Question

How do you calculate the mass of a supermassive black hole?

Answer 1

You can calculate the mass of a supermassive black hole from the orbit of a star orbiting the black hole.

Explanation:

You can calculate the mass of an object from the orbit of a body orbiting around it. A form of Kepler's third law is `a^3=MT^2`. Where `a` is the semi-major axis distance in AU, M is the mass of the central body inn Solar masses and T is the orbital period in years.

Evidence for the supermassive black hole at the centre of our galaxy, Sagittarius A*, came from the discovery of several fast moving stars orbiting the centre of the galaxy. One of the first ones to be discovered is called S2. It has a period of about 15.56 years and a semi-major axis of about 1,000AU.

Putting the figures into Kepler's equation `1000^3=15.56^2M`. This gives the value of `M=4,130,000` solar masses. Current estimates for the mass of Sagittarius A* are 4,300,000 solar masses.