Edward A. LeMaster, Lockheed Martin Space

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Both special and general relativity present significant impacts on the time and frequency management of satellite-based systems. Although GPS is the most well-known system for which relativity must be considered, relativity also influences applications such as terrestrial timekeeping, satellite communications, and geodesy. The mathematics required for analyzing most satellite-based systems is relatively simple and is well-understood, at least within the GNSS community. But this knowledge is somewhat less-well understood outside of the GNSS community, or when applied to non-GNSS satellite systems. This paper seeks to make this topic more accessible to mission architects and satellite-system engineers by presenting a general mathematical discussion of relativity as it applies to a wide range of orbits. Emphasis is placed on the differentiation between secular frequency bias and the additional cyclic frequency and time variation that repeats each orbit, because it is this cyclic variation that often causes the greatest challenges for users of satellite systems. The paper presents the secular and cyclic relativistic components of frequency and time offset for several different common orbits, spanning a representative range of altitudes, eccentricities, and inclinations. Users can start from these charts and examples to gain a broad-base understanding of how satellite clocks in various classes of orbits will behave, before proceeding with detailed computations for any specific orbits under consideration.