Mathematical Study Related to Centre of Mass in Modified Newtonian Dynamics
Abstract
In this study we discussed the general two-body problem within the MOND radius in the gravitational field of MOND like galaxy and derived the expression for the total force between the system of test particles, with small masses and a point mass with a big mass as compare to them. Derived the results for the Centre of mass of acceleration for the isolated particles in purely Newtonian regime, for the isolated particles in the galactic neighbourhood of the Sun but in the influence of the gravitational field of mother system, MOND galaxy and for the non-isolated system which is in the gravitational field of large mass. The derived results always approach Newtonian dynamics in the regions of high accelerations. Emphasis is put on the alternative physics in the framework of MOND.