What the movie Interstellar got right and wrong?

[RandyD123]

We all know that getting too close to the gravity well of a massive object like a black hole causes time to move more slowly for you than it would for people on Earth. But is it possible for a planet to exist close enough to a black hole and have a person actually stand on that planet? And if possible is there math that could be use to figure out how much time has passed on earth vs. your time?

 

[sophiecentaur]

If you get close enough for these effects to be relevant, I would expect the gradient of the fields to be great enough that one end of the ship would be getting older at a detectably different rate from the other end. Anyone could get into an orbit around a black hole and it would feel the same as the orbit around a star. . . . only you wouldn't see the central attractor.
Time dilation and other effects are detectable under pretty mild conditions, of course.

 

[russ_watters]

The idea is that the black hole is big, keeping tidal forces down, while providing significant time dilation. It's certainly possible to have hours on such a planet be years on Earth.

Hyperphysics has that equation:
http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/gratim.html

You wou'd want to select a maximum comfortable tidal acceleration and set the mass and distance parameters equal. I'd probably plug them into a spreadsheet and play with the parameters until I liked the result

 

[RandyD123]

But can a human walk on that planet? And can that planet have atmosphere to support a human?

 

[russ_watters]

But can a human walk on that planet? And can that planet have atmosphere to support a human?

There's no reason why it couldn't and it isn't clear to me what you think would happen. Remember, when you are in orbit, everything is in orbit together So orbiting the black hole while on a planet orbiting the black hole doesn't have a noticeable effect on you if the tidal force is low.

 

[PeterDonis]

If you get close enough for these effects to be relevant, I would expect the gradient of the fields to be great enough that one end of the ship would be getting older at a detectably different rate from the other end.

Not if the hole is large enough. The hole in Interstellar is supermassive (I believe a billion or so solar masses), so tidal gravity even very close to its horizon will be small.

 

[PeterDonis]

Hyperphysics has that equation

The equations on that page only apply to an observer hovering at rest above a non-rotating black hole's horizon. The situation in Interstellar is more complicated, because the hole is rotating and the planet is in a circular orbit. I can't find any online reference that gives the exact equation in question, but it should be fairly straightforward to derive it from the Kerr metric; if I have time later I'll try to do that.

Kip Thorne has published a book giving the detailed math that he worked out for the movie:

https://www.amazon.com/dp/0393351378/?tag=pfamazon01-20

 

[Sorcerer]

Slightly off topic, but what about the frozen “clouds” on the other planet. Seems implausible. I mean, unless they weren’t really clouds but were large ice mountains or something.