Final answer:
Yes, it's true that the mass of a black hole can be determined by observing a star orbiting around it. Kepler's laws are used to calculate the mass based on the star's orbital characteristics. Accurate measurements are complex and require sophisticated instruments and a deep understanding of both the star and the black hole.
Step-by-step explanation:
True, if we find a star orbiting around a black hole, we can determine the mass of the black hole. Utilizing Kepler's laws, specifically Kepler's third law which relates the orbital period of a star to its distance from the object it orbits, astronomers can deduce the mass of the unseen companion, in this case, the black hole. This calculation assumes that the gravitational effects can be considered as originating from a point at the center of mass.
When studying systems like this, if the partner's mass is well above 3 Msun (solar masses), it largely suggests the presence of a black hole. However, it's crucial to confirm that the object is indeed a collapsed star. Observational techniques involve measuring the orbital speed and distance of a star from the black hole, as was done with the stars orbiting the center of our own Milky Way galaxy, providing clear evidence for the existence of a supermassive black hole.
It is important to note that the precision of these measurements is complex and requires understanding various factors about the orbiting star and the system overall. Sophisticated instruments and methods are used to ascertain these measurements and distinguish black holes from other dense objects like neutron stars, which can exhibit similar properties, such as the presence of accretion disks producing X-rays.