Is the planet from Interstellar impossible?

[HansMustermann]

Well, here comes another black hole question from yours truly. I'm sure everyone is surprised

So I've heard arguments from physicists before, saying that the planet near a blackhole in Interstellar would be unstable, or bathed in lethal radiation from the accretion disk, etc. But it just dawned upon me that it should be flat out impossible for it to be there.

Of course, that's calculated from my position of not understanding most of GR, so I might be wrong. (I know, it surprises me too.) If anyone knows better, please do correct me.

So for a Schwarzschild kind of black hole, the time dilation effect in relation to a far far away observer is the square root of (1 - 2GM/rc²). So as you get closer to the Schwarzschild radius, that approaches infinity.

Black holes also have a photon sphere, i.e., a radius under which even photons can't maintain a stable orbit. In the recent photo of a black hole, yeah, that was what the black blob in the middle was. It wasn't the event horizon itself.

That radius, again for a Schwarzschild kinda black hole, is 3GM/c².

Thing is, if you substitute the latter formula into the former, you're still at VERY tame time dilation.

Ok, so at this point I should probably add SR time dilation, since that planet or its star would be orbiting around the star, not hovering in place. And the thing is, we still have some thousands of times worth of time dilation for that to explain. The OVERWHELMING difference in how fast time flows would in fact be from it moving incredibly close to the speed of light, rather than the black hole itself.

I.e., that planet wouldn't be somewhere at the outer edge of the accretion disk. It would be right at the INNER edge of the accretion disk, and at that, quite spaghettified.

So am I wrong there?

Also, obviously I'm not qualified to touch the maths for a ROTATING black hole with a 10 lightyear pole. Which the one in Interstellar probably would be. So if anyone wants to shed light on that one, please help.

 

[CORed]

Okay, I am by no means an astrophysicist, or anything remotely resembling one, but I suspect that tidal forces -- due to the difference in gravitational acceleration on the near and far side of a planet, would be strong enough near a black hole to pull a planet to pieces. I don't remember the formula for the Roche Limit (which determines whether the tidal stress is too much for a planet or moon), nor do I know relevant details for the planet and black hole in Interstellar if I did know the formula, but I do know that is one important constraint on whether a planet can exist.

ETA: IIRC, Roche's Limit and tidal effects are pretty much a Newtonian thing, although, as you get closer to a black hole, Newtonian Physics doesn't really work that well.

 

[HansMustermann]

Oh, at that point not only it would have been broken apart, even its star would have long been slurped into the accretion disk.

My point was more like it's impossible to reconcile the stated time dilation factor, which boils down to over 60,000 times, with where that planet is in the movie.

 

[smartcooky]

Okay, I am by no means an astrophysicist, or anything remotely resembling one, but I suspect that tidal forces -- due to the difference in gravitational acceleration on the near and far side of a planet, would be strong enough near a black hole to pull a planet to pieces. I don't remember the formula for the Roche Limit (which determines whether the tidal stress is too much for a planet or moon), nor do I know relevant details for the planet and black hole in Interstellar if I did know the formula, but I do know that is one important constraint on whether a planet can exist.

ETA: IIRC, Roche's Limit and tidal effects are pretty much a Newtonian thing, although, as you get closer to a black hole, Newtonian Physics doesn't really work that well.

The tidal forces will depend on how close the planet is to the black hole, the closer the planet, the greater the tidal force... the gravitational force of the black hole is effectively trying to force the near and far sides of the planet into two separate orbits.

In answer to HansMustermann's question IMO, whether or not such a planet could exist will depend largely on the mass of the black hole and the planet's orbital distance. The film's science advisor, Kip Thorne, didn't seem to have any problem with the feasibility of Miller's planet.

(these kinds of questions always remind me of Larry Niven's sci-fi short story "Neutron Star". Its worth a read)

 

[HansMustermann]

Yes, they do depend on that, but so does the time dilation factor, which the movie states to be 7 years on Earth for 1 hour there. Which is where that over 60,000 factor came from in my post.

You also have the photon sphere limitation, which gives you a second equation there.

Essentially at the end of the day you can't get an answer in km, but you can get a pretty good idea in relation to the photon sphere radius, which is in turn related to the event horizon radius, i.e., Schwarzschild radius. Obviously this would be larger in km for a larger black hole, and smaller for a smaller black hole, but it still says it has to be at the inner edge of the accretion disk for either, which is also dependent on that mass. Linearly, in fact.

