Mapping the spacetime metric with GNSS: a preliminary study

TL;DR

This paper explores three methods to determine null coordinates in Schwarzschild spacetime for relativistic gravimetry using GNSS, comparing their accuracy and computational efficiency in Earth's weak gravitational field.

Contribution

It introduces and compares three novel methods for calculating null coordinates in Schwarzschild geometry relevant to GNSS-based relativistic gravimetry.

Findings

All three methods successfully compute null coordinates.

Method accuracy varies with computational complexity.

The study provides insights into the most efficient approach for practical applications.

Abstract

In order to do relativistic gravimetry one needs to define a system of null coordinates for a given constellation of satellites. We present here three methods in order to find the null coordinates of an event in a Schwarzschild geometry. We implement these three methods for the weak gravitational field of the Earth, compare their precision and time of computation.