The Fastest Stars at the Galactic Centre: Pericentre Velocity Budgets for S62, S4716 and Their Companions

The innermost known stars of the Galactic centre are the fastest macroscopic objects in the Galaxy whose motions are fully tracked. This paper computes pericentre velocity budgets for six of them from their published periods and eccentricities, using a central mass of 4.297 million solar masses. The extremes are striking: the star S62, on a 9.9-year orbit of eccentricity 0.976, dives to 18.0 AU and reaches 20463 kilometres per second, 0.068 of the speed of light, while S4716, with the shortest securely reported period of 4.0 years, reaches 8183 kilometres per second on a much rounder orbit. S62 moves 2.6 times faster at pericentre than the better-known S2. These speeds, a few per cent of light speed sustained by stars of roughly solar type, make the inner cluster a mildly relativistic stellar system, and they set the scale for the relativistic signals the next generation of instruments can target. All values are computed from published orbital elements; no new astrometry is presented.