Astronomers can’t see a black hole directly, but they can study the stars that are orbiting around one. By carefully measuring the speed and radius of these stars’ orbits, the astronomers can then use the laws of gravity to deduce the mass of black holes.
The technique has been applied to stars in orbit around the black hole at the centre of the Milky Way galaxy. This calculation showed the black hole to be about 3 million times as big as the Sun.
By averaging the speeds of all the stars orbiting the central black hole in the Andromeda spiral galaxy (our nearest large galactic neighbour), astronomers deduced that it has a mass of about 30 million of our Suns.
Another technique uses a mathematical model of how material spirals into black holes. By comparing observations of the energy emitted by this material to the model, astronomers can estimate the mass of the black hole.