if the active core of a galaxy contains a black hole of 10^6 solar masses...?
what will the orbital period for matter orbitting the black hole at a distance of 0.33 au?
According the Newton's form of Kepler's third law we have
P^2 = constant r^3/M
The constant equals one if we use years, AUs and M_Sun as units.
Here we have P^2 = 0.33^3/10^6 = 3.6x10^-8, so P=1.9x10^-4 year
Or 1.7 hours.
This is assuming Newton's non-relativistic gravity laws still apply this close to the black hole, and the orbit is still outside the event horizon.
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