# Relativistic Positioning System. Exact techniques for geodesy on a spacetime manifolds

**Speaker:**Lorenzo Fatibene, Università di Torino

**Date:**January 30th, 2023

**Time:**3:00 pm

**Location:**LH3058 (Lazaridis Hall, Room 3058)

**Bio:**

Since 2011 Lorenzo Fatibene is full professor of Mathematical Physics at the Department of Mathematics “Giuseppe Peano” of the University of Torino (Italy).

He had a degree in Physics (1992) and PhD in Mathematics (1999) and he has been researcher at University of Torino between 1999 and 2011.

His research interests are in geometrical methods for field theory, variational calculus and conservation laws in generally covariant and gauge theories.

Recently, he is investigating extended theories of gravitation and their applications to astrophysical and cosmological models.

**Abstract:**We shall discuss how to build a completely relativistic, exact, positioning system without resorting to weak field approximation. Such a positioning system is even well suited to work near a black hole or any other compact body. We also want to control motion of satellites by the system itself, without external ground control, that also without using Newtonian gravity which may be invalid due to strong field regime. While we are at it, we want also the system to self-detect deviations for the assumptions, suspend operation while the assumptions are violated, return back operational when deviations finish. From a theoretical viewpoint, we argue that all this is analogous to geodesy campaigns just on a Lorentzian spacetime manifold instead on space. It is no surprise that geodesy can detect intrinsic geometry which, in the case of general relativity, is equivalent to the gravitational field. Therefore, relativistic positioning systems are also detectors of the gravitational field.