# What is this black hole merger orbital speed?

If space craft nears a black hole we see it getting slower and slower to the point it would appear to stop moving due to red shift. Then how fast are these black holes moving?

• Another question by OP about the same video: physics.stackexchange.com/q/225673/2451 Jun 29, 2016 at 22:47
• Please don't cut and paste random stuff on the internet without attribution. It's rude. Who is the person who made the video? Also, there's no way we can possibly give you a quantitative answer to this question based on a video. There is nothing that sets a time or distance scale. What is the point of offering a bounty on the question when you haven't even provided any of the information that would be needed in order to answer it?
– user4552
Feb 12, 2019 at 22:17
• @BenCrowell Well the video is at least watermarked. Hence we know it is made by the SXS collaboration. Feb 13, 2019 at 8:30
• How can a user with a reputation of 1 offer any bounty at all? Feb 14, 2019 at 1:20
• @D.Halsey The bounty amount is subtracted from the offerer's rep as soon as the bounty is started, so you're seeing the post-subtraction rep. See meta.stackexchange.com/questions/16065 and physics.stackexchange.com/users/148704/muze?tab=topactivity Feb 14, 2019 at 4:13

That being said we can have a go at giving an approximate answer. Based on the relative sizes of the two photon spheres in the video, we can estimate the ratio of the two black hole masses to be roughly 1:4. Furthermore, lets assume the individual black holes are not spinning. From simulation data it can be read off (e.g. from the peak of the gravitational wave frequency) that the merger happens at angular velocity $$\omega = 0.16 c^3/(GM)$$, where $$G$$ is the gravitational constant, $$c$$ the speed of light, and $$M$$ the total mass of the binary. From Effective One Body descriptions it is known that the merger happens there and about a radial separation from the "center of mass" $$r = 3 GM/c^2$$. We can thus roughly estimate the orbital velocity as $$r\omega =0.6\,c$$.