original version of this story Appeared in Quanta Magazine.
In October, the Falcon Heavy rocket carrying NASA’s European Clipper mission is scheduled to lift off from Cape Canaveral, Florida. The $5 billion mission aims to test whether Jupiter’s fourth largest moon, Europa, can support life. However, Europa is constantly exposed to strong radiation produced by Jupiter’s magnetic field, so the Clipper spacecraft cannot orbit the moon itself. Instead, it will collect data by repeatedly swinging near Europa (53 times in total) before slipping into an eccentric orbit around Jupiter and retreating from the worst of the radiation. Each time the spacecraft orbits Jupiter, its path will be slightly different, allowing it to take photos and collect data from Europa’s poles to its equator.
To plan such complex tours, trajectory planners use computer models that meticulously calculate the trajectory step by step. The plan takes into account hundreds of mission requirements and is powered by decades of mathematical research into trajectories and how to combine them into complex tours. Mathematicians are currently developing tools they hope can be used to more systematically understand how trajectories relate to each other.
“What we have is the calculations we’ve made so far, and that guides us in making our current calculations. But it’s not a complete picture of all the options we have,” he said. Ta. Daniel Sealesan aerospace engineer at the University of Colorado Boulder.
“I think that was my biggest frustration as a student,” said Dayun Ko, an engineer at NASA’s Jet Propulsion Laboratory. “We know these orbits exist, but we don’t know why they are the way they are.” Given the cost and complexity of missions to the moons of Jupiter and Saturn, knowing why their orbits are in the position they are. The problem is that you can’t. What if there was a completely different trajectory that could get the job done with fewer resources? Koh said: Anything else? I can’t say that. ”
After earning her PhD at the University of Southern California in 2016, Koh became interested in how orbitals can be classified into families. Jupiter’s orbit far from Europa forms such a system. The same goes for orbits close to Europa. But other family members are less clear. For example, two of her objects, such as Jupiter and Europa, have a midpoint where the gravitational effects of the two objects balance out and form a point of stability. A spacecraft can orbit around this point even though there is nothing in the center of the orbit. These orbitals form a family called Lyapunov orbitals. If you ignite the spacecraft’s engine and add a little energy to such an orbit, it will initially stay in the same family. But if you add enough, you end up with another family, say one that includes Jupiter in its orbit. Some orbital families may require less fuel than others, stay in the sun all the time, or have other useful features.