The original version by this story appeared in Quanta magazine.
In October, a Falcon Heavy rocket will launch from Cape Canaveral in Florida, carrying NASA's Europa Clipper mission. The $5 billion mission aims to find out whether Europa, Jupiter's fourth-largest moon, can support life. But because Europa is constantly bombarded by intense radiation caused by Jupiter's magnetic field, the Clipper spacecraft cannot orbit the moon itself. Instead, it will enter an eccentric orbit around Jupiter and collect data by flying past Europa repeatedly – a total of 53 times – before retreating from the worst of the radiation. Each time the spacecraft orbits Jupiter, its path will be slightly different, allowing it to take pictures and collect data from the poles of Europa to the equator.
To plan complicated trips like this, route planners use computer models that accurately calculate the route step by step. The planning takes into account hundreds of mission requirements and is backed by decades of mathematical research into orbits and how to piece them together into complex tours. Mathematicians are now developing tools that they hope can be used to create a more systematic understanding of how orbits relate to each other.
“What we have are the previous calculations we have done, which guide us in carrying out the current calculations. But it is not a complete picture of all the options we have,” he says Daniel Scheeresan aerospace engineer at the University of Colorado, Boulder.
“I think that was my biggest frustration when I was a student,” says Dayung Koh, an engineer at NASA's Jet Propulsion Laboratory. “I know these jobs are there, but I don't know why.” Given the cost and complexity of missions to the moons of Jupiter and Saturn, not knowing why orbits are where they are is a problem. What if there is a completely different job that could get the job done with fewer resources? As Koh said: “Have I found them all? Are there more? I can't tell you that.”
After earning her doctorate from the University of Southern California in 2016, Koh became interested in how jobs can be cataloged across families. Jovian orbits far from Europa form such a family; this also applies to jobs close to Europe. But other families are less obvious. For example, for any two bodies, such as Jupiter and Europa, there is an intermediate point where the gravitational effects of the two bodies balance out to create stable points. Spacecraft can orbit this point even though nothing is in the center of the orbit. These orbits form a family called Lyapunov orbits. Add a little energy to such an orbit by firing a spacecraft engine, and initially you remain in the same family. But add enough of them, and you move to another family, for example one that includes Jupiter in its orbits. Some track families may require less fuel than others, remain in sunlight at all times, or have other useful functions.