The Mathematics of a Trip to Mars?

hakonhaugnes wonders: "Since trips to Mars seems commonplace (NASA has sent one every 26 months), I thought it made sense to try to understand how the interplanetary trajectory is calculated. NASA's page is deploringly void of intricate details. I found this excellent page, but it still left me feeling that I was missing something. Surely the calculus must go beyond two bodies (mars/earth)? (It seems there are commercial MATLAB scripts available but at $150 it went beyond the defensible to satisfy my curiosity). Are there any curious Slashdot readers with the usual great insight into how to calculate a trip to Mars?"

Comments

JPL has a good intro

[cunniff]

I was an intern at JPL a couple of decades ago, and they always started with a "porkchop plot" (or "butterfly plot") of possible trajectories and their energy requirements. Here is a webpage that documents that to some extent:

http://marsprogram.jpl.nasa.gov/spotlight/porkchop All.html

Worth a prize

[radtea]

I helped judge the Canada-Wide Science Fair a few years ago, and the person my judging team ranked the highest had set himself precisely this problem: how do you really calculate the trajectory of a spacecraft from Earth to Mars? His solution was a wonderful exploration of the gory details of the problem--he had parts of the orbit that could be approximated reasonably in closed form (basically when the spacecraft was far away from everything, especially Jupiter) and other bits where there were three-body and more calculations.

He understood error estimation and the importance of computing the same quantity several different ways so that they act as a check on each other. He also had modeled aspects of the spacecraft itself, the rotational moments, effects of changing fuel mass, etc, etc, etc. In short, he understood that science is more of an art than a science. It was really nice work.

Re:Trajectory Math

[barawn]

Hohmann transfers are not always the minimum orbit energy orbit.

Hohmann transfers are never the minimum energy orbital transfer. IPS (interplanetary superhighway) orbits are lower energy for all cases, although they take much longer. (To be fair, IPS orbits are new - 1997-ish - and before that, Hohmann transfers were the minimum energy orbital transfer). IPS orbits are so low energy that it basically takes the same delta-V to get almost anywhere in the solar system - the delta-V to get to a Lagrange point.

For manned missions, however, you don't really care about lowest-energy, because orbits are always tradeoffs between transit time and energy, and manned missions want the shortest transit time feasible.