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

Elliptic Integrals for Calculation of the Propagation Time of a Signal, Emitted and Received by Satellites on One Orbit