Geometric approach to the definition of emission coordinates
arXiv:2111.13423 · doi:10.1016/j.asr.2022.04.011
Abstract
We investigate a relativistic positioning system where the coordinates of the users are determined by the proper times broadcasted by clocks in motion in spacetime: these are the so-called emission coordinates. In particular, we focus on emission coordinates in flat spacetime: in this case, we show that these coordinates can be defined using an approach based on simple geometrical properties of geodesic triangles. We analyse the 2-dimensional case and then we show how the whole procedure can be applied to 4 dimensions, also in terms of ordinary three-dimensional spheres. An analytic solution for the coordinates of the receiver is obtained. The solution remains valid at almost any place, in particular when redundancy in the number of emitters can be exploited.
revised version: discussion extended and references added
References in corpus (7)
- Emission vs Fermi coordinates: applications to relativistic positioning systems
- Relativistic Positioning Systems
- Pulsars as celestial beacons to detect the motion of the Earth
- Relativistic positioning: errors due to uncertainties in the satellite world lines
- Relativistic positioning systems: Perspectives and prospects
- Mapping Cartesian Coordinates into Emission Coordinates: some Toy Models
- Relativistic positioning: including the influence of the gravitational action of the Sun and the Moon and the Earth's oblateness on Galileo satellites