Conservation of angular momentum and virial theorem in variable mass dynamics

Abstract

Whittaker’s mass variation law in variable mass dynamics is applied to many body problem of celestial mechanics with a view to re-establishing thereof some important theorems. It is proved that the conservation of angular momentum still holds irrespective of the manner of mass variation. The virial theorem, in several forms, with the same mass variation principle as Whittaker’s has been proposed and proved. Needless to mention that classical Celestial Mechanics is based on a single physical law viz universal law of gravitation which in the present subject is coupled with a relevant mass-variation law, Sundman’s inequality and the law of energy are modified in the light of mass-variation principle in case of a system of n bodies, for which the sum of kinetic and potential energies represents an integral equation with time as an independent variable. A sharp form of virial theorem and hence growth of the system with variable masses are studied and analyzed in comparison with fixed mass criteria [1]. Mathematical analysis including L’Hospital’s rule and convolution theorem of integral equation are applied to evaluate some limiting functions involving the moment of inertia, total mass and time and also to set forth some inequality identities involving the initial total mass and the distance of maximum and minimum spacing between the particles (celestial bodies).