<p>If you are orbiting a 1-sun-mass black hole at 1 AU, gravity-wise it would be just like it is for us orbiting the sun.  Gravity is gravity and mass is mass.  The planets would have to have been captured after formation of the black hole or moved in from distant orbits.  However, the accretion disk would be likely to be emitting lots of X-rays and not anywhere near enough visible light, so life on that planet would be pretty grim.</p>

CC BY-SA 3.0
2015-08-12T03:49:40.450Z
2015-08-12T03:49:40.450Z
user7936
<p>For those who haven't seen it:</p>
<blockquote class="spoiler">
<p>Some human explorers land on a planet orbiting a black hole. The black hole is surrounded by a large accretion disk. The planet orbits at a distance such that going any closer to the black hole will mean that your odds of getting out are slim; it's also composed of water. Finally, time dilation from the black hole means that even though the characters spend about two hours on the planet, a decade or so passes for their colleague on board.</p>
</blockquote>
<p>The basic answer is that a planet can orbit a black hole. There are stable circum-black-hole orbits, just as there are stable orbits around just about any celestial body. There's a problem: A black hole typically forms as a result of a supernova. This will eject most nearby planets out of the stellar system. Alternatively, it's unlikely that a planet could be captured by a black hole and be in a stable orbit, so the whole premise - while possible - is highly unlikely. Then again, it's improbable that a planet will be made out of water, a wormhole will open up near Jupiter, or Matthew McConaughey will star in a decent sci-fi movie, so why should anything else in the story be normal?</p>
<hr />
<p>However, you can't just put a planet anywhere near a black hole, give it a strong enough push, and hope it orbits. The innermost orbit is at the boundary of the <a href="https://en.wikipedia.org/wiki/Photon_sphere" rel="nofollow noreferrer">photon sphere</a>. On this sphere, only photons can orbit. Inside it, nothing can orbit. However, the only stable orbit is twice as far away, at <span class="math-container">$2r_p$</span>.</p>
<p>The radius of the sphere is
<span class="math-container">$$r_p=\frac{3GM}{c^2}$$</span></p>
<p>We'll assume that the object is not rotating (I don't remember exactly if it is or isn't rotating, but it's simpler in this demo to say it isn't.). The formula for <a href="https://en.wikipedia.org/wiki/Gravitational_time_dilation" rel="nofollow noreferrer">gravitational time dilation</a> is
<span class="math-container">$$t_0=t_f \sqrt{1-\frac{3r_0}{2r_f}}$$</span>
where
<span class="math-container">$$r_0=\frac{2GM}{c^2}$$</span>
Assuming that <span class="math-container">$t_0$</span> (the time for the observer inside the field) is two hours (7200 seconds) and <span class="math-container">$t_f$</span> is ten years (315360000 seconds),
<span class="math-container">$$\frac{t_0}{t_f}=\frac{1}{43800}=1-\frac{(3)2GM}{(2)r_fc^2}$$</span>
Simplifying, and saying that <span class="math-container">$\frac{2GM}{c^2}=\frac{2}{3}r_p$</span>,
<span class="math-container">$$\frac{r_p}{r_f}=\frac{43799}{43800}$$</span>
<span class="math-container">$$r_f \approx 1.0000228315715 r_p$$</span>
which is outside the photon sphere, but just barely. However, it's well inside <span class="math-container">$2r_p$</span>, and so most likely instable. The planet is, in short, not going to survive for long. And so giant waves - mini-spoiler - are the least of Matthew McConaughey's problems.</p>
<hr />
<p>Post-question-edit modifications:</p>
<p>It couldn't have been a <a href="https://en.wikipedia.org/wiki/Supermassive_black_hole" rel="nofollow noreferrer">supermassive black hole</a>; these form at the center of galaxies. It could have been a <a href="https://en.wikipedia.org/wiki/Stellar_black_hole" rel="nofollow noreferrer">stellar-mass black hole</a>, though an <a href="https://en.wikipedia.org/wiki/Intermediate-mass_black_hole" rel="nofollow noreferrer">intermediate-mass black hole</a> is also likely - if not likelier, if the massiveness is emphasized.</p>
<p>The existence of the neutron star is interesting. If the black hole were intermediate-mass, I would expect that it would have gobbled up the neutron star by now - and the planets, too. So I'd bet the black hole is a slightly-more-massive-than-average stellar-mass black hole. I highly doubt that multiple planets could orbit a black hole - for the reason I gave above; the supernova would have destroyed them or flung them out of the system.</p>
<p>Would any of the planets be habitable? I doubt it. The accretion disk could heat up enough to provide some light, but there probably wouldn't be a lot. I'll write up the calculations either later today or possibly tomorrow, as I'm a bit LaTeXed-out after writing a math-heavy answer on Worldbuilding to find the luminosity, but I suspect it'll be negligible - as will Hawking radiation, in case any smart-aleck was planning on bringing that up.</p>

