[hencq]

Maybe, but as he explains a normal parabola (like a satellite dish) wouldn't work, since the shots themselves are arced because of pesky gravity. I thought using a Monte Carlo analysis and finding a fixed point was actually a very clever way to solve it.

[carlob]

Yeah but the acceleration from gravity is constant so maybe there is just a (possibly non linear) change of coordinates that can be applied to the regular paraboloid.

Also a paraboloid would work only for rays that are parallel to one another.

[mannykannot]

Another difference from optics is that the vlocity is not fixed, and that affects the extent to which gravity modifies the trajectory.