Volume 23: Pages 540-549, 2010

Transforming global positioning system to the solar barycentric frame: Kinematic effects

Ronald R. Hatch ¹

¹1142 Lakme Avenue, Wilmington, California 90744, USA

A consistent procedure for mapping the global positioning system (GPS) from Earth’s frame to the solar barycentric frame is developed. The process is first analyzed in reverse, i.e., by a general mapping from the solar frame to Earth centered inertial frame. In the process of developing the correct mapping, several peripheral issues are addressed. These include (1) an analysis of the Sagnac effect, which is generally incorrectly ascribed to a rotational effect, and (2) an analysis of Thomas precession, which is generally incorrectly ascribed to infinitesimal Lorentz transformations. The true transformation between the solar frame and the ECI frame is shown to be a combination of a Selleri transformation and clock bias effects due to velocity and gravitational potentials which combine to form an apparent Lorentz transformation (ALT). The longitudinal length contraction effects embedded within the Selleri transformation are shown to be the result of the conservation of momentum. There are several significant differences between the ALT and the Lorentz transformation (LT). First, sequential noncollinear ALTs do not induce rotational effects such as sequential noncollinear LTs. Second, there is a natural change of scale in the ALT but not in the LT. In addition, momentum and energy are conserved in the ALT but not in the LT. The reverse ALT is derived and it differs from the reverse LT in that the original scaling is recovered by the reverse ALT but compounded by the reverse LT. Finally, it is shown that the use of space based very long baseline interferometry (VLBI) may provide a means to verify the derived ALT mapping procedure by revealing the longitudinal orbital contraction, which is obscured in visual and electromagnetic experiments but revealed in precise VLBI angular measurements.

Keywords: Global Positioning System, GPS, Sagnac Effect, Thomas Precession, One-Way Speed of Light, Lorentz Transformation, Selleri Transformation, Special Relativity, General Relativity, Equivalence Principle, Conservation of Momentum, Conservation of Energy, VLBI, SVLBI, Length Contraction

Received: May 10, 2010; Accepted: July 31, 2010; Published Online: September 1, 2010