Scientists have developed a new approach for lunar navigation, making use of the Fibonacci spiral to calculate the optimum criteria for a GPS-like system on the Moon. The innovative method assists improve lunar automobile navigation, offering more accurate mapping based on the Moons distinct ellipsoidal shape, which is characterized by unique semi-major and semi-minor axes.
Navigation systems suitable for lunar surface area exploration to chart future expeditions.
Kamilla Cziráki, a geophysics trainee from the Faculty of Science at Eötvös Loránd University (ELTE), is pioneering a novel technique to study navigation systems ideal for lunar surface explorations. In collaboration with Professor Gábor Timár, the head of the Department of Geophysics and Space Sciences, theyve used the method of the 800-year-old mathematician, Fibonacci, to adjust the specifications of Earths GPS system for the Moon.
Their findings have been released in the journal Acta Geodaetica et Geophysica.
Now, as humankind prepares to go back to the Moon after half a century, the focus is on possible techniques of lunar navigation. It promises that the modern-day followers of the lunar automobiles of the Apollo missions will now be helped by some type of satellite navigation, comparable to the GPS system on Earth.
Why is the shape of the ellipsoid that finest fits the Moon intriguing, and what specifications can be used to explain it? Why is it fascinating that, compared to the Moons mean radius of 1737 kilometers, its poles are about half a kilometer more detailed to its center of mass than its equator? If we want to apply the software solutions tried and checked in the GPS system to the Moon, we require to specify two numbers, the semi-major and the semi-minor axis of this ellipsoid so that the programs can be quickly moved from the Earth to the Moon.
The Moon turns more gradually, with a rotation period equal to its orbital duration around the Earth. For the mapping of the Moon that has actually been done so far, it has been enough to approximate the shape of a sphere, and those who have been more interested in the shape of our celestial companion have used more complex designs.
In the case of the Earth, these systems do not consider the real shape of our planet, the geoid, not even the surface specified by water level, but a rotation ellipsoid that finest fits the geoid. Its crossway is an ellipse that is outermost from the Earths center of gravity at the equator and closest to it at the poles. The radius of the Earth is simply under 6400 kilometers, and the poles are about 21.5 kilometers better to the center than the equator.
Why is the shape of the ellipsoid that best fits the Moon fascinating, and what parameters can be used to describe it? Why is it intriguing that, compared to the Moons mean radius of 1737 kilometers, its poles are about half a kilometer more detailed to its center of mass than its equator? If we wish to apply the software application solutions attempted and tested in the GPS system to the Moon, we need to define two numbers, the semi-major and the semi-minor axis of this ellipsoid so that the programs can be easily transferred from the Earth to the Moon.
The Moon turns more gradually, with a rotation duration equivalent to its orbital period around the Earth. This makes the Moon more round. It is nearly a sphere, but not quite. For the mapping of the Moon that has been done so far, it has actually been sufficient to approximate the shape of a sphere, and those who have actually been more interested in the shape of our celestial companion have utilized more complicated designs.
Interestingly, the approximation of the Moons shape with a rotating ellipsoid has actually never been done before.
The last time such calculations were made remained in the 1960s by Soviet area scientists, utilizing information from the side of the Moon visible from Earth.
Kamilla Cziráki, a second-year geosciences trainee specializing in geophysics, worked with her manager, Gábor Timár, head of the Department of Geophysics and Space Sciences, to calculate the specifications of the turning ellipsoid that finest fit the theoretical shape of the Moon.
To do this, they used a database of an existing possible surface, called the lunar selenoid, from which they took a height sample at evenly spaced points on the surface area and browsed for the semi-major and semi-major axes that best fit a rotation ellipsoid. By slowly increasing the number of sampling points from 100 to 100,000, the worths of the 2 specifications stabilized at 10000 points.
One of the main actions of the work was to examine how to organize N points uniformly on a spherical surface area, with several possible solutions; Kamilla Cziráki and Gábor Timár chose the most basic one, the so-called Fibonacci sphere. The Fibonacci spiral can be carried out with extremely brief and instinctive code, and the foundations of this approach were laid by the 800-year-old mathematician Leonardo Fibonacci. The approach has also been used to the Earth as a confirmation, rebuilding a good approximation of the WGS84 ellipsoid used by GPS.
Recommendation: “Parameters of the finest fitting lunar ellipsoid based upon GRAILs selenoid design” by Kamilla Cziráki and Gábor Timár, 27 June 2023, Acta Geodaetica et Geophysica.DOI: 10.1007/ s40328-023-00415-w.
