Knot theory aids in mapping efficient space routes
by Sophie Jenkins
London, UK (SPX) Apr 18, 2024

Scientists at the University of Surrey have devised a method to chart the most efficient routes for spacecraft, mirroring the way drivers use sat-nav to navigate on Earth. This new technique harnesses mathematics to outline potential paths from one orbit to another, sidestepping the need for extensive computational resources or trial-and-error approaches.

Danny Owen, from the Surrey Space Centre, developed the method. He explains, "Traditionally, plotting a course in space could be haphazard, relying on extensive calculations or educated guesses. Our method systematically identifies all viable spacecraft trajectories between two orbits with a shared energy level, much like a tube map guides commuters through metropolitan transit systems."

The concept, rooted in knot theory, simplifies the complex mathematics traditionally used to find 'heteroclinic connections'-paths allowing spacecraft to switch orbits without fuel. The theory provides a preliminary sketch of trajectories, which are then refined to offer a comprehensive set of options for mission planners.

The utility of this technique has been validated across various celestial settings, including the Moon and Jupiter's Galilean moons-key targets in ongoing and upcoming space missions. Dr. Nicola Baresi, a lecturer in Orbital Mechanics at the university, highlighted its relevance: "As excitement builds around NASA's Artemis programme and the renewed lunar exploration race, our technique offers a streamlined method to explore these and other celestial bodies more effectively."

Research Report:Applications of knot theory to the detection of heteroclinic connections between quasi-periodic orbits

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