CC BY-SA 3.0
2015-01-07T00:21:51.533Z
+1 for saving me the bother to watch the movie :) Also, wait... giant waves? As in, not stationary w.r.t. the surface tidal bulges but proper, moving waves? How tall did they stretch the poor Matthew McConaughey as the tides came?
TildalWave
CC BY-SA 3.0
2015-01-07T00:34:23.113Z
@TildalWave Yep, actual giant waves. You're going to have to watch the movie for that one - the mechanism was never explained. Mr. McConaughey made it out alive when he - ah, that's a spoiler. It seems he kept his normal height, though.
HDE 226868
CC BY-SA 3.0
2015-01-07T03:47:16.750Z
Thanks HDE! That answer is perfect. I appreciate the effort for the equations as well!
DrShakalu
CC BY-SA 3.0
2015-01-08T00:10:41.100Z
The black hole is almost certainly rotating, but for the nonrotating case, the innermost stable circular orbit is at $r = 6M$, not the $r = 3M$ photon sphere. The photon sphere is the innermost *possible* circular orbit, but it is always unstable.
Stan Liou
CC BY-SA 3.0
2015-01-08T01:15:21.327Z
@StanLiou I shall fix that; thank you. Are there any cases where an orbit just outside there *is* stable?
HDE 226868
CC BY-SA 3.0
2015-01-08T02:21:22.697Z
The calculations in this answer are done for a non-rotating black hole. For a rotating BH, there are stable orbits much closer to it. Kip Thorne has said that the BH in the movie is the rotating kind. So the orbit of the water planet can be stable.
Florin Andrei
CC BY-SA 3.0
2015-01-08T20:12:43.957Z
What Florin said--rotating black holes can have orbits much closer to the event horizon, see the equation for the "innermost stable circular orbit" on [this page](http://relativity.livingreviews.org/Articles/lrr-2013-1/articlese2.html). And Kip Thorne's book "The Science of Interstellar" indicates that the black hole *is* a supermassive one, with a mass of about 100 million Suns, and that it's supposed to be spinning by only 1 part in 100 trillion less than the rotation rate of an "extremal" rotating black hole (beyond that rate it becomes a naked singularity).
Hypnosifl
CC BY-SA 3.0
2015-01-08T20:14:58.733Z
If anyone's interested in the detailed calculations showing that the math makes sense for the planet to be in a stable orbit close enough to the event horizon to have such a large time dilation factor, see [this thread](http://www.physicsforums.com/threads/equation-for-time-dilation-of-body-in-orbit-around-kerr-black-hole.781691/), especially post #8 where I worked out the numbers given some equations that had been posted by stevebd1 in post #2.
Hypnosifl
CC BY-SA 3.0
2015-01-09T00:26:50.843Z
@Hypnosifl You've shown in the past that you're very knowledgeable about black holes. Do you want to write up an answer for this question?
HDE 226868
CC BY-SA 4.0
2023-09-07T17:15:31.917Z
@HDE226868, "I'll write up the calculations either later today or possibly tomorrow", c'mon, it's never too late. I'm still interested!
Rafael
CC BY-SA 4.0
2023-09-11T00:59:21.693Z
"It couldn't have been a supermassive black hole; these form at the center of galaxies." Actually, if I remember correctly, it absolutely was an SMBH, at the center of a distant galaxy.
Mark Foskey
CC BY-SA 4.0
2015-01-06T23:59:04.163Z
2020-10-14T16:02:54.007Z
2020-10-14T16:02:54.007Z
HDE 226868
<p>Recently, I got around to seeing the movie <em>Interstellar</em>. In it, the characters of the movie visit a stellar system that appears to be built around a black hole instead of a star. On top of this, their mission is to find a habitable planet in this system. Question: <strong>I was wondering how stable the system, as a whole, would be in terms of operation and would any of the planets be habitable at all due to the obvious differences between a star and a black hole.</strong></p>
<p>In the movie the black hole is supposed to be a 'supermassive rotating black hole'. As for being a binary star system, it's never stated as such nor depicted as such. It's depicted visually as the black hole alone being the center. However one of the characters does mention a &quot;Neutron Star&quot; as part of the system so it could possibly be a binary star system. The ambient lighting for the planets is generated by the accretion disk of the black hole. The size and rotation speed of the event horizon are not defined in the movie. At least not that I can remember.</p>
<p>As for the planets, their proximity varies, with the first planet depicted as being so close to the event horizon that it is effected by time dilation. The distances of the other two are not specified directly, but traveling to the second planet out seemingly takes days, while traveling to the third planet out is stated to take months, if I remember correctly. As for their surface gravity, the first planet is depicted as having higher surface gravity than Earth but not so much higher that movement is impossible, just strained. The second planet is depicted as being '80% Earth's gravity', if memory serves me correctly.</p>
<p>To better help define certain variables relevant to the question I found an info-graphic related to the movie that illustrates the size of the black hole and it's rotational speed: <a href="http://tinyurl.com/pqph8wl" rel="nofollow noreferrer">http://tinyurl.com/pqph8wl</a></p>

