A MASS TENSOR IN RELATIVISTIC SPACECRAFT MOTION

摘要

In a previous paper the Covariant Propulsion Principle for spacecraft relativistic motions was introduced. A mass tensor was found, by the closed system consisting of the spacecraft and its propellant mass, provided a "solidification point" different that the spacecraft mass centre. In this paper is introduced a new expression for the mass tensor. This alternative formulation possesses advantages with regard to the previous one: 1 - it is simpler, 2 - it can be extended on non-Euclidean spaces, 3 - the mass tensor coefficients are easier to calculate, 4 - the new formulation shows the connection between the mass tensor and the spacecraft acceleration, 5 - the new expression permits quantify the propulsive effects. The main contribution resides in the possibility of expressing the mass tensor as a function of the global system momentum. By means of this new formulation is possible to show, for relativistic motions, that if the solidification point coincides with the global system mass centre the mass tensor reduces to the scalar mass. A diagonal expression for the mass tensor is obtained; it shows the coupling between the mass tensor and the spacecraft acceleration. Numerical results of the propulsive effects as a function of the mass tensor are shown.