The Gravitational Redshift of S2 at Pericentre: Separating the Two Relativistic Terms

Near its closest approach to Sagittarius A*, the star S2 moves at 0.0259 of the speed of light at a distance of only 2815 gravitational radii, and its spectral lines carry two relativistic imprints at once. This paper separates them. From the published orbit, the pericentre speed is 7757 kilometres per second; the gravitational redshift contributes an equivalent velocity of 106 kilometres per second and the transverse Doppler effect 100 kilometres per second, for a combined relativistic excess of 207 kilometres per second over the classical Doppler prediction. The two terms are nearly equal, their ratio being 0.94, which is precisely why the pericentre passage of 2018 could test their sum but not either term alone. At apocentre the gravitational term falls to 6.5 kilometres per second. Both observing teams that reported the effect in 2018 and 2019 measured a combined signal consistent with this budget. Computed from published orbital elements; not a new spectroscopic measurement.