CC BY-SA 3.0
2015-01-06T23:13:46.433Z
@TildalWave Oof, no spoilers are going to be tough. The system - from what I got out of the movie - wasn't a binary system *per se*, in the same way that Cygnus X-1 is a binary system. The black hole was the only object that could be considered the primary, and I'm not sure if any other planets were mentioned.
HDE 226868
CC BY-SA 3.0
2015-01-06T23:34:31.500Z
@HDE226868 Then either the movie is terribly dark, or it simply doesn't make much sense? I mean, if it's not the former, then where does the light come from? Torchlights? I don't know much about the movie's plot but I got the impression (also from this question) that astronauts spend quite some time in that system? Or it's just some FTL jump to the place, _"Right, nothing to see here!"_ (pun ... optional), and they're off to another system?
TildalWave
CC BY-SA 3.0
2015-01-06T23:39:25.987Z
@TildalWave I got the impression that the black hole's accretion disk was apparently emitting so much light that the planet was illuminated. . . Not sure how plausible that was. For the last bit of your comment - they use a wormhole opening near Jupiter to travel to a variety of worlds. (*Cringe*). Matthew McConaughey also travels through dimensions, so aside from the stuff Kip Thorne was consulted on, there's some scientific inaccuracy - "artistic license". They end up spending - for outside observers - quite some years on the planet, though apparently the dilation makes it hours for them.
HDE 226868
CC BY-SA 3.0
2015-01-06T23:56:14.143Z
@HDE226868 I see! OK the accretion glow seems plausible but I'm not so sure about huge time dilation. Not one with the other at least, because accretion does imply a fast spinner, if for nothing else then due to angular momentum of the in-falling matter and you wouldn't be able to survive so close next to a fast spinning black hole at all, just the frame drag alone would cause all kinds of colorful effects on you. And black holes also tend to be rather messy _eaters_, if it eats matter, then lots of it is also all over the place, at near light speed relative velocities. I.e. not habitable LOL
TildalWave
CC BY-SA 3.0
2015-01-06T23:59:49.893Z
@TildalWave Yeah, I just did the time dilation calculations for a Schwarzschild black hole - screw rotation for now - and that planet is in trouble. Even without taking into account those effects. I suppose you could avoid the "messy eating" by having the planet orbit above the disk's plane, but that would be tough, and unlikely.
HDE 226868
CC BY-SA 3.0
2015-01-07T00:06:32.583Z
Hey guys, thanks for the comments and the response! Sorry to take so long getting back to this. Even though there's already more details and an answer I'll update my post with some info I found online about the black hole depicted in the movie. Thanks again!
DrShakalu
CC BY-SA 3.0
2015-01-07T00:11:41.090Z
@HDE226868 If you're not in-plane you'd still have to cross the plane, which might be worse than _cruising_ along with it. How was the tidal stress depicted in the movie? I mean, sounds like these astronauts would have to be terribly [spaghettified](https://en.wikipedia.org/wiki/Spaghettification) (yes, it's a proper scientific term LOL) by then. :D
TildalWave
CC BY-SA 3.0
2015-01-07T00:35:28.860Z
@TildalWave No spaghettification (I love using that term!), as far as I could see. The tidal effects appear to have been ignored.
HDE 226868
<orbit><black-hole><exoplanet><habitable-zone>
Ramifications of black hole stellar system
DrShakalu
# Ramifications of black hole stellar system

