The unique model of this story appeared in Quanta Magazine.

In October, a Falcon Heavy rocket is scheduled to launch from Cape Canaveral in Florida, carrying NASA’s Europa Clipper mission. The $5 billion mission is designed to seek out out if Europa, Jupiter’s fourth-largest moon, can assist life. However as a result of Europa is consistently bombarded by intense radiation created by Jupiter’s magnetic subject, the Clipper spacecraft can’t orbit the moon itself. As an alternative, it should slide into an eccentric orbit round Jupiter and collect knowledge by repeatedly swinging by Europa—53 occasions in complete—earlier than retreating from the worst of the radiation. Each time the spacecraft rounds Jupiter, its path will probably be barely completely different, making certain that it may take footage and collect knowledge from Europa’s poles to its equator.

To plan convoluted excursions like this one, trajectory planners use laptop fashions that meticulously calculate the trajectory one step at a time. The planning takes a whole bunch of mission necessities under consideration, and it’s bolstered by a long time of mathematical analysis into orbits and the right way to be a part of them into difficult excursions. Mathematicians at the moment are growing instruments which they hope can be utilized to create a extra systematic understanding of how orbits relate to 1 one other.

“What we have now is the earlier computations that we’ve executed, that information us as we do the present computations. But it surely’s not an entire image of all of the choices that we have now,” stated Daniel Scheeres, an aerospace engineer on the College of Colorado, Boulder.

“I believe that was my largest frustration once I was a pupil,” stated Dayung Koh, an engineer at NASA’s Jet Propulsion Laboratory. “I do know these orbits are there, however I don’t know why.” Given the expense and complexity of missions to the moons of Jupiter and Saturn, not figuring out why orbits are the place they’re is an issue. What if there’s a fully completely different orbit that might get the job executed with fewer assets? As Koh stated: “Did I discover all of them? Are there extra? I can’t inform that.”

After getting her doctorate from the College of Southern California in 2016, Koh grew eager about how orbits will be cataloged into households. Jovian orbits which are removed from Europa kind such a household; so do orbits near Europa. However different households are much less apparent. As an example, for any two our bodies, like Jupiter and Europa, there’s an intermediate level the place the 2 our bodies’ gravitational results steadiness to create secure factors. Spacecraft can orbit this level, regardless that there’s nothing on the middle of the orbit. These orbits kind a household known as Lyapunov orbits. Add a bit of vitality to such an orbit by firing a spacecraft engine, and at first you’ll keep in the identical household. However add sufficient, and also you’ll cross over into one other household—say, one that features Jupiter inside its orbits. Some orbit households may require much less gasoline than others, stay in daylight always, or produce other helpful options.