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Several space missions such as GRACE, GRAIL, ACES and others rely onintersatellite communications (ISC) between two satellites at a large distanceone from another. The main goal of the theory is to formulate all thenavigation observables within the General Relativity Theory. The same approachshould be applied also to the intersatellite GPS-communications (in perspectivealso between the GPS, GLONASS and Galileo satellite constellations). In thispaper a theoretical approach has been developed for ISC between two satellitesmoving on (one-plane) elliptical orbits, based on the introduction of twogravity null cones with origins at the emitting-signal and receiving-signalsatellites. The two null cones account for the variable distance between thesatellites during their uncorrelated motion.The intersection of the two nullcones defines a distance, which can be found from a differential equation infull derivatives. This distance is the space-time interval in GRT. Applyingsome theorems from higher algebra, it was proved that this space-time distancecan become zero, consequently it can be also negative and positive. But inorder to represent the geodesic distance travelled by the signal, thespace-time interval has to be "compatible" with the Euclidean distance. So this"compatibility condition", conditionally called "condition for ISC", is themost important consequence of the theory. The other important consequence isthat the geodesic distance turns out to be the space-time interval, but withaccount also of the "condition for ISC". This interpretation enables the strictmathematical proof that the geodesic distance is greater than the Euclideandistance - a result, entirely based on the "two null cones approach" andmoreover, without any use of the Shapiro delay formulae. Consistency betweenseveral other newly derived numerical parameters is noted.

Two null gravitational cones in the theory of GPS-intersatellite  communications between two moving satellites. I. Physical and mathematical  theory of the space-time interval and the geodesic distance on intersecting  null cones