FT: Vortex gravity gradient question

Dreaded Cloaking Lurker Mode Off, AGAIN!

Does anyone out there have a simple equation (no PDE's or poorly behaved
ODE's) to calculate the pull of a vortex (such as a Black Hole or
Neutron Star) both towards it and around it?  Something in cylindrical
or spherical coordinates would be excellent.  

The idea is to model the pull of a Black Hole or Neutron Star on ships
fighting a battle around the vortex.  Moving the ship straight towards
the vortex according the inverse of the distance to the vortex loses out
the entire effect of acceleration around the vortex.  Basically, I want
crippled ships to spiral in and die as opposed to simply being pulled
straight in and die.  

Thank You,

ias