Friday, May 17, 2024

4472 - KNOT THEORY ORBITS - what are they for?

 

-  4472   -  KNOT  THEORY  ORBITS  -   what are they for?  -    When a spacecraft arrives at its destination, it settles into an orbit for science operations. But after the primary mission is complete, there might be other interesting orbits where scientists would like to explore. Maneuvering to a different orbit requires fuel, limiting a spacecraft’s number of maneuvers.


---------------  4472    -   KNOT  THEORY  ORBITS  -   what are they for?

-   Researchers have discovered that some orbital paths allow for no-fuel orbital changes. But the figuring out these paths also are computationally expensive. “Knot theory” has been shown to find these pathways more easily, allowing the most fuel-efficient routes to be plotted. This is similar to how our GPS mapping software plots the most efficient routes for us here on Earth.

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-   In mathematics, “knot theory” is the study of closed curves in three dimensions. Think of it as looking at a knotted necklace or a tangle of fishing line, and figuring out how to untangle them in the most efficient manner.

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-   In the same way, a spacecraft’s path could be computed in a crowded planetary system, around Jupiter and all its moons, for example, where the best, simplest and least tangled route could be computed mathematically.

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-   Applications of knot theory to the detection of “heteroclinic connections” between “quasi-periodic orbits,” using knot theory to untangle complicated spacecraft routes would decrease the amount of computer power in plotting out changes in spacecraft orbits.

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-   Previously, when  NASA wanted to plot a route, their calculations relied on either brute force or guesswork.   These new techniques neatly reveal all possible routes a spacecraft could take from A to B, as long as both orbits share a common energy level.  This new process makes the task of planning missions much simpler.

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-   Spacecraft navigation is complicated by the fact that nothing in space is a fixed position. Navigators must meet the challenges of calculating the exact speeds and orientations of a rotating Earth, a rotating target destination, as well as a moving spacecraft, while all are simultaneously traveling in their own orbits around the Sun.

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-    Since fuel is a limited resource for space missions, it would be beneficial to require the least amount of fuel possible in making any changes to the course of a spacecraft in orbit. Spacecraft navigators use heteroclinic orbits, which are paths that allow a spacecraft to travel from one orbit to another using the most efficient amount of fuel,  or sometimes no fuel at all.

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-     When a spacecraft arrives at its destination, it settles into an orbit for science operations. But after the primary mission is complete, there might be other interesting orbits where scientists would like to explore. Maneuvering to a different orbit requires fuel, limiting a spacecraft’s number of maneuvers.   But this usually takes a large amount of computer power or a lot of time to figure out. 

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-   By using “knot theory”, they have developed “a method of robustly detecting “heteroclinic connections,” to quickly generate rough trajectories which can then be refined. This gives spacecraft navigators a full list of all possible routes from a designated orbit, and the one that best fits the mission can be chosen.

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-    The researchers tested their technique on various planetary systems, including the Moon, and the Galilean moons of Jupiter.  Spurred on by NASA’s Artemis program, the new Moon race is inspiring mission designers around the world to research fuel-efficient routes that can better and more efficiently explore the vicinity of the Moon.

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-      Not only does this technique make that cumbersome task more straightforward, but it can also be applied to other planetary systems, such as the icy moons of Saturn and Jupiter.

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May 16, 2024               KNOT  THEORY  ORBITS  -   what are they for?           4472

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--------------------- ---  Friday, May 17, 2024  ---------------------------------

 

 

 

 

 

           

 

 

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