The original version from this story appeared in Quanta Magazine.
In October, a Falcon Heavy rocket is scheduled to launch from Cape Canaveral, Florida, carrying NASA’s Europa Clipper mission. The $5 billion mission aims to find out whether Europa, Jupiter’s fourth-largest moon, can harbor life. However, because Europa is constantly bombarded by intense radiation generated by Jupiter’s magnetic field, the Clipper spacecraft cannot orbit the moon itself. Instead, it will slip into an eccentric orbit around Jupiter and collect data by flying past Europa repeatedly – 53 times in total – before retreating from the worst of the radiation. Each time the spacecraft orbits Jupiter, its orbit changes slightly, allowing it to take photos and collect data from the poles of Europe to the equator.
To plan complicated tours like this, trajectory planners use computer models that meticulously calculate the trajectory step by step. The planning takes into account hundreds of mission requirements and is supported by decades of mathematical research into orbits and how they coalesce into complicated tours. Mathematicians are now developing tools that will hopefully provide a more systematic understanding of how orbits relate to one another.
“What we have are the previous calculations that we have done that guide us in making the current calculations. But it’s not a complete picture of all the options we have,” said Daniel Scheeres, an aerospace engineer at the University of Colorado at Boulder.
“I think that was my biggest disappointment as a student,” said Dayung Koh, an engineer at NASA’s Jet Propulsion Laboratory. “I know these orbits exist, but I don’t know why.” Given the cost and complexity of missions to the moons of Jupiter and Saturn, not knowing why the orbits are where they are is a problem are. What if there was a completely different orbit that could do the job with fewer resources? As Koh said, “Have I found them all? Are there more? I can not say that.”
After completing her doctorate at the University of Southern California in 2016, Koh became interested in how to catalog orbits in families. Jupiter orbits far from Europa form one such family; This also applies to orbits near Europe. But other families are less obvious. For example, for two bodies such as Jupiter and Europa, there is an intermediate point where the gravitational effects of the two bodies balance out and stable points are created. Spacecraft can orbit this point even if there is nothing in the middle of the orbit. These orbits form a family called Lyapunov orbits. Add a little energy to such an orbit by igniting a spacecraft’s engine, and you’ll stay in the same family for now. But add enough and you’ll move on to a different family – say, one that includes Jupiter in its orbits. Some orbital families may require less fuel than others, remain constantly in sunlight, or have other useful features.