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Relevance of the relativistic effects in satellite navigation

Kulbiej E.

Zeszyty Naukowe Akademii Morskiej w Szczecinie

2016

nr 47 (119)

85--90

Position determination of Global Navigation Satellite Systems (GNSS) depends on the stability and accuracy of the measured time. However, since satellite vehicles (SVs) travel at velocities significantly larger than the receivers and, more importantly, the electromagnetic impulses propagate through changing gravitational potentials, enormous errors stemming from relativity-based clock offsets would cause a position error of about 11 km to be accumulated after one day. Based on the premise of the constancy of light, two major relativistic effects are described: time dilation and gravitational-frequency shift. Following the individual interests of the author, formulas of both are scrupulously derived from general- and special-relativity theory principles; moreover, in the penultimate section, the equations are used to calculate the author’s own numerical values of the studied parameters for various GNSSs and one Land Navigation Satellite System (LNSS).