What is a reasonably accurate but simple model of the Milky Way's gravitational field? I am putting together a toy program which shows how stars move around in the galaxy.
To run the simulation I need to know strength of the Milky Way's gravitational field at any location in it. I'm looking for a model (e.g. a collection of uniformly dense planes/rods) rather than a database of potentials.
Where can I get such a model?
I could simply construct an infinite plane of uniform density, but is that good enough? This is only a toy so I'm looking for something which preserves integrity of the overall shape and statistics of the galaxy, rather than worrying about the specific location of any particular star.
 A: Note first that there are three different sources of gravitational potential: the disk, the bulge, and the dark halo.
There are a few different models of the gravitational field of the disk, two of the more common potentials are:


*

*Kuzmin model:
$$\Phi(r,z)=-\frac{GM}{\sqrt{r^2+(a+|z|)^2}}$$

*Miyamoto-Nagai model:
$$\Phi(r,z)=-\frac{GM}{\sqrt{r^2+(a+\sqrt{z^2+b^2})^2}}$$
where $a$ and $b$ are scale lengths.


For the bulge, you can use spherically symmetric potentials such as


*

*Plummer model:
$$\Phi(r)=−\frac{GM}{\sqrt{r^2+a^2}}$$

*Jaffe model:
$$\Phi(r)=\frac{GM}{a}\ln\left(\frac{r}{r+a}\right)$$
where $a$ also is a scale length and not necessarily the same as those for the disk.


The dark halo takes a spherical form,
$$
\Phi(r)=\frac12V_h^2\ln\left(r^2+a^2\right)
$$
where $V_h$ is the radial velocity of the galaxy at far distances ($\sim200$ km/s) and $a$ another scale length that isn't necessarily the same as above.
See also


*

*http://www.ifa.hawaii.edu/~barnes/ast626_97/gp.html

*http://www.astro.utu.fi/~cflynn/galdyn/lecture4.html
A: Deriving the galactic mass from rotation has the following chart (on the right) for the enclosed mass as a function of radius

