Final answer:
The movements of stars near Sagittarius A* allow astronomers to determine its mass, which is about 4 million solar masses, indicating the presence of a supermassive black hole.
Step-by-step explanation:
Understanding the Massive and Mysterious S g r A*
The movements of the stars close to Sagittarius A* (S g r A*) at the center of the Milky Way enable astronomers to determine its mass. Observations using infrared telescopes and techniques such as adaptive optics have allowed us to observe individual stars within a few light-days of our Galaxy's core. Their rapid orbital motions around Sgr A* suggest the presence of a supermassive object with a mass approximately 4 million times that of the Sun. This object is believed to be a black hole, inferred by the fact that the mass is crammed into an extraordinarily small volume.
Since a black hole does not emit radiation, its presence is discerned indirectly through the impact it has on its surroundings, particularly the effect of its gravity on nearby stars. The measurement of proper motion of these stars—in arcseconds per year—provides crucial data. The proper motion is observed as the change in the relative positions of stars on the celestial sphere, and by applying the laws of gravity and knowing the distance to these stars, astronomers can calculate the mass of the object they are orbiting.
The immense gravitational pull of Sgr A* accounts for the extremely swift orbits of these stars. The proper motion analysis, along with the concept of Schwarzschild radius, aids in estimating the size of the event horizon of a black hole, which is directly proportional to its mass. Therefore, tracking the motions of stars near Sgr A* is key to not only determining its mass but also confirming the existence of the black hole at the center of our Galaxy.