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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Relativistic Time Dilation in GPS Satellites: Physical Foundations, Mathematical Derivation, and Receiver-Side Implementation

Relativistic Time Dilation in GPS Satellites: Physical Foundations, Mathematical Derivation, and Receiver-Side Implementation

Horner, Michael

Paperback

General Science

ISBN10: 3389201394
ISBN13: 9783389201398
Publisher: Grin Verlag
Published: Jul 23 2026
Pages: 26
Weight: 0.10
Height: 0.06 Width: 5.83 Depth: 8.27
Language: English
Global Positioning System (GPS) positioning is fundamentally a time-transfer problem. A receiver estimates its position by comparing the transmission and reception epochs of radio signals from several satellites whose orbital states and clock corrections are broadcast in the navigation message. Because the satellites move at approximately 3,9 km/s and orbit in a gravitational potential that differs substantially from the terrestrial reference geoid, their atomic clocks do not accumulate proper time at the same rate as clocks on or near the Earth. Special relativity predicts a motion-related slowing of roughly 7.2 microseconds per day, whereas general relativity predicts a gravitational speeding of roughly 45.7 microseconds per day in a simplified spherical-Earth model. The operational GPS reference-rate adjustment is approximately 38.6 microseconds per day, corresponding to a fractional frequency pre-offset of about -4.4647 x 10 -10. If this secular effect were ignored, the equivalent range discrepancy would grow by roughly 11.6 km per day. This article develops the result from the Lorentz factor and the weak-field gravitational redshift, explains the distinction between proper time and coordinate time, and connects the physics to the algorithms implemented in a navigation receiver. Particular attention is given to the broadcast satellite clock polynomial, the periodic eccentricity correction specified in IS-GPS-200, the Sagnac correction caused by Earth rotation, coordinate-frame handling, week-crossover logic, and software verification. The article also places relativity within the wider GNSS measurement model, which includes atmospheric delay, satellite ephemeris and clock uncertainty, multipath, receiver noise, and geometry. The goal is not to report new experimental results but to provide a technically accurate bridge between relativistic physics and implementable software engineering.

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