Illustration of each model described in Sect. 3.1, only focusing on the different effects affecting the astrometric measurements of the S2 star. The positions of both the star (blue line) and the photon (red line) at two dates t1 and t2 are represented for models B to G. At some particular observation time tobs, the apparent position of the star on the observer screen, is highlighted by the symbols A to G. The corresponding emitting position of the star along its orbit is also represented. In model A, the difference Δt = tobs−tem is zero since the photon has an infinite speed. In models B to G, the Roemer time delay, noted ΔtR, is included, thus Δt depends on it. In model D, the star trajectory is described by GR but only accounts for the pericenter advance (PA) since the Lense-Thirring effect is neglected. Contrary to model D, model E takes into account this latter effect on the time-like geodesic (LTS for Lense-Thirring on the Star). Model F is analogous to model E but approximates the gravitational lensing effect (GL). Model G is the full-GR model; gravitational lensing is thus better estimated, the Lense-Thirring effect on the photon path (LTP) is naturally taken into account, and the quantity Δt depends on the Shapiro time delay, ΔtS, in addition to ΔtR.
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