High School What is the reasoning behind MOND's modification of gravity?

[PhDnotForMe]

I've been reading a lot about MOND, an alternate theory attempting to explain the rotation of galaxies without using dark matter. It claims that at large distances gravity is proportional to 1/r rather than 1/r^2. In the published article, there are countless experiments done providing evidence that the idea holds possible. However, I can't seem to find any reasoning behind why gravity may behave this way. Is there any?

 

[Bandersnatch]

No. MOND is just that - modifying the equation to fit the rotation curve. It's a toy model, with no deeper reasoning attached.

 

[Vanadium 50]

It claims that at large distances gravity is proportional to 1/r rather than 1/r^2.

It most certainly does not.

 

[PhDnotForMe]

It most certainly does not.

https://arxiv.org/ftp/astro-ph/papers/0601/0601478.pdf
https://ned.ipac.caltech.edu/level5/March01/Battaner/node28.html
According to the links above, it does.
If you disagree, I'd love to hear about it.

 

[Vanadium 50]

According to the links above, it does.

Untrue. You are misrepresenting what they are saying, and that's not a very nice thing to do. The first link does not say it, and the second discusses a gravitational law of that form to say it's not MOND.

 

[Lord Crc]

With these assumptions, the weak acceleration limit of gravity is:
a = sqrt(GMa_0)/r
with dependence 1/r on distance r from the body of mass M generating the field.

To me that is pretty explicitly saying a ~ 1/r at large distances, so if it's wrong it's not just him...

 

[Vanadium 50]

You need to read the entire derivation paragraph. MOND changes Newton's Laws so that there is a minimum acceleration, a0. It has been known for a long time (some of which is referenced in the 2nd paper) that you can't make this work by changing only the distance dependence of the gravitational force. The closest you can come to that statement is that in a single system, if I have two points at r1 and r2, the difference between the accelerations at those points is proportional to (1/r1 - 1/r2). But even that is misleading - if you want MONDy behavior, you have to change the acceleration, not the distance dependence.