Hermes Hohmann Transfer Orbit, from The Martian

Source : Brian Koberlein’s One Universe At A Time Blog
 
In 1925 Walter Hohmann proposed an elliptical orbit between Earth and Mars which would permit spacecraft to transfer between the two planets along a low delta-v trajectory. The Hohmann transfer orbit, as it came to be known, relies on Earth and Mars to be in the right positions relative to each other. This occurs about every 26 months.

While it has its advantages, the one big disadvantage is that each Hohmann orbit has a different orientation each time. Another problem is that the orbits of Earth and Mars are not quite in the same plane, so things aren’t quite as simple as Hohmann proposed.

To have a large spacecraft that passes Earth and Mars with each orbit, you need some kind of thrust to adjust your orbit. In ”The Martian” the spacecraft Hermes ion drives accelerate the Hermes at a constant 2 mm/s, which is enough to continually adjust the orbit to match Earth and Mars.

If a spacecraft is continuously accelerating, its trajectory has to be determined computationally. This posed a real challenge for Andy Weir as he was writing the book. To get realistic trajectories for the Hermes he had to write a program to calculate them, and fiddle with parameters until he got a set of trajectories that worked.

You can see the resulting trajectories here.

*Delta-v, sometimes expressed as ΔV, means change in velocity, more specifically it is a spacecrafts capacity to change velocity and can be, roughly, thought of as the amount of propellant in the tank. See : Delta-v