Newton Gravity Minimum Distance

[J.C.MacSwell]

Does anyone know the experimentally measured minimum distance where the inverse square law holds?

[insane_alien]

there is only a minimum distance for non-pointsource objects.

 

and it depends on how rigorously you define it as holding. for instance, the earth has a slightly lumpy gravitational field. in theory this would show deviations from a point source up to infinity meters away but they wouldn't really matter much closer than that.

 

it does have a slight effect on LEO orbits but nothing spectacular.

 

we'd need some definitions of what counts and what doesn't to answer.

[John Cuthber]

Arguably it's still following the inverse square law when it's being lumpy.

If you calculate the effect on the satellite of each lump of the earth following the inverse square law you get the right answer.

Also, it has been measured on a tabletop scale as well as on the astronomical scale.

[J.C.MacSwell]

there is only a minimum distance for non-pointsource objects.

 

and it depends on how rigorously you define it as holding. for instance, the earth has a slightly lumpy gravitational field. in theory this would show deviations from a point source up to infinity meters away but they wouldn't really matter much closer than that.

 

it does have a slight effect on LEO orbits but nothing spectacular.

 

we'd need some definitions of what counts and what doesn't to answer.

 

Hi IA

 

I'm not looking for anything to rigorous, just a more or less accepted (proven) distance where if you move 2 objects closer you get roughly the expected change. The nature of the decreasing distance would, I think, make measurement difficult as other forces dominate and the masses would have to be correspondingly smaller...but I wondered how close they have reasonably come to approaching zero distance and to what accuracy with inverse square still apparent.

[timo]

I think MacSwell asked for actually performed experiments, not for an explanation of school physics. From theory, you would btw. not only expect a breakdown at small distances, but also at large massed. Iow, if you were define a cut-off distance d in some way, it would probably not be a constant but a function of the masses involved.

[elfmotat]

Just like when going from Newtonian physics to special relativity with increasing speed, there is no clear-cut line where one "takes over." When speeds get faster and faster the effects of SR become more and more evident, until eventually Newtonian predictions are no longer useful. There's no distinct speed where this happens; it's a gradual change. Likewise, going to smaller and smaller scales will result in the inverse square law becoming less and less accurate until eventually it's nonsensical to even talk about, and you'd need quantum gravity to explain what's happening.

Edited June 5, 2012 by elfmotat

[insane_alien]

I think MacSwell asked for actually performed experiments, not for an explanation of school physics. From theory, you would btw. not only expect a breakdown at small distances, but also at large massed. Iow, if you were define a cut-off distance d in some way, it would probably not be a constant but a function of the masses involved.

 

I was only asking what the criteria were. there isn't going to be a defined cutoff but a gradual divergence from the 1/r^2 relationship.

 

you could take every satellite we have in orbit as an experiment. the non-spherical gravity of earth plays a role in orbit perturbances of LEO satellites but not much for GEO satelites.

 

its even the mechanism of how the mapped the earths gravitational field as well as the moons.

 

as his question was posted it was a bit like 'how far out does gravity go?' the true answer is infinity but really, the effects become practically insignificant LONG before that.

 

I don't think any specific experiments have been done just reviews of the orbits of various satellites if anything.

 

J.C. googling "Osculating Orbits" and variants there of might return something useful.

 

http://articles.adsabs.harvard.edu//full/1934PASP...46..305K/0000305.000.html

 

http://en.wikipedia.org/wiki/Osculating_orbit

 

But as before, the limit where you can ignore the perturbations is going to vary from application to application, planet to planet and even how close the other gravitational bodies happen to be.

[D H]

Does anyone know the experimentally measured minimum distance where the inverse square law holds?

It's in the sub-millimeter range. Gravitation is an extremely weak force, so looking for potential small-scale violations is rather difficult. There are multiple groups that do just this. Two of them: The Eöt-Wash Group at the University of Washington and the Birmingham Gravitation Group at the University of Birmingham.

[J.C.MacSwell]

It's in the sub-millimeter range. Gravitation is an extremely weak force, so looking for potential small-scale violations is rather difficult. There are multiple groups that do just this. Two of them: The Eöt-Wash Group at the University of Washington and the Birmingham Gravitation Group at the University of Birmingham.

