Special Relativity and Intersatellite Tracking

Paul S. Jorgensen

Abstract:	Starting in the mid-1990s, the replenishment GPS Block IIR satellites will be launched. These new satellites will incorporate crosslink ranging; i.e., inter-satellite tracking. The relative velocity between pairs of satellites can be very high, which suggests a question regarding the treatment of special relativity. This paper addresses this question. In particular, the well known relativity effect of moving clocks appear to slow down as seen by a stationary observer. At first blush, irreconcilable contradictions appear. Is the stationary observer the receiving satellite making the crosslink ranging measurements, or is the observer really fixed in earth-centered inertial coordinates? Each point of view gives a different answer for the special relativity effect. A mathematical derivation has been formulated that resolves the contradiction. The key to the resolution is a consideration of classical Doppler in satellite tracking, for classical Doppler also gives differing results when viewed in different coordinate frames. Taken by itself, Doppler confronts us with an impossible Newtonian task: find absolute space. It is only when special relativity and classical Doppler are taken together that both of these seemingly irreconcilable differences are removed. In considering alternative coordinate frames, the differences in special relativity exactly counterbalance those in classical Doppler. Einstein's special relativity is the great equalizer of coordinate systems. We are given the option of choosing the one most convenient to our needs and in the case of GPS, this is an earth-centered inertial frame. This paper further explores other aspects of special relativity and how it relates to the overall design of the GPS control segment architecture. The manner in which the satellite and ground clocks are tied together is discussed as well as how GPS time is precisely defined.
Published in:	Proceedings of the 44th Annual Meeting of The Institute of Navigation (1988) June 21 - 23, 1988 U.S. Naval Academy Annapolis, Maryland
Pages:	72 - 77
Cite this article:	Jorgensen, Paul S., "Special Relativity and Intersatellite Tracking," Proceedings of the 44th Annual Meeting of The Institute of Navigation (1988), Annapolis, Maryland, June 1988, pp. 72-77.
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