Geophysicist kamilla cziráki uses fibonacci method to calculate parameters for lunar navigation

Kamilla Cziráki, a geophysics student at Eötvös Loránd University’s Faculty of Science, along with Professor Gábor Timár, the head of the Department of Geophysics and Space Sciences, have taken an innovative approach to study navigation systems for lunar exploration. Their research aims to pave the way for future lunar journeys by adapting Earth’s GPS methods for the moon.

On Earth, GPS systems use an ellipsoid shape that best fits the geoid, the actual shape of our planet, taking into account its rotation. This ellipsoid is an ellipse, with the furthest point from the Earth’s center at the equator and the closest at the poles. Earth’s radius is approximately 6,400 kilometers, and the poles are about 21.5 kilometers closer to the center compared to the equator.

Understanding the shape of the ellipsoid that best fits the moon is of great interest because it allows for the adaptation of GPS-like systems for lunar navigation. Describing this shape requires two parameters: the semi-major and semi-minor axes of the ellipsoid. For Earth, these parameters have been well-established, but for the moon, they needed to be determined.

The moon’s slower rotation makes it more spherical, almost a perfect sphere. Despite this, previous mapping efforts have approximated the moon’s shape as a sphere or used more complex models. What makes Cziráki and Timár’s work interesting is that they used a rotating ellipsoid model, something never done before for the moon.

To calculate the parameters of the rotating ellipsoid that best fit the theoretical shape of the moon, they utilized a database of the lunar selenoid, taking height samples at evenly spaced points on the surface. They used the Fibonacci sphere, a method based on the work of mathematician Fibonacci from 800 years ago, to arrange these sampling points uniformly on the spherical surface.

By gradually increasing the number of sampling points from 100 to 100,000, they determined that the values of the semi-major and semi-minor axes stabilized at 10,000 points. This allowed them to specify the necessary parameters for the rotating ellipsoid representing the moon’s shape.

The findings of Cziráki and Timár’s research have potential implications for future lunar exploration. By adapting GPS software solutions to the moon using the parameters of the rotating ellipsoid, lunar navigation for upcoming missions could be greatly facilitated. Their work fills a significant gap in lunar shape approximation, and it offers a novel way to approach satellite navigation on the moon as humanity prepares to return to our celestial neighbor after a long hiatus.

Source: Eötvös Loránd University