A Brief Essay on "Newtonian Gravity", Escape Velocity and "Dark Matter" for Galaxies and Star Clusters. - Dialynas, Thanassis (European Journal of Applied Sciences, 2023)
What is attempted in this article is to be introduced the "Newtonian gravity" as a non-relativistic theory which can for instance be applied in mass formations such as the stars, the globular and open star clusters and the galaxies. In this paper the attention is focused on clusters and galaxies that are more easy to handle since their "dynamics" depends solely on matter [no gas, fermion and radiation pressure]. Initially the field eqs. for a vector gravity field ( ) are introduced rather than tensor field . Then the gradient of a scalar field is found which is related to the vector field ( ) in the 3-D (dimensional) case. Since the case of a galaxy is actually 2-D with its thickness being ( )th of its Diameter, the 2-D eqs. are solved toward the solution of the mass distribution with radial symmetry. The next step which is done is to show compatibility (but only an approximate one) of the field eqs. for NN "objects" (NN»1) consisting a Galaxy. Subsequently the Effective Potential is introduced by using an "object" not as one of the NN-Newton ones, but as an object moving in the effective potential. With this “equipment” (one-object-potential) one can easily define the escape velocity of an object found in position r far from the center of a galaxy. A discussion of “dark matter” is done. Finally the radial and angular eqs. of motion are attempted to be solved and an integral of time with respect to radial distance is given which unfortunately cannot be inverted. However when the motion is bounded then a condition of periodicity can be found.