Dark Matter in the Planetary System

Abstract

In this analysis, we use the data from the eight planets in our planetary system to show that it is stress-free, and then by radial (R) extension show that is consistent with an inner spherical Universe of radius, Ro =1.25 1016 m, where Ro is the radius at which  the azimuthal orbital velocity(U) attains the velocity of light.  The orbital data are fitted by the extended Newtonian gravitational model,  U2 = G Mo/R ( 1 – (R/Ro)3) + c2 (R / Ro)2, where G is the universal gravitational constant, Mo  is the mass of the Sun, and the first term on the right hand side is potential energy and the second term, which  arises from the mass of dark matter (M = 1/3 ρ2 R3) where ρ2 = 3c2/(Ro2G) is dark energy.  This model applied to the complete inner Universe predicts that the ratio of the mass of ordinary matter to the  mass of dark matter, 1 / (1 + 3π/2),  is 17.5 %, in close agreement with the Central Density data [1], and that the mass-energy density ratio of dark energy to ordinary energy is 66.7% in substantial agreement with observational data [2]. The nature of dark matter is investigated, guided by the planetary data, in which the ratio of ordinary matter to dark matter for Earth (and also Mercury and Jupiter) is close to one, whereas for the outer planets it is much less than unity.  This has led us to believe that the key property of dark matter is the absence of the organising principle, which is present in ordinary matter.   The ratio of ordinary matter to dark matter in the complete inner Universe attests to a creative universe.    We also show that the inner Universe is bounded by a macro-constant stress layer in  which galaxies are created in partnership with the micro-constant layer in which photons are created.