(Asked by: username_0 on 2015-01-06)

Recently, I got around to seeing the movie *Interstellar*. In it, the characters of the movie visit a stellar system that appears to be built around a black hole instead of a star. On top of this, their mission is to find a habitable planet in this system. Question: **I was wondering how stable the system, as a whole, would be in terms of operation and would any of the planets be habitable at all due to the obvious differences between a star and a black hole.**

In the movie the black hole is supposed to be a 'supermassive rotating black hole'. As for being a binary star system, it's never stated as such nor depicted as such. It's depicted visually as the black hole alone being the center. However one of the characters does mention a "Neutron Star" as part of the system so it could possibly be a binary star system. The ambient lighting for the planets is generated by the accretion disk of the black hole. The size and rotation speed of the event horizon are not defined in the movie. At least not that I can remember.

As for the planets, their proximity varies, with the first planet depicted as being so close to the event horizon that it is effected by time dilation. The distances of the other two are not specified directly, but traveling to the second planet out seemingly takes days, while traveling to the third planet out is stated to take months, if I remember correctly. As for their surface gravity, the first planet is depicted as having higher surface gravity than Earth but not so much higher that movement is impossible, just strained. The second planet is depicted as being '80% Earth's gravity', if memory serves me correctly.

To better help define certain variables relevant to the question I found an info-graphic related to the movie that illustrates the size of the black hole and it's rotational speed: <http://tinyurl.com/pqph8wl>

