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Mathematicians think abstract tools from a field called symplectic geometry might help with planning missions to far-off moons and planets. 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 find out if 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 can’t orbit the moon itself. Instead, it will slide into an eccentric orbit around Jupiter and gather data by repeatedly swinging by Europa—53 times in total—before...

(Image credit: NASA/JPL-Caltech/SETI Institute) NASA's Juno spacecraft made a close flyby of Jupiter's intriguing moon Europa in 2022, revealing potential hints of present day surface activity. The spacecraft's Stellar Reference Unit (SRU), which is a star camera designed to assist Juno's onboard attitude determination, was used to image Europa's surface with high resolution while being lit up by Jupiter-shine, or sunlight scattered off Jupiter. The SRU image from the flyby is explored in an article published in the journal JGR Planets on Dec. 22, 2023. The image shows an oddly-shaped area of the icy surface, measuring 23 miles by 42...

Its frozen shell is encrusted with a layer of white and orange ice. The endless twisting and pulling of Jupiter’s gravity leaves a surface crisscrossed by deep valleys, ridges, and not yet fully understood “chaos zones” of deep tectonic activity. Its immense dark oceans, heated by underwater volcanoes, are hidden by this icy surface — that is, except for when it explodes outwards in titanic geysers, shooting plumes of liquid water hundreds of miles into space.No, this isn’t science fiction — this is Europa, the hauntingly beautiful yet bizarre ocean moon of Jupiter. Scientists have called Europa “the most...