How to find mass of blackholes.

As we have seen in the previous article that it is believed that every galaxy( galaxy is a cluster of stars and other astronomical objects stuuded in an area of the universe) has a black hole at the center.

Also we saw that the stars revolve around this supermassive black hole which is million or billion times of mass of sun. The stars or we can say the system including stars and its planets revolve around this black hole.

Likewise our galaxy- the galaxy in which we reside i.e; the milky way has a suppermassive black hole at its center. This black hole is named as Sagittarius A* .The sun or the solar system revolves around this black hole in almost a circular orbit. We can determine the distance of this black hole from our solar system( we will see in the next article how?), however it is not feasible to calculate the time period of sun around the black hole. We will use the following formula to estimate mass of black hole( the same we used to find mass of sun by knowing time period of Earth).

the keplers law preditcs the formula approximately as-
Where T is the orbital period
r is radius of cirular orbit or semi major axis of elliptical orbit
G is gravitational constant
M is mass of star around which the planet revolves.

here the star is black hole.

Since distance of sun from the Sagittarius A* is very large 'r' is very large and r to the power 3/2 is larger. Hence we cant practically wait for such a long time to record one period of sun( we will calculate time period of sun in next article).

hence we observe a star that is feasibly closer to the black hole.

Astronomers have observed several such stars closer to black hole.
One such star is the star S2 . S2 follows an elliptical orbit around Sagittarius A*. We can easliy find its distance( semi major and minor axis by tignometry. Similar to parallax method seen in my article "how to find mass of planets and sun in solar system")
Thus after finding semi major axis and its period which is found to be 15.2years (small and feasible to count!).
Hence using above formula we can easily find mass of the black hole.)

For black holes of other galaxies we use the same method.
The mass of Sagittatius A* is 4.1million solar mass.
One solar mass= Mass of Sun

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