Sakholian Radius-To-Mass Ratio Postulate Applied to the Calculation of the Mass or the Radius of a Satellite in the Solar System and in the Milky Way

Abstract

In this work, it is demonstrated that the ratio of the radius of a satellite to that of its center of rotation is equal to the ratio of the mass of the satellite to that of its center of rotation raised to a power. This new radius-to-mass ratio relationship postulated, is referred as Sakholian radius-to-mass ratio (SRMR) postulate. For a given satellite, The SRMR-postulate indicates clearly that the Solar system contains three categories of planets: terrestrial planets (Mercury, Venus, Earth, and Mars : \(\alpha\)\(\approx\)0.40), dwarf planets (Ceres, Pluto, Haumea, Makemake, and Eris ; \(\alpha\) = 0.34) and giant planets (Jupiter, Saturn, Uranus, and Neptune : \(\alpha\) = 0.33). The value of \(\alpha\) equal to 0.34 is a theoretical argument in favor of the status of dwarf planet attributed to Pluto since the very controversial Prague 2006 IAU vote. In addition, SRMR-postulate is applied in the calculations of the mass and the density (volumic mass) of 64 small regular planetary moons: 24 for Jupiter (\(\alpha\) = 0.331), 12 for Saturn (\(\alpha\) = 0.330), 22 for Uranus (\(\alpha\) = 0.334) and 6 for Neptune (\(\alpha\) = 0.326). For all these 64 satellites, it is seen that \(\alpha\)\(\approx\) 0.33. Excellent agreements are obtained with literature masses of small regular satellites calculated assuming a constant density and using a given radius. Besides, it is demonstrated that the SRMR-postulate can be applied to the calculation of the mass or the radius of a given star belonging to the Milky Way. For particular cases of fourth stars, calculations of the \(\beta\)-parameter give \(\beta\)  = 0.662 for both Alpha Centauri B and Rigel and \(\beta\)  = 0.390 for both Alpha Centauri A and Capella A. These primary results indicate the possibility to use the SRMR-postulate to estimate the mass or the radius of a given star of the Milky Way containing between 200 to 400 billion stars. For all the Solar system bodies (satellites and planets), the radius-to-mass ratio condition is 0.3 < \(\alpha\)  < 0.4. Out of this range, the mass or the radius determined must be revised. Then, \(\alpha\)  may be very useful parameter for modeling the size (diameter or mass) of a given celestial satellite.