 

[smartcooky]

Yes, they do depend on that, but so does the time dilation factor, which the movie states to be 7 years on Earth for 1 hour there. Which is where that over 60,000 factor came from in my post.

You also have the photon sphere limitation, which gives you a second equation there.

Essentially at the end of the day you can't get an answer in km, but you can get a pretty good idea in relation to the photon sphere radius, which is in turn related to the event horizon radius, i.e., Schwarzschild radius. Obviously this would be larger in km for a larger black hole, and smaller for a smaller black hole, but it still says it has to be at the inner edge of the accretion disk for either, which is also dependent on that mass. Linearly, in fact.

OK, so in interstellar, Gargantua is a supermassive black hole with a mass of about about 100m solar masses.

Here is what the film's science advisor, Kip Thorne had to say when asked about this very issue of the plausibility of a planet that close

"This business of the enormous time differential between one of the planets orbiting very close to Gargantua and the flow of time back on Earth – the problem seemed to be that no planet could endure the resulting gravitational forces. This was something that even I thought was impossible, intuitively, until I went and slept on it and did a few hours of calculations. I came to the conclusion that in fact it is possible. The black hole needs to be spinning very fast, but is possible for the spin to be fast enough for a planet in the necessarily close, stable, circular orbit to not be ripped apart. I can’t fault anyone for saying, “Hey, that’s not possible,” without having first having the benefit of my book! Unless it’s someone who is very deep into general relativity and who I would’ve expected to go do the calculations!"​

​

https://blogs.scientificamerican.co...stellar-with-physicist-kip-thorne/?redirect=1

 

[HansMustermann]

Yes, well, that's kinda what I'm asking: can anyone show me the calculations?

 

[smartcooky]

Yes, well, that's kinda what I'm asking: can anyone show me the calculations?

I have sent you a link to a pdf in a PM

I am not sure if would be wise for me to share that link here (mods might not like it)

Check out page 173 (Ch 17 - Miller's Planet) and page 326 (Technical Notes on Ch 17 - Miller's Planet)


Hopefully this is something like what you are looking for.

 

[HansMustermann]

Thank you, and I mean it, but neither of those answer my question. The information starting at page 173 is common knowledge, although it misses the Roche problem that even CORed spotted without being an astrophysicist. And 326 is still for a non-rotating black hole.

The problem is that a rotating black hole actually makes the Roche problem, as well as general tidal effects, even worse. The dragging of space time, yes, allows you to get closer to the black hole, but essentially that just made the planet's diameter bigger compared to that distance. So essentially the gravity differential just got higher.

The dragging of space-time also would not be at a uniform angular velocity. Essentially the closer you are to the event horizon, the faster it moves, and at a very far away distance your space isn't moving at all. At the scale of a planet THAT close, the drag differential alone is quite significant.

At that distance also any orbit eccentricity would cause MASSIVE tidal deformation, and that's not even going into the prograde orbits around a rotating black hole, where you can be slinged around to higher speeds and back. It's technically possible that the planet in Interstellar just hit the jackpot and is in a perfect circular orbit, it's, shall we say, exceedingly improbable. Even by the information on page 173, even if that planet was at the exact right spot, in the second intersection on the graph, any kind of slowing down over time would push it into the unstable zone where its orbit starts to wobble. And so would GAINING speed, which things tend to do when they're inside the ergosphere of a rotating black hole.

It also ignores the issue of how the planet got into that situation in the first place. All tidally locked planets and moons got to be so by starting as having a rotation, and then tidal effects slowing them down to match the orbital period. The rest of the rotation energy essentially, yes, got dissipated as heat. So if you have a planet which would disintegrate if it were anything but almost perfectly tidally locked with the black hole, well, how did it survive the time before that was the case?

And then there are issues like radiating vast amounts of energy as gravitational waves.

But essentially I don't understand how it being a rotating black hole solves anything. I would like to see the actual maths somewhere, rather than some "you can't disagree with me unless you did the maths yourself." That're reversing the burden of proof even when it's a physicist doing it.

 

[smartcooky]

Thank you, and I mean it, but neither of those answer my question. The information starting at page 173 is common knowledge, although it misses the Roche problem that even CORed spotted without being an astrophysicist. And 326 is still for a non-rotating black hole.<polite snip>

Well, what you're asking for would be moot for me, because the kind of complex mathematics required would be an order of magnitude beyond my pay grade. Aeronatical engineers don't need to deal in the mathematics of general relativity.

