We have been observing the central arcsecond in the Galactic Center for three decades since 1992, and tracked the motions of the stars in the field. Many of the stars show curved trajectories, an unambiguous sign of the gravitational force of the central massive black hole. Combining astrometry and spectroscopy, we have measured in total roughly 50 stellar orbits around Sgr A*. The stars on these orbits are commonly referred to as the "S-stars" (Schödel et al. 2002, Eisenhauer et al. 2005, Gillessen et al. 2009, Gillessen et al. 2017). The following figure shows what the projections of some of the orbits onto the plane of the sky look like.
The actual orbits are measured in three dimensions, and hence we were able to build a full 3D model of the motions of the S-stars:
The visual impression of this stellar system is that the inner orbits follow no apparent order; however, a bit further out, there are a few stars that orbit on similar planes. The randomness of the inner orbits holds true in two senses: in the distribution of how the individual planes are oriented, and how the eccentricities are distributed:
The combination of random orientations and (slightly) supra-thermal eccentricity distribution means the system is close to a dynamically relaxed configuration. These stellar motions do hence not carry information about how he stars came to be so close to the black hole. The best hypothesis is that the inner S-stars have reached their orbits by means of the Hills-mechanism, a cosmic pool game, where a binary star passes close to the massive black hole, capturing one member and ejecting the other at high speed, potentially creating hypervelocity stars.