 

Thanks DH. That seems more in line with what I was after, although it is closer than I expected. I'm not sure how much could have been inferred from variances of orbits, unless I am missing something that would still be distant affects.

 

At sub millimeter the masses have to be quite small just to "fit" in the experiment so I wonder what assumptions are in place to get that result.

 

So, the gravitational attraction of 2 (very small) masses at 1mm could be measured to quadruple (approximately) at 0.5mm?

Edited June 5, 2012 by J.C.MacSwell

[D H]

Google is your friend. Why don't you do some of your own research first? A good start is with "small-scale test of gravity inverse square law".

[J.C.MacSwell]

Google is your friend. Why don't you do some of your own research first? A good start is with "small-scale test of gravity inverse square law".

 

Thanks. I had tried different wording and found nothing prior to posting, but will try that.

[timo]

I would have googled for the groups that DH mentioned and looked at their homepages and publications.

[D H]

I would have googled for the groups that DH mentioned and looked at their homepages and publications.

That, too. I was hoping that that search would have been kinda obvious.

[J.C.MacSwell]

That, too. I was hoping that that search would have been kinda obvious.

 

It was. I meant prior to originally posting the thread.

 

Thanks again.

[juanrga]

Does anyone know the experimentally measured minimum distance where the inverse square law holds?

 

The Newtonian inverse square law (1/R²) dependence has been tested up to the 10 micrometres (micro = 10^-6) without finding any deviation.

Edited June 6, 2012 by juanrga

[Enthalpy]

The Newtonian inverse square law (1/R²) dependence has been tested up to the 10 micrometres (micro = 10^-6) without finding any deviation.

 

On gravity? (well, of course on gravity, because electric force has been measured to far smaller distances)

 

I feel this is extremely difficult because interacting masses of D<10µm are so tiny! Do you confirm? Or even, have a link describing the experiment?

[J.C.MacSwell]

On gravity? (well, of course on gravity, because electric force has been measured to far smaller distances)

 

I feel this is extremely difficult because interacting masses of D<10µm are so tiny! Do you confirm? Or even, have a link describing the experiment?

 

The first half of this video describes the Oet-Wash Group effort

 

http://www.learner.org/courses/physics/unit/unit_vid.html?unit=3

 

Rather than tiny masses they are using discs with coincidental rings of holes that, when rotationally misaligned, create a gravitational torque.

Edited June 6, 2012 by J.C.MacSwell

[juanrga]

On gravity? (well, of course on gravity, because electric force has been measured to far smaller distances)

 

I feel this is extremely difficult because interacting masses of D<10µm are so tiny! Do you confirm? Or even, have a link describing the experiment?

 

Last paragraph of section "2.3.2 Short-range modifications of Newtonian gravity" on http://relativity.livingreviews.org/open?pubNo=lrr-2006-3&page=articlesu3.html

[D H]

The Newtonian inverse square law (1/R²) dependence has been tested up to the 10 micrometres (micro = 10^-6) without finding any deviation.

Last paragraph of section "2.3.2 Short-range modifications of Newtonian gravity" on http://relativity.livingreviews.org/open?pubNo=lrr-2006-3&page=articlesu3.html

Answering "10 microns" to the original post is a bit strong. That 10 micron figure is from Geraci et al., Improved constraints on non-Newtonian forces at 10 microns, Phys. Rev. D 78:2 (2008). What Geraci et al. were looking to rule out at very small distances were large forces, 10⁴ to 10⁸ times the gravitational force between the test masses.

 

A picture (source: http://physicsworld.com/cws/article/news/2008/mar/05/gravity-test-constrains-new-forces) tells a thousand words:

 

 

In the above image, the horizontal axis is length and the vertical axis, α, is the magnitude of a non-inverse square force, with α=1 representing a force equal to the gravitational force between the test masses. The shaded part of the graph represents areas where a non-inverse square reaction has been excluded. Different experiments focus on different portions of the distance/force region in that plot. The Stanford group focused on large forces. The University of Washington group has focused on forces comparable to gravity, so length is inherently a bit larger.

