2019/07/23 by Juan Sebastián Ardenghi, Ardenghi, Juan Sebastián
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Planetary Science and Exploration #Popular Physics (physics.pop-ph) #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.1907.13597
openalex publication_date 2019/07/23 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
By applying Monte-Carlo method, the Moon radius is obtained by counting craters in a spherical square over the surface of it. As it is well known, approximate values for π can be obtained by counting random numbers in a square and in a quarter of circle inscribed in it in Euclidean geometry. This procedure can be extend it to spherical geometry, where new relations between the areas of a spherical square and the quarter of circle inscribed in it are obtained. When the radius of the sphere is larger than the radius of the quarter of circle, Euclidean geometry is recovered and the ratio of the areas tends to π. Using these results, theoretical deviations of π due to the Moon radius R are computed. In order to obtain this deviation, a spherical square is selected located in a great circle of the Moon. The random points over the spherical square are given by a specific zone of the Moon where craters are distributed almost randomly. Computing the ratio of the areas, the deviation of π allows us to obtain the Moon radius with an intrinsic error given by the finite number of random craters.