Sat-Nav in Space: Best Route Between Two Worlds Calculated Using 'Knot Theory' [Study]

We have been exploring the space for decades. However, scientists just discovered the best routes between two words in the cosmos using the "knot theory."

Satellite Navigation in Space Using Knot Theory

In a new study, researchers have developed a method to determine the optimal paths for orbiting one planet or Moon to orbit another using mathematics. Additionally, this new approach reduces the need for guesswork and a significant amount of computer power, both of which are used in the present orbit-changing procedure.

"Previously, when the likes of NASA wanted to plot a route, their calculations relied on either brute force or guesswork," Danny Owen, a postgraduate research student in astrodynamics at the University of Surrey's Surrey Space Centre, said in a statement. "Our new technique neatly reveals all possible routes a spacecraft could take from A to B, as long as both orbits share a common energy level."

Since fuel is a finite resource, it would be ideal for a spaceship to alter its trajectory while in orbit, utilizing the least amount of fuel feasible. Astronomers do this by identifying "heteroclinic connections," or routes that require the least fuel to move a spacecraft from one orbit to another, such as between Earth and Mars or Jupiter and its moons. However, determining the heteroclinic linkages typically requires significant computational power or laborious guesswork.

Aerodynamicists can swiftly produce a large number of rough pathways, which they can subsequently improve to be more accurate by applying an area of mathematics called "knot theory." As a result, they can produce a lot of rough pathways and select the best one for their mission.

It is envisaged that this method may make it easier for spacecraft to move between orbits around the Moon and other planets, such as Mars, or even between Jupiter and its Moons in the future.

The new Moon race is encouraging mission planners worldwide to look for fuel-efficient ways to better and more effectively explore the Moon's neighborhood, according to study co-author Nicola Baresi, a lecturer in Orbital Mechanics at the University of Surrey. He added that their method not only simplifies that difficult operation but may be extended to other planetary systems, including the icy moons of Jupiter and Saturn.

What Is Knot Theory?

Knot theory is the mathematical study of three-dimensional closed curves and potential deformations without a segment passing through another. One way to construct a knot is to loop and interlace a piece of string in any way, then link the ends.

The first question that comes to mind is whether or not such a curve can be deformed in space into a typical unknotted curve, such as a circle, or if it can only be untangled. More generally, the second question asks if any two given curves represent distinct knots or are actually the same knot in the sense that they can be continually deformed into each other.

The fundamental method for categorizing knots is to project each knot onto a plane and count the number of times the projection crosses itself, noting which direction goes "under" and which goes "over" at each crossing. The complexity of a knot is determined by the minimum number of crossings that occur when the knot is moved in all possible directions.

The trefoil knot, also known as the overhand knot, has three of these crossings, making it the simplest genuine knot that can exist. As a result, its order is three. Even this basic knot has two configurations that are mirror reflections of one another yet cannot be bent into one another.

None of the knots have less than four crossings; all of them have at least four. As the order increases, the number of knots that can be distinguished quickly rises.

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