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The frequent flaring events in the X-ray and the NIR radiation of Sgr A* seemnot to be periodic in time. However, statistical regularities, here termed"modulations by a pacemaker", are found in the recorded arrival times of bothtypes of events. The characteristic time of the X-ray pacemaker is 149 min andthat of the NIR pacemaker is 40 min. Their reality as derived from observeddata can be accepted at larger than 4.6{\sigma} and 3.8{\sigma} levels ofstatistical confidence, respectively. These results can be interpreted asevidence for a star that revolves around the BH of Sgr A* in a slightlyelliptical precessing orbit, at a distance of 3-3.5 Schwarzschild radii of theBH. The period of the X-ray pacemaker, which is not a periodicity of the flareoccurrences themselves, is the epicyclic period of the star orbital motion.This is the time interval between 2 successive passages of the star through theperi-center of its orbit. The NIR pacemaker period is the sidereal binaryperiod of the star revolution. The origin of the X-ray flares is in episodes ofintense mass loss from the star that occur preferably near the pericenter phaseof the binary revolution. The NIR flares originate or are triggered byprocesses that are internal to the star. The radiation emitted in the directionof Earth is slightly modulated by the changing aspect ratio of the twocomponents of the BH\star binary to the line of sight from Earth at thesidereal binary frequency.

Possible evidence from the flaring activity of Sgr A* for a star at a distance of ~3.3 Schwarzscild radii from the blackhole