# Why is Sgr A* moving so much?

This answer mentions that the supermassive black hole at the center of our galaxy is constantly moving.

Sagittarius A Star is 1000 times faster and smaller. Its like a toddler who is moving constantly. In comparison, M87 is much slower, like a big bear

What causes Sgr A* to move?

• Could be related to the fact that, since it’s smaller, the mass of the whole galaxy around it makes it move, like in a similar way the sun moves just a little bit from the orbits of all the bodies around it, but I’m not 100% sure Commented Apr 18, 2022 at 15:10

If a star of mass $$m$$ hits a black hole of mass $$M$$ at velocity $$v$$, conservation of momentum means that the black hole now moves at velocity $$\Delta v=\frac{mv}{m+M}=\frac{1}{1+\frac{M}{m}}v.$$ The bigger $$M$$ is compared to $$m$$, the less the change in velocity.
(This is not 100% as straightforward as the above argument: to make a mass $$M$$ black hole out of $$N=M/m$$ stars you have to add their random velocities, and a heavy black hole will have more added momentum than a small one. To properly calculate it one needs to add a sum of random velocity vectors rescaled by the mass accumulated to that date. However, $$N$$ random Gauss-distributed momentum vectors will produce a Gaussian vector with mean 0 and a variance $$\sigma^2/N$$: even if they all contributed equally the spread of black hole momentum around 0 would tend towards zero. Dividing by the growing mass gives an even slower velocity distribution.)