Inflection Points of Potential and Polar Moments of Inertia of Spherical Celestial Bodiesстатья
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Аннотация:Abstract—A simple existence criterion of inflection points of the potential in nonuniform spherical bodies is
formulated. The criterion states that geometric loci of inflection points of the potential appear not only at
density discontinuities but also at locations where the density ρ(r) is twothirds of the average matter density
inside a sphere of a specified radius. The criterion is universal and is fulfilled as for bodies with a contin
uous density distribution, and for bodies consisting of layers of finite thickness, and also in mixed models. The
method of separation of extreme points method of separation of inflection points is given. The criterion is
tested on many models including isothermal, polytropic, and isochronous spheres. The family of models
within which there are no inflection points is specified. Testing of the method on the Earth’s model confirms
its adequacy. A lower limit for the axial (polar) moment of inertia of a spherical body that sep
arates planets and moons of the solar system into two groups is also obtained using the 3/2 criterion. The first
and the largest group includes celestial bodies that have internal extreme points of the attraction force. The
second group consists of planets and satellites that have no internal extreme points. These are the Moon, Io,
Phobos, and, significantly, Mars.
Keywords: Newtonian potential, nonuniform gravitating spheres, inflection points of potential, polar
moments of inertia, model of planets