After the summer session ended around August 21, 1988, I bundled up all my Mars research and met with my advisor, Roger Broucke, in his small office at Woolrich Labs. Keep in mind that Prof. Szebehely’s admonition, “Add time to your calculations, and you’ll get your name lit up in lights,” was never far from my consciousness. Any mention of TIME and my awareness spikes.
Dr. Broucke was very excited about my choosing Mars as a Three Body Problem (3BP). He did his PhD dissertation on the 3BP and many more papers at JPL. He said he had not studied it for over twenty years.
As I showed him my FORTRAN code, he rambled on, keen on the pages. He wore very thick glasses and could see no further than the hand in front of his face, so he held the pages close.
You write very precise code.
I passed him diagrams of my method – patching two Three Body Problems together at conjunction – and he rambled on about how I did the integration. Did I use the ugly nonlinear optimization methods that iterated back and forth at each small step?
Dr. Broucke had given me his Runge-Kutta 7/8 integrator – with his custom numbers (the fastest, most accurate routine ever; he was a real FORTRAN aficionado) – which takes about 100 steps at double precision (accurate to 16 significant digits). I explained that it was a direct integration. None of that backward time stuff.
… TIME. There it is.
More drawings. A data dump; graphical plots. He explains that the reverse integration works because gravity is a central force. But if you have other forces in a model, your steps must be short. This makes the routine less accurate because of accumulated roundoff error.
Earlier in the summer, he had asked if I had solved the singularity problem with integrating close to Earth and Mars. I said I’d set up a trap to stop when it got close to Mars, but leaving Earth was a real bugger. He said that would make a good PhD project, setting up around Earth as a singularity problem. I said no, I’d figure it out…
Here’s the flow diagram of the final approach to Mars, a subroutine called HAWKEY-Mars with integral subroutines INITIAL, PHOENIX and TAILHOOK. It stops the integration from conjunction at Mars’ Sphere of Influence (SOI), changes coordinates, and continues on toward Mars proper. Don’t worry about the flow chart; there’s a diagram later.
On June 3rd, Dr. Broucke had sent me an email with an abstract of a paper he was working on about the singularity problem. He published the paper not long after I was dismissed. It was his last paper.
Anyway, Dr. Broucke seemed satisfied with my efforts after only about four months; I got up and left.