Gravity, Time Dilation & Black Holes: Q&A

[mileymo]

I'm wondering if a ship orbited a black hole for a year, how large would the black hole be for it to equal 10,000 years on earth?

 

[rootone]

It would depend not only on the mass of the BH, but also on the distance at which the ship is orbiting.
The closer it is to the event horizon the more noticeable would be the time dilation for a distant observer.

 

[Janus]

No matter what the size of the black hole, orbiting at ~1.500000015 times its [URL='https://en.wikipedia.org/wiki/Schwarzschild_radius']Schwarzschild radius will give you that 1 to 10,000 ratio. (1.5 times the Schwarzschild radius is the limit to how close you can orbit a black hole, inside of that, even photons cannot maintain an orbit.)

 

[PeterDonis]

orbiting at ~1.500000015 times its Schwarzschild radius

It's worth noting that this will be an unstable free-fall orbit; any small perturbation will either send you into the hole, or send you out to infinity. The closest stable free-fall orbit is at 3 times the Schwarzschild radius, where the time dilation factor is much smaller, only $\sqrt{2}$.

 

[mileymo]

Thanks very much!