Numerical experience with the finite speed of gravitational interaction

We discuss numerical solution of a system of nonlinear ordinary differentia l equations with a time-varying delay. This system describes the mutual inf luence between mass bodies in the case of a finite speed of the gravitation al interaction. We show that this fact has to be taken into account in inte rplanetary flights, because minor changes in the velocity are continuously cumulated during a long time, which affects the position of a satellite. A method to determine an approximate value of the speed of gravitational inte raction is introduced. We observed that in two-body problems with delays, t here are no periodic solutions as in the classical two-body problem. We als o demonstrate that the finite speed of gravitational interaction contribute s to the expansion of the universe, slightly protects stars against collisi ons and thus makes, e.g., globular clusters more stable. (C) 1999 IMACS/Els evier Science B.V. All rights reserved.