Movie Interstellar - Question about Escape Velocity The movie Interstellar shows people on a water planet where time is dilated so much that 1 hour is equal to 7 years back on Earth.  Even though they lift off from Earth using a Saturn-V two stage rocket, they leave this water planet in a shuttle craft.
Can someone provide the escape velocity for a place where time is dilated by 60,000 times?  The stated mass of the black hole creating the gravity well is 100 million solar masses, but I'm not sure that would work into the calculation.
 A: The gravity from the black hole (BH) will have no effect on their ability to take off from the water planet itself. Objects in orbit feel weightless (think astronauts in the ISS). If you're only worried about getting off the water planet then there should be no problem.
However, if they were to try to put some distance between themselves and the BH then they'd find it a much more difficult task.
Assuming the BH isn't rotating very fast, the time dilation factor for a body in orbit relative to a stationary observer at infinity is:
$$\frac{d \tau}{dt} = \sqrt{1-\frac{3GM}{c^2 r}}$$
The escape velocity of a BH looks the same as it does in Newtonian mechanics:
$$v_0^2 = \frac{2GM}{r}$$
So if the mass of the BH is ~100 million solar masses, the radius at which the time dilation is 60,000 times normal is at $r \approx$ 275 million miles $\approx$ 3x average Earth-Sun distance. The event horizon itself is at $r \approx$ 2x the average Earth-Sun distance. Meanwhile the escape velocity at the planet radius is about 82% the speed of light, or $v_0 \approx$ 250 million meters/second.
