8 Meanwhile, the structure of Milky Way and other spiral galaxies provides a simple explanation of the paradox using the classical Newton-Galileo mechanics and Newton’s law of gravitation which is the right approach because in the scale of galaxies so that the cosmic field can be ignored. The gravitational matter of Milky Way is uniformly distributed along the logarithmic spirals having the common pole at the center of Milky Way. These spirals are welldocumented. The length of an arc of a logarithmic spiral equals where is the constant angle between the radius-vector of a point on the spiral and the tangent to the spiral at the point while are the distances between the pole and the ends of the arc. The arc length is directly proportional to the distance of a point from the center of the galaxy when Mass inside of the galactic disc of radius is also directly proportional to because such proportionality remains for any number of spirals. In other words, where is a certain structural constant of the galaxy. The force of attraction of a star of mass to the center of the galaxy is equal to . This force is balanced by the inertia force of Galileo-Newton. From here, the orbital speed of stars is as follows (14) For Milky Way and . This value is close to astrophysical data. About the same value of the orbital speed of stars has been observed in all galaxies. It means that the density of gravitational matter in all galaxies obeys the following general law (15) Here, is the mass of gravitational matter inside unit area of the galactic disc, is the distance from the center of the galaxy, and is the universal galactic constant. And so, the matter density is infinite at the center which is the galaxy’s Black Hole. The logarithmic spiral is the only spiral that corresponds to this general law, see Eq. (15). 7. The Einstein equivalence principle and no annihilation paradox The general relativity is based on the equivalence principle which says that the gravity is the inertial force in the curved space-time. The cosmic-gravitational field does not obey this principle. We illustrate the difference using the following simple example. Let a mass , being fixed to a point by an inextensible string of length , rotate at a constant speed around the point. In absence of cosmic field, the inertia force is balanced by the extension force in the string. Replacing the action of this string by a gravitational mass placed at the center of rotation, such that , we come up with the equivalence principle. (It can be also formulated as the equity of inertial mass to gravitational one).
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