**Tags:** orbit, black-hole, exoplanet, habitable-zone
> **Comments:**
> **username_1**: @TildalWave Oof, no spoilers are going to be tough. The system - from what I got out of the movie - wasn't a binary system *per se*, in the same way that Cygnus X-1 is a binary system. The black hole was the only object that could be considered the primary, and I'm not sure if any other planets were mentioned.  
> **username_2**: @HDE226868 Then either the movie is terribly dark, or it simply doesn't make much sense? I mean, if it's not the former, then where does the light come from? Torchlights? I don't know much about the movie's plot but I got the impression (also from this question) that astronauts spend quite some time in that system? Or it's just some FTL jump to the place, _"Right, nothing to see here!"_ (pun ... optional), and they're off to another system?  
> **username_1**: @TildalWave I got the impression that the black hole's accretion disk was apparently emitting so much light that the planet was illuminated. . . Not sure how plausible that was. For the last bit of your comment - they use a wormhole opening near Jupiter to travel to a variety of worlds. (*Cringe*). Matthew McConaughey also travels through dimensions, so aside from the stuff Kip Thorne was consulted on, there's some scientific inaccuracy - "artistic license". They end up spending - for outside observers - quite some years on the planet, though apparently the dilation makes it hours for them.  
> **username_2**: @HDE226868 I see! OK the accretion glow seems plausible but I'm not so sure about huge time dilation. Not one with the other at least, because accretion does imply a fast spinner, if for nothing else then due to angular momentum of the in-falling matter and you wouldn't be able to survive so close next to a fast spinning black hole at all, just the frame drag alone would cause all kinds of colorful effects on you. And black holes also tend to be rather messy _eaters_, if it eats matter, then lots of it is also all over the place, at near light speed relative velocities. I.e. not habitable LOL  
> **username_1**: @TildalWave Yeah, I just did the time dilation calculations for a Schwarzschild black hole - screw rotation for now - and that planet is in trouble. Even without taking into account those effects. I suppose you could avoid the "messy eating" by having the planet orbit above the disk's plane, but that would be tough, and unlikely.  
> **username_0**: Hey guys, thanks for the comments and the response! Sorry to take so long getting back to this. Even though there's already more details and an answer I'll update my post with some info I found online about the black hole depicted in the movie. Thanks again!  
> **username_2**: @HDE226868 If you're not in-plane you'd still have to cross the plane, which might be worse than _cruising_ along with it. How was the tidal stress depicted in the movie? I mean, sounds like these astronauts would have to be terribly [spaghettified](https://en.wikipedia.org/wiki/Spaghettification) (yes, it's a proper scientific term LOL) by then. :D  
> **username_1**: @TildalWave No spaghettification (I love using that term!), as far as I could see. The tidal effects appear to have been ignored.  

---

## 2 answers

### Answer by username_1 on 2015-01-06. Score: 5 | Accepted answer

For those who haven't seen it:

> Some human explorers land on a planet orbiting a black hole. The black hole is surrounded by a large accretion disk. The planet orbits at a distance such that going any closer to the black hole will mean that your odds of getting out are slim; it's also composed of water. Finally, time dilation from the black hole means that even though the characters spend about two hours on the planet, a decade or so passes for their colleague on board.

The basic answer is that a planet can orbit a black hole. There are stable circum-black-hole orbits, just as there are stable orbits around just about any celestial body. There's a problem: A black hole typically forms as a result of a supernova. This will eject most nearby planets out of the stellar system. Alternatively, it's unlikely that a planet could be captured by a black hole and be in a stable orbit, so the whole premise - while possible - is highly unlikely. Then again, it's improbable that a planet will be made out of water, a wormhole will open up near Jupiter, or Matthew McConaughey will star in a decent sci-fi movie, so why should anything else in the story be normal?

---

However, you can't just put a planet anywhere near a black hole, give it a strong enough push, and hope it orbits. The innermost orbit is at the boundary of the [photon sphere](https://en.wikipedia.org/wiki/Photon_sphere). On this sphere, only photons can orbit. Inside it, nothing can orbit. However, the only stable orbit is twice as far away, at $2r\_p$.

