Suppose the gravitation has very very tiny deviation from inverse square law……

[magnetar]

If the gravitation has very very tiny deviation from inverse square law！our solar system became unstable? If so ,how long people on the Earth can notice it?

Thank you in advance!

 

[Naty1]

Good question for the relativity section...a discussion under the thread DARK MATTER QUESTION discusses this issue.

Gravity is relatively weak so its tough to test in lab environments...

In some spiral galaxies, there appears to be a significant deviation from Newtonian mechanics beyond radius c^2/R (where R is the scale of the observable universe) ...the deviation results in constant velocities of orbiting stars and was originally discovered experimentally and verified by Vera Rubin...the variation is hypothesized to be caused by dark matter,,,but nobody really knows...

At the other end of the distance spectrum tests are being doing to see if gravity "leaks" into other dimensions at sub millimeter distances...so far the inverse square law appears to hold..

 

[arildno]

Hi, magnetar!

I will divide your question into three:

If the gravitation has very very tiny deviation from inverse square law

Many physicists are involved into theoretical and experimental considerations of this issue.
There are basically two lanes along which experementalists can take:
1. Fundamental breakdown of inverse-square law at tiny distances
This is by no means IM-possible that such a breakdown occurs, but with high-precision torque measurements, it has been established that the breakdown does not occur at distances in excess of 60 micro-meters, or so. (See referenced article from physicsworld)
2. Breakdown at astronomical distances.
As yet, high-precision measurements of the Moon's precession have not identified any such deviation within the exceeding the limits of experimental accuracy, so also here, the inverse-square law is not yet debunked (that would be cool, wouldn't it?)

3. Theoretical justifications for possible deviations:
The main thrust behind the idea that the inverse square law might be wrong, is that it does not take into account the quite possibly existing "hidden, curled-up dimensions" theoreticians postulate.
You might read the following article from physicsworld, which go into some detail:
http://physicsworld.com/cws/article/print/21822

！our solar system became unstable?

It is true that we may deduce from simplified equations (say, a two-body problem) that only the inverse square law provides for stability (unless my memory is false on this issue).
However, by possibly new features of gravitation, or other "complications", stability might well hold, even though the (then falsified) inverse square law could not any longer be the explanatory mechanism behind that stability.

If so ,how long people on the Earth can notice it?

That would be wholly dependent upon how strong the instability actually is (if there is one at all!), so any figure would be mere guesswork.

 

[magnetar]

Thank you for your answer! arildno and Naty1

 

[atyy]

The stability of the solar system is unknown.

Scott Tremaine's Lecture 1:
http://www.astro.princeton.edu/~tremaine/alex/

http://streamer.perimeterinstitute.ca/Flash/e74a4975-9f9b-4d31-9f65-b01ef7add6f5/index.html