Hi Clayton,
What about the data ? Fireworks ! Bang ! Bang ! Bang !
I think you can see that natural phenomena are more three-dimensional and messier than your predictions.
Another thing, whenever you use Mathematica to calculate trajectories, you ignore a long history constrained by less sophisticated implements. It's useful to look at Harter's calculations, because he is the real lifetime master of all this. Around Lecture 25, he gets into compass and straight-edge construction for all sorts of envelopes, including the example of Rutherford scattering, which involves another conic section, the hyperbola.
In the past I have written mathematica notebooks showing the step-by-step construction of geometric diagrams. In this case, there are old methods of algebraic-geometry for constructing hyperbolas, parabolas, and ellipses. These techniques don't require Mathematica in the least. However, we can, and I think should, program the compass and straightedge geometry into Mathematica. This improves backwards-compatibility, which is important for research students.
Izidor Hafner has started on a project like this: Constructing Quadratic Curves, but I think Bill Harter's work is much more thorough and impressive, sets a higher standard. Mathematica programmers should be interested in following that direction.
Thanks,
Brad