ETA: Maybe you should write to Kip Thorne.

 

[Loss Leader]

The time dilation puts the planet way too close for the planet to remain in one piece (let alone in any way habitable). The physics doesn't work.

But that's not what bothers me. What bothers me is that this is the third movie where everybody has to drop everything and go rescue Matt Damon.

 

[rjh01]

I have a few issues with a planet orbiting close to a black hole that would kill off any life
1. If the black hole absorbed any matter it would radiate a lot of deadly rays.
2. Planets need to have a constant source of heat from a star.
3. If the black hole grew by absorbing another black hole (which they do) then that would wrack havoc with anything orbiting it.


One thing that might be interesting to think about and discuss is how about a planet that is orbiting a star which is orbiting a super-massive black hole? There are several stars orbiting close to the black hole in the center of our galaxy. Astronomy will be very interesting from that planet. It would be easy to observe stars wobble due to its sun orbiting the black hole. Plus see other stars also orbiting the black hole.

 

[3point14]

2. Planets need to have a constant source of heat from a star.

I'm not entirely sure this is true.

I think it's not a stretch to posit life on a planet that orbits a black hole and has no sun.

 

[rjh01]

I'm not entirely sure this is true.

I think it's not a stretch to posit life on a planet that orbits a black hole and has no sun.

I do not see how. The planet's temperature would be the same as space, which is very cold. The only way for life on such a planet to exist would be if it had a hot interior like our own. Life might exist using this energy.

If you know how life can exist in any other way please say so. Would love to have a good idea from you.

 

[3point14]

I do not see how. The planet's temperature would be the same as space, which is very cold. The only way for life on such a planet to exist would be if it had a hot interior like our own. Life might exist using this energy.

If you know how life can exist in any other way please say so. Would love to have a good idea from you.

A planet orbiting a black hole would have massive tidal forces acting on it.

This would / may produce a very hot interior, complete, possibly, with steam vents under an ocean with a frozen surface.

Life exists by such vents way down in the ocean floor on earth. I don't see it as a stretch to consider the possibility of a similar situation on a dark planet orbiting a black hole.

 

[HansMustermann]

TBH, I have no problem with the idea that a planet would receive more than enough energy from the accretion disc of a black hole, especially seein' as that one would have to be IN the accretion disc. Depending on the exact configuration, an accretion disc can convert anywhere between 10% and 40% of the infalling mass into energy, which is immense. By contrast fission only converts about 0.7% of mass into energy. So that accretion disc will radiate a LOT of energy.

The main problem I see is that this would probably be more like a lot of X-ray than what you'd get from our Sun. The implications don't just include the absence of an ozone layer, but such a spectrum could break apart N2 molecules and allow even more of the atmosphere to escape into space.

Though how does it have a stable circular orbit while everything else spirals in, that's an extra question.

 

[dann]

I'm pretty sure that the bookshelf is impossible ....

 

[smartcooky]

But that's not what bothers me. What bothers me is that this is the third movie where everybody has to drop everything and go rescue Matt Damon.

Well its actually the seventh, and the eighth was The Martian

You were probably thinking of Interstellar, Saving Private Ryan, and The Martian. However, there is also Elysium, Courage Under Fire, Titan A.E., The Green Zone and Syriana.

Also there might almost have been a ninth. Damon was one of the actors in line to play Tom Bishop alongside Robert Redford in Tony Scott's movie "Spy Game", but the role went to Brad Pitt.

 

[phunk]

OK, so in interstellar, Gargantua is a supermassive black hole with a mass of about about 100m solar masses.

100 billion isn't it?

 

[crescent]

Well its actually the seventh, and the eighth was The Martian

You were probably thinking of Interstellar, Saving Private Ryan, and The Martian. However, there is also Elysium, Courage Under Fire, Titan A.E., The Green Zone and Syriana.

Also there might almost have been a ninth. Damon was one of the actors in line to play Tom Bishop alongside Robert Redford in Tony Scott's movie "Spy Game", but the role went to Brad Pitt.

Gerry, don't forget Gerry, although he mostly self-rescued himself in that one.

I got to be a film monitor for a few days on that one. I stayed at the filming location to prevent them from damaging the national park they were filming in.