  Several space missions such as GRACE, GRAIL, ACES and others rely on
intersatellite communications (ISC) between two satellites at a large distance
one from another. The main goal of the theory is to formulate all the
navigation observables within the General Relativity Theory (GRT). The same
approach should be applied also to the intersatellite GPS-communications (in
perspective also between the GPS, GLONASS and Galileo satellite
constellations). In this paper a theoretical approach has been developed for
ISC between two satellites moving on (one-plane) elliptical orbits based on the
introduction of two gravity null cones with origins at the emitting-signal and
receiving-signal satellites. The two null cones account for the variable
distance between the satellites during their uncorrelated motion. This
intersection of the two null cones gives the space-time interval in GRT.
Applying some theorems from higher algebra, it was proved that this space-time
distance can become zero, consequently it can be also negative and positive.
But in order to represent the geodesic distance travelled by the signal, the
space-time interval has to be "compatible" with the Euclidean distance. So this
"compatibility condition", conditionally called "condition for ISC", is the
most important consequence of the theory. The other important consequence is
that the geodesic distance turns out to be the space-time interval, but with
account also of the "condition for ISC". The geodesic distance is proved to be
greater than the Euclidean distance - a result, entirely based on the "two null
cones approach" and moreover, without any use of the Shapiro delay formulae.
Application of the same higher algebra theorems shows that the geodesic
distance cannot have any zeroes, in accord with being greater than the
Euclidean distance.
