Comment by pavel_lishin

  Feature                  Primary Black Hole              Secondary Black Hole
  -----------------------  ------------------------------  ------------------------------
  Mass                     1.8 × 10^10 M                   1.5 × 10^8 M
  Schwarzschild Radius     356 AU                          3.0 AU
 
  --- Circular / Average Orbital Properties ---
  Orbital Period           12 years
  Semi-Major Axis          13,800 AU (~0.22 ly)
  Orbital Speed (avg)      282 km/s (0.094% c)             33,900 km/s (11.3% c)

  --- Elliptical Orbit (e ≈ 0.65) ---
  Pericenter Distance      4,830 AU                        (same)
  Orbital Speed (peri)     613 km/s (0.20% c)              73,600 km/s (24.5% c)

  Apocenter Distance       22,800 AU                       (same)
  Orbital Speed (apo)      130 km/s (0.043% c)             15,600 km/s (5.2% c)

[1] https://archive.is/Ccy5M

In Newtonian gravity, the relation between the orbital period T and the semimajor axis a of the orbital ellipse is a^3 / T^2 = GM / 4π^2, where M is the reduced mass of the system (in this case, with 99% of the mass being in one of the two black holes, it's simply the mass of the heavier one).

Plugging 12 years and 18e9 solar masses gives about 2e12 kilometers, or roughly a fifth of a lightyear. This also means the smaller black hole is zipping around the bigger one at around 6% of the speed of light, which is low enough that the Newtonian approximation is probably reasonable accurate (at least to give a rough idea of how large the distances must be).

You made me wonder about the orbital speed of a planet circling one of these supermassive black holes, and how fast it would be... and then I realized, of course, the orbital speed would approach the speed of light at the event horizon.

There's a SF story waiting to be written about a planet just over that radius, traveling at something like 0.99c. Years would takes seconds, and seem even faster since they'd be significantly time-dilated. Of course, they'd quickly spiral in.

Kepler’s laws should still provide a pretty good estimate, at least until black holes get much closer. I did a quick back of the envelope calculation, and looks like they’ll be roughly 14k astronomical units, or 0.22 light years apart.

How much time dilation do you get at those masses though?

I’m having more trouble visualizing how accretion disks would work for a binary black hole. Because the light is coming from the disks, not the black holes. So those are what are actually pulsing/girating.