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 trian- gles. We analyze 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.

Geometric definition of emission coordinates / Ruggiero, Matteo Luca; Tartaglia, Angelo; Casalino, Lorenzo. - In: ADVANCES IN SPACE RESEARCH. - ISSN 0273-1177. - ELETTRONICO. - 69:12(2022), pp. 4221-4227. [10.1016/j.asr.2022.04.011]

### Geometric definition of emission coordinates

#### 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 trian- gles. We analyze 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11583/2961121`