Celestial Mechanics Computer Programs

Can anyone here help me find a program which will allow me to not only
compute and display the ephemeris of known objects e.g. planets, moons, etc
but to introduce a specific object into the equation such as an unknown
comet or asteroid with given conditions of distance, velocity, etc and to
determine the ultimate orbit?

I am concerned not about about being hit on the head by a unwelcomed visitor
as much as finding out what the true maximum and minimum values of impact
velocities for families of comets or astroids may be.  I know that some of
the values given in the media vary radically from what I think is practical.

Also,  I am curious if there are any known asteroids in a retrograde orbit.


Gary