been a long time since I ran across this concept and I am not familiar with its current details.

TURTLEMEISTER: While the arXiv article appeared to download, I was unable to open the pdf file. This has happened to me before. I think it is a configuration problem with the Adobe Reader which I'll have to look into.

NUGATORY: Newton postulated his Law, which had previously been suggested by others, and found the calculated orbits of planets closely matched the observations. I too pondered whether this could be deemed an empirical confirmation, but, logically, "If F ~ 1/R^2 => Calculated orbits closely match observations"; does not imply that "Observed orbits matching calculations => F ~ 1/R^2". That is, unless STEVENDARYL's reference to Bertrand's theorem is completely applicable: "that noncircular orbits are not stable except for a perfect inverse square law".

STEVENDARYL: What's nice about this forum is that often one encounters new ideas. Bertrand's theorem is new to me. I found no reference to it in any of my classical mechanics books. It must be something one encountered by astrophysicists.

Bertrand's theorem is predicated on stable, exactly closed orbits. Questions: How stable & exactly closed is Earth's orbit? How do you quantify a deviation from stability and being exactly closed (this would impact on estimating a bound on any deviation from inverse square)? Since the Sun is not stationary, does a finite propagation time for gravity need to be incorporated? Given that Pluto's orbital period is 246 years, has its orbit been sufficiently observed to be deemed stable and exactly closed? If not, and if Bertrand's theorem holds, it can only confirm inverse square to solar system dimensions?

DALESPAM: Good synopsis of theory testing. So, how do you test for 1/R^(2.000001) as opposed to 1/R^2? I presume, given experimental errors, it can't be done??

My original query was about whether direct empirical tests of the inverse square law exist. Other the short sub-millimeter torsion balance tests mentioned there don't seem to be any!

DaleSpam

How you test for 2.000001 is the same as how you test for 2. You still use a test theory, measure x, and see if 2.000001 is within the experimental error. Now, one thing that you have to do is to decide if your theory predicts exactly x = 2.000001, or if it predicts some range for x, e.g. [1.999998,2.000002]. In general, having such free parameters makes your theory more able to fit the data, but less able to predict new data.

Regarding the current level of experimental errors. The main test theory used today is the parameterized post Newtonian formalism. It has ten parameters, but I am not sure which of those correspond to the exponent for Newtonian gravity. But that is where I would start looking if I were you.

D H

That, too, is incorrect. Those are the only central forces where the force follows a radial power law (force proportional to rⁿ) for which noncircular orbits are closed. All that is needed for stability is that n > -3.

stevendaryl

Yes, you are right!