When traveling to Mars in a space craft, you want to find a compromise between flight duration and fuel consumption. One common trajectory for achieving this is the so-called Hohmann transfer which takes about 9 months from Earth and needs two maneuvers, both of which are accelerations!
Usually, when modeling movement of space crafts, one uses the Kepler model of two massive bodies attracting each other via gravitation. In case you have more time available for a space journey, however, you might consider a third body in your calculations. This introduces a very chaotic behavior, which you can use in turn to find very special trajectories that allow you to get to various places spending a lot less fuel. Unfortunately this will be much slower.
These special trajectories are called low-energy transfers and form a part of the so-called interplanetary transport network. There have been a handful of missions already using these trajectories, e.g. JAXA’s Hiten probe in 1990 and ESA’s BepiColombo which is en route to Mercury right now.
In this talk we will have a short introduction to the ever-surprising world of orbital mechanics followed by a discussion of the three-body problem including Lagrangian points. We will then see what the so-called weak stability boundary is and how chaos can help us understand why these strange trajectories exist. No math knowledge required!