Estimation of the parameters of a lunar ellipsoid of revolution based on GRAIL selenoid data and Fibonacci mesh

Because the Moon is much less flattened than the Earth, most lunar GIS applications use a spherical datum. However, nowadays, with the renaissance of lunar missions approaching, it seems worthwhile to define an ellipsoid of revolution that better fits the lunar gravity potential surface. The main long-term benefit of this might be to make the lunar adaptation of methods already implemented in terrestrial GNSS, gravimetry and GPS applications easier and somewhat more accurate.

In our work, we used a 660^th degree and order potential surface called GRGM 1200A Lunar Geoid, developed in the frame of the GRAIL project. Samples were taken from the potential surface along a mesh that represents equal area pieces of the surface. The method of point grid selection was provided by a relatively simple Fibonacci sphere. We tried Fibonacci spheres with 100, 1000, 3000, 5000, 10000 and 100000 points and also separately examined the effect of rotating the network by length for a given number of points on the estimated parameters, but these differences was only noticeable for the lower resolution networks.

We estimated the best-fitting rotation ellipsoid semi-major axis and flatness data for the selenoid undulation values at the network points, which were obtained for a=1,737,576.6 m and f=0.000305. This parameter pair is already obtained for a 10000 point grid, while the case of reducing the points of the equidistant grid to 3000 does not cause a deviation in the axis data of more than 10 centimetres. As expected, the absolute value of the selenoid undulations has decreased compared to the values taken with respect to the spherical basal surface, with maxima exceeding +400 m still being found for Mare Serenitatis and Mare Imbrium, and the largest negative values for South Pole Aitken and Mare Orientale.

Supported by the ÚNKP-22-6 New National Excellence Program of the Ministry for Culture and Innovation from the source of the National Research, Development and Innovation Fund.