Home Tech An ancient abstract field of mathematics is uncovering the deep complexity of spacecraft orbits

An ancient abstract field of mathematics is uncovering the deep complexity of spacecraft orbits

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the original version of 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 is designed to discover whether Europa, Jupiter’s fourth-largest moon, can support life. But because Europa is constantly bombarded by intense radiation created by Jupiter’s magnetic field, the Clipper spacecraft cannot orbit the moon itself. Instead, it will slide into an eccentric orbit around Jupiter and collect data by repeatedly passing by Europa (53 times in total) before retreating from the worst of the radiation. Each time the spacecraft orbits Jupiter, its trajectory will be slightly different, ensuring it can take photographs and collect data from Europa’s poles to its equator.

To plan complicated routes 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 backed by decades of mathematical research into orbits and how to link them into complicated paths. 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 that we have done, which guide us as we do the current calculations. But it is not a complete picture of all the options we have,” he said. Daniel Scheeresaerospace engineer from the University of Colorado, Boulder.

“I think that was my biggest frustration when I was a student,” said Dayung Koh, an engineer at NASA’s Jet Propulsion Laboratory. “I know these orbits 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 the orbits are where they are is a problem. What if there was a completely different orbit that could do the job with fewer resources? As Koh said: “Did I find them all? There is more? I can not say that”.

After earning his PhD at the University of Southern California in 2016, Koh became interested in how orbits can be categorized into families. Jovian orbits that are far from Europa form such a family; so do orbits 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 to create stable points. Spacecraft can orbit this point, even if there is nothing in the center of the orbit. These orbits form a family called Lyapunov orbits. Add a little energy to that orbit by firing up a spaceship engine and you’ll stay in the same family at first. But add enough and you’ll move on to another family, say, one that includes Jupiter within its orbits. Some families of orbits may require less fuel than others, remain exposed to sunlight at all times, or have other useful features.

Dayung Koh, an engineer at NASA’s Jet Propulsion Laboratory, is trying to come up with a systematic understanding of how the orbits of a planetary system relate to each other.

PHOTO: Courtesy of Dayung Koh

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