Elliptic integrals for calculation of the propagation time of a signal, emitted and received by satellites on one orbit

The propagation time of a signal, emitted by moving along an elliptical orbit satellite from the GPS (or GLONASS) confi gurations is very important ingredient theory, based on formalism null cone and accounting for effects General Relativity Theory. For case satellites, orbiting plane elliptic orbit, it has been proved that signal between satellites given combination integrals first, second third kind. more general space-distributed expressed higher (fourth) order integrals, which according to standard theory can be recurrently means lower-order integrals. In concrete case, fourth are irrational functions zero-order integral in Legendre form. It investigated second-order elementary functions.