Gravitic Field of Rotating Disk-Shaped Mass Along Ecliptic

[havonasun]

I am curious to know if the gravitic field of a rotating, disk-shaped mass is denser along its ecliptic. I'm referring to rotating bodies such as stellar systems, galaxies, etc. I would like to know if a second mass, passing through the ecliptic, would experience a difference such as tidal forces or perturbations. Basically, does a massive disk have any difference in its gravitic pull axially vs radially? From a great distance, it would just be a point-source, but up close I'm thinking that the magnitude of the vectors of individual bodies comprising the whole would be less axially than radially.

 

[mfb]

The gravitational field of a disk is different from the field of a sphere. For a disk of uniform mass, this website has some plots of the gravitational potential. The force is orthogonal to the equipotential lines and stronger where the lines are denser.

 

[havonasun]

From what I can interpret, the graph I would be using would be 'rotating w/star.' The field is densest at the center because of law of squares, and weakest horizontally from the center. It shows another dense region outside the disk radially. So, yes?

 

[mfb]

The page doesn't load right now, but as far as I remember the "rotating" probably included effective potentials for orbiting bodies. I'm not sure if you want that.

If the disk has a cylindrical symmetry, its rotation does not matter for the gravitational potential (ignoring relativistic effects).

Edit: Looks like relativistic effects are considered. Do you really want that?