It ain't easy!

Let's assume it's something nice and regular, like an asteroid in an elliptical orbit.

At minimum, you need two good sightings and the exact time. The more sightings, the better (obviously.)

In theory, mathematically, this is enough to establish the orbit. (K.F. Gauss pulled it off!)

From here on, though, I can't describe it neatly, as it starts getting into some really gnarly equations...

Silas