# Gravity versus Time Dilation Question

Tags:
1. Oct 14, 2015

### 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?

2. Oct 14, 2015

### 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.

Last edited: Oct 14, 2015
3. Oct 14, 2015

### Janus

Staff Emeritus
4. Oct 15, 2015

### Staff: Mentor

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 $\sqrt{2}$.

5. Oct 15, 2015

### mileymo

Thanks very much!