 

Expanding that graph to an even broader scale results in this figure (Adelberger, E.G., Heckel, B.R., and Nelson, A.E., “Tests of the gravitational inverse-square law”, Annu. Rev. Nucl. Sci., 53 (2003), http://arXiv.org/abs/hep-ph/0307284):

 

[juanrga]

Answering "10 microns" to the original post is a bit strong. That 10 micron figure is from Geraci et al., Improved constraints on non-Newtonian forces at 10 microns, Phys. Rev. D 78:2 (2008). What Geraci et al. were looking to rule out at very small distances were large forces, 10⁴ to 10⁸ times the gravitational force between the test masses.

 

A picture (source: http://physicsworld....ains-new-forces) tells a thousand words:

 

 

In the above image, the horizontal axis is length and the vertical axis, α, is the magnitude of a non-inverse square force, with α=1 representing a force equal to the gravitational force between the test masses. The shaded part of the graph represents areas where a non-inverse square reaction has been excluded. Different experiments focus on different portions of the distance/force region in that plot. The Stanford group focused on large forces. The University of Washington group has focused on forces comparable to gravity, so length is inherently a bit larger.

 

Expanding that graph to an even broader scale results in this figure (Adelberger, E.G., Heckel, B.R., and Nelson, A.E., "Tests of the gravitational inverse-square law", Annu. Rev. Nucl. Sci., 53 (2003), http://arXiv.org/abs/hep-ph/0307284):

 

 

The physicsworld news article affirms that Newtonian gravitational interaction means α ~1. I do not know why. In fact, a modification of Newtonian gravity due to a hypothetical fat graviton does not fit into a Yukawa potential with α ~1.

 

In any case, the Adelberger et al. review, reports tests of the inverse-square-law up to a distance λ = 200 μm for α = 1. And this recent work sets the limit on λ = 56 μm for α = 1.

Edited June 7, 2012 by juanrga

[D H]

And this recent work sets the limit on λ = 56 μm for α = 1.

That recent work is from the Eöt-Wash Group, which I previously referenced in post #8. I initially thought to cite that 56 micron figure in that post, but as you noted, even that is a bit fuzzy. I instead decided to be intentionally vague with the phrase "sub-millimeter range".

Edited June 7, 2012 by D H

[imatfaal]

Both the Article by Kapner et al (posted by Juanrga) here and the phys.org write up here use the term dark-energy length scale (about 85 micrometres) - what is the dark-energy length scale and does it have any empirical basis?

[J.C.MacSwell]

That recent work is from the Eöt-Wash Group, which I previously referenced in post #8. I initially thought to cite that 56 micron figure in that post, but as you noted, even that is a bit fuzzy. I instead decided to be intentionally vague with the phrase "sub-millimeter range".

 

If I am reading the graph correctly the Eöt-Wash Group experiments around 56 microns indicate there is no excess gravity at that distance. They have not ruled out a drop in gravity from what would be predicted by the inverse square law.

 

I assume the discs would have to be even closer than 56 microns apart to make the test in any case, to produce any torque attributed to gravity within that range.

[D H]

You are reading the graph incorrectly.

[J.C.MacSwell]

Answering "10 microns" to the original post is a bit strong. That 10 micron figure is from Geraci et al., Improved constraints on non-Newtonian forces at 10 microns, Phys. Rev. D 78:2 (2008). What Geraci et al. were looking to rule out at very small distances were large forces, 10⁴ to 10⁸ times the gravitational force between the test masses.

 

A picture (source: http://physicsworld.com/cws/article/news/2008/mar/05/gravity-test-constrains-new-forces) tells a thousand words:

 

 

In the above image, the horizontal axis is length and the vertical axis, α, is the magnitude of a non-inverse square force, with α=1 representing a force equal to the gravitational force between the test masses. The shaded part of the graph represents areas where a non-inverse square reaction has been excluded. Different experiments focus on different portions of the distance/force region in that plot. The Stanford group focused on large forces. The University of Washington group has focused on forces comparable to gravity, so length is inherently a bit larger.

 

You are reading the graph incorrectly.

 

At 56 microns it looks to me like everything where α >1 is in the excluded or shaded area, and everything where α<1 is not excluded.

 

So what is the correct interpretation of this if not what I stated?

Edited June 9, 2012 by J.C.MacSwell