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The S stars orbiting the Galactic center black hole reach speeds of up to afew percent the speed of light during pericenter passage. This makes, forexample, S2 at pericenter much more relativistic than known binary pulsars, andopens up new possibilities for testing general relativity. This paper developsa technique for fitting nearly-Keplerian orbits with perturbations fromSchwarzschild curvature, frame dragging, and spin-induced torque, to redshiftmeasurements distributed along the orbit but concentrated around pericenter.Both orbital and light-path effects are taken into account. It turns out thatabsolute calibration of rest-frame frequency is not required. Hence, if pulsarson orbits similar to the S stars are discovered, the technique described herecan be applied without change, allowing the much greater accuracies of pulsartiming to be taken advantage of. For example, pulse timing of 3 microsec overone hour amounts to an effective redshift precision of 30 cm/s, enough tomeasure frame dragging and the quadrupole moment from an S2-like orbit,provided problems like the Newtonian "foreground" due to other masses can beovercome. On the other hand, if stars with orbital periods of order a month arediscovered, the same could be accomplished with stellar spectroscopy from theE-ELT at the level of 1 km/s.

Towards relativistic orbit fitting of Galactic center stars and pulsars