# Question about MOND and gravity

Sorry if I'm in the wrong section to ask this question.

I'm trying to find out when astronomers discovered that the solar system oscillates through the galactic plane. I just can't imagine the Mayans having the ability to determine that it actually occurs on a 26,000 (or whatever) year period.

Thanks for the consideration

123 mark

Lets give it a shot. Where would you like to start?
Let me just sketch out the problem.

You have a function X. You have a set of rules to convert that function into another function Y.

The problem is here is that learning what those rules are is a one semester course in calculus. Look at 18.02 on MIT OCW.

Let me just sketch out the problem.

You have a function X. You have a set of rules to convert that function into another function Y.

The problem is here is that learning what those rules are is a one semester course in calculus. Look at 18.02 on MIT OCW.
So lets start with the basics and go from there, how do they calculate for ρ? Do they just take the average for the mass of the entire galaxy or is it based on what is inside the area swept by a star?

With DMT I was told by an astrophysicist that the dark matter is put into the model and essentially is an adjustment to the mass to have the stars match newtons gravitation formula. Is that right? Is Gm/r^2 modified in any way?

Jonathan Scott
Gold Member
So lets start with the basics and go from there, how do they calculate for ρ? Do they just take the average for the mass of the entire galaxy or is it based on what is inside the area swept by a star?
The local density of matter in the form of stars or gas is estimated from the luminosity of that part of the galaxy in various parts of the spectrum.

The Newtonian acceleration is then calculated in the usual way by integration (summing the effect of all the mass). With spherical symmetry, Newtonian gravity would simplify to being equivalent to having all the mass inside a given orbit concentrated at the center, but for galaxies the shape is more complicated. The MOND acceleration can then be calculated in terms of the Newtonian acceleration.
With DMT I was told by an astrophysicist that the dark matter is put into the model and essentially is an adjustment to the mass to have the stars match newtons gravitation formula. Is that right? Is Gm/r^2 modified in any way?
Yes, Dark Matter simply adds additional invisible source mass obeying the standard Newtonian gravitational formula (as an approximation to GR).

A very weird feature of the MOND rule is that for a wide range of galaxies it correctly predicts the velocity distribution based only on the distribution of visible matter. If dark matter is the real explanation, this suggests that the distribution of the dark matter in galaxies must somehow be strongly linked with the distribution of the visible matter in such a way as to reproduce the MOND result, but so far there is no theoretical explanation for this.

Sorry it took a few days to get back to you, had finals last couple days.

The Newtonian acceleration is then calculated in the usual way by integration (summing the effect of all the mass). With spherical symmetry, Newtonian gravity would simplify to being equivalent to having all the mass inside a given orbit concentrated at the center, but for galaxies the shape is more complicated. The MOND acceleration can then be calculated in terms of the Newtonian acceleration.
I'm a little surprised that would work, how is the integretion setup? Is it a function of the gravity of each sun and it's affect on the next by putting together an artificail layout based on average distances apart or is it simply the sum of all the masses thrown into the center for the swept area of the galaxy by a particular star?

I was told by an astrophysicist that it has only been recently that papers were published changing the model from a spherical density to a more disc like shape, I found this surprising as well.

A very weird feature of the MOND rule is that for a wide range of galaxies it correctly predicts the velocity distribution based only on the distribution of visible matter. If dark matter is the real explanation, this suggests that the distribution of the dark matter in galaxies must somehow be strongly linked with the distribution of the visible matter in such a way as to reproduce the MOND result, but so far there is no theoretical explanation for this.
That's very interesting, so MOND at least is able to show a possible correlation between matter and dark matter (that is if DMT is correct).

Jonathan Scott
Gold Member
I'm a little surprised that would work, how is the integretion setup? Is it a function of the gravity of each sun and it's affect on the next by putting together an artificail layout based on average distances apart or is it simply the sum of all the masses thrown into the center for the swept area of the galaxy by a particular star?

I was told by an astrophysicist that it has only been recently that papers were published changing the model from a spherical density to a more disc like shape, I found this surprising as well.
I don't know the practical details. For a simple case, I guess one could assume one could treat the mass as a series of rings of varying density surrounding a spherical nucleus. In a more complex cases one could use numerical methods to sum the effects of mass density over a modelled shape of the galaxy consistent with the observations. There's certainly no need to model the individual stars, because from sufficient distance the gravitational effect is essentially the same as that of a continuous medium with an appropriate average density.

I don't know the practical details. For a simple case, I guess one could assume one could treat the mass as a series of rings of varying density surrounding a spherical nucleus. In a more complex cases one could use numerical methods to sum the effects of mass density over a modelled shape of the galaxy consistent with the observations. There's certainly no need to model the individual stars, because from sufficient distance the gravitational effect is essentially the same as that of a continuous medium with an appropriate average density.
Where do you think would be a good place to start to find the actual formulas used for these calculations? I looked online and came up with very little. Are there members on the board that would be helpful?

I am going to quiz the proffesors at school again and see if I can get a more complete answer. I was told by one it was basically the same as you stated originally; the mass is essentially summed and put into the center and then calculated.

That seems overly simplified and frankly I don't see how that could calculate anything properly.