The Martian Chronicles
Issue 6, July 2000

2001 - Odyssey to Mars
by William H. Clark

The Earth to Mars trajectory is the subject of my dissertation research. NASA makes it seem quite simple, but itís not! Consider a few details.

The Mars missions typically follow an elliptical path and meet the red planet at the opposite side, at apoapse. (See illustration.) This is the minimum energy trajectory. At apoapse, the velocity of Mars is 24.13 km/sec and the spacecraft is going 21.5 km/sec. They are both going about the same direction, but Mars is going 3 km/sec faster. In practical terms, Marsí diameter is 6800 km, so the entire planet will pass by the spacecraft in about half an hour. Thatís a pretty small target, in a 250+ day mission!

These relative speeds mean that, because the s/c is moving slower, it must wait at the railroad crossing for Mars, as it comes barreling down; then deftly maneuver into orbit at just the precise moment.

  The Earth-to-Mars Trajectory  
The Earth-to-Mars Trajectory

Folks, thereís only one technology in the universe that I would trust to get me out of that kind of situation - my own legs! Itís asking a lot for an autonomous s/c to maneuver its way to safety on its own (timely feedback from Earth is not available because of the time lag.)

The July 4 landing of Sojourner intersected Mars before apoapse. In this circumstance the spscrcraft was able to make a proactive approach to Mars, versus reactive. Their relative velocities werenít much different, but the geometry is a little more tractable because the spacecraft is approaching at an acute angle, not head-on.

It is a very subtle thing that you must experience for yourself. You can do so with a free computer program available at [link inactive]. You input some numbers, then the program finds an optimum trajectory, and displays all the results - where and when all five of the Trajectory Correction Maneuvers (TCMs) were done, just like on a real mission! There is also a free four chapter introduction to orbital mechanics that describes in laymenís terms all the facets of the trajectory itself.

Youíll find - just like the mission planners - that it is a very slippery situation. Change one value by 1% and the s/c might not reach Mars at all, but follow it around the curve of apoapse, and not catch up for months! Change it the other way and you might get there, but the total energy requirement doubles - so, practically speaking, you wonít have the fuel to really get there at all. Other values will, unexpectedly, add 30 days to the mission!

All of which is not the programís fault - itís values are accurate to 14 significant digits (1/10th of a centimeter!). Itís because it is an extremely non-linear problem. Youíll see!