I just read a short piece in New Scientist about a binary black hole system 5 billion LY away that seems to be mutually orbiting each other and they give the numbers as 0.3 LY apart and taking 100 years to orbit one another. Given they are about the same mass, they would be mutually orbiting one another, can you calculate the orbital velocity as if one were stationary and the other moving sort of like the Earth orbiting the sun? If so, I get a mutual orbital velocity of about 5600 Km/sec. Does that # hold up? 0.3 LY =~ 2.8 E12 Km radius, * 6.28 (2 PI) =~ 1.75 E13 Km circumferance / 100 years (3.1E9 seconds)=~5600 Km/sec,
if you consider one not moving. Is that a valid assumption? If not, how do you really calculate the mutual orbital velocity of two equal orbiting masses?

Originally posted by sonhouse I just read a short piece in New Scientist about a binary black hole system 5 billion LY away that seems to be mutually orbiting each other and they give the numbers as 0.3 LY apart and taking 100 years to orbit one another. Given they are about the same mass, they would be mutually orbiting one another, can you calculate the orbital velocity as if one were ...[text shortened]... n? If not, how do you really calculate the mutual orbital velocity of two equal orbiting masses?

Without doing any calcuation, the assumption that the two eqaually massed black holes, of which one is stationary and fixed in space, must be false.

However, in order to keep the fomula simple I can agree to the assumptions, but then we have to make an error estimate accordingly.

If the black holes are equally massive, they will orbit around their center of mass, if you assume the orbit is circular you can get the speed by using half the distance between the black holes as the radius of the circle.

The difficulty is that the estimates of the masses of the black holes are between 20 million and 1 billion solar masses. So there´s a fairly large margin of error in the mass, If one of them is much more massive than the other then you can make the approximation that the heavier one is stationary. But since we don´t know the masses very accurately you can´t do that for a rigorous calculation.

The largest possible error you can introduce by assuming that one of the black holes is stationary is a factor of 2. Since the errors in the estimates of the masses are around a factor of 100 you do not really introduce much more of an error by assuming this. Your calculation is therefore fine.

Figures for mass estimates from: http://news.bbc.co.uk/1/hi/sci/tech/7924414.stm