Two-dimensional approach to relativistic positioning systems

TL;DR

This paper explores a simplified two-dimensional model of relativistic positioning systems using four clocks, analyzing their properties, data implications, and applications in gravimetry.

Contribution

It introduces a two-dimensional framework for relativistic positioning systems, detailing their properties and potential in measuring space-time metrics.

Findings

Analysis of data from relativistic positioning systems on space-time intervals

Development of a model with geodesic emitters in flat spacetime

Discussion of applications in gravimetry

Abstract

A relativistic positioning system is a physical realization of a coordinate system consisting in four clocks in arbitrary motion broadcasting their proper times. The basic elements of the relativistic positioning systems are presented in the two-dimensional case. This simplified approach allows to explain and to analyze the properties and interest of these new systems. The positioning system defined by geodesic emitters in flat metric is developed in detail. The information that the data generated by a relativistic positioning system give on the space-time metric interval is analyzed, and the interest of these results in gravimetry is pointed out.