The radius of the sphere is
$$r\_p=\frac{3GM}{c^2}$$

We'll assume that the object is not rotating (I don't remember exactly if it is or isn't rotating, but it's simpler in this demo to say it isn't.). The formula for [gravitational time dilation](https://en.wikipedia.org/wiki/Gravitational_time_dilation) is
$$t\_0=t\_f \sqrt{1-\frac{3r\_0}{2r\_f}}$$
where
$$r\_0=\frac{2GM}{c^2}$$
Assuming that $t\_0$ (the time for the observer inside the field) is two hours (7200 seconds) and $t\_f$ is ten years (315360000 seconds),
$$\frac{t\_0}{t\_f}=\frac{1}{43800}=1-\frac{(3)2GM}{(2)r\_fc^2}$$
Simplifying, and saying that $\frac{2GM}{c^2}=\frac{2}{3}r\_p$,
$$\frac{r\_p}{r\_f}=\frac{43799}{43800}$$
$$r\_f \approx 1.0000228315715 r\_p$$
which is outside the photon sphere, but just barely. However, it's well inside $2r\_p$, and so most likely instable. The planet is, in short, not going to survive for long. And so giant waves - mini-spoiler - are the least of Matthew McConaughey's problems.

---

Post-question-edit modifications:

It couldn't have been a [supermassive black hole](https://en.wikipedia.org/wiki/Supermassive_black_hole); these form at the center of galaxies. It could have been a [stellar-mass black hole](https://en.wikipedia.org/wiki/Stellar_black_hole), though an [intermediate-mass black hole](https://en.wikipedia.org/wiki/Intermediate-mass_black_hole) is also likely - if not likelier, if the massiveness is emphasized.

The existence of the neutron star is interesting. If the black hole were intermediate-mass, I would expect that it would have gobbled up the neutron star by now - and the planets, too. So I'd bet the black hole is a slightly-more-massive-than-average stellar-mass black hole. I highly doubt that multiple planets could orbit a black hole - for the reason I gave above; the supernova would have destroyed them or flung them out of the system.

Would any of the planets be habitable? I doubt it. The accretion disk could heat up enough to provide some light, but there probably wouldn't be a lot. I'll write up the calculations either later today or possibly tomorrow, as I'm a bit LaTeXed-out after writing a math-heavy answer on Worldbuilding to find the luminosity, but I suspect it'll be negligible - as will Hawking radiation, in case any smart-aleck was planning on bringing that up.

> **Comments:**
> **username_2**: +1 for saving me the bother to watch the movie :) Also, wait... giant waves? As in, not stationary w.r.t. the surface tidal bulges but proper, moving waves? How tall did they stretch the poor Matthew McConaughey as the tides came?  
> **username_1**: @TildalWave Yep, actual giant waves. You're going to have to watch the movie for that one - the mechanism was never explained. Mr. McConaughey made it out alive when he - ah, that's a spoiler. It seems he kept his normal height, though.  
> **username_0**: Thanks HDE! That answer is perfect. I appreciate the effort for the equations as well!  
> **username_4**: The black hole is almost certainly rotating, but for the nonrotating case, the innermost stable circular orbit is at $r = 6M$, not the $r = 3M$ photon sphere. The photon sphere is the innermost *possible* circular orbit, but it is always unstable.  
> **username_1**: @StanLiou I shall fix that; thank you. Are there any cases where an orbit just outside there *is* stable?  
> **username_5**: The calculations in this answer are done for a non-rotating black hole. For a rotating BH, there are stable orbits much closer to it. Kip Thorne has said that the BH in the movie is the rotating kind. So the orbit of the water planet can be stable.  
> **username_6**: What Florin said--rotating black holes can have orbits much closer to the event horizon, see the equation for the "innermost stable circular orbit" on [this page](http://relativity.livingreviews.org/Articles/lrr-2013-1/articlese2.html). And Kip Thorne's book "The Science of Interstellar" indicates that the black hole *is* a supermassive one, with a mass of about 100 million Suns, and that it's supposed to be spinning by only 1 part in 100 trillion less than the rotation rate of an "extremal" rotating black hole (beyond that rate it becomes a naked singularity).  
> **username_6**: If anyone's interested in the detailed calculations showing that the math makes sense for the planet to be in a stable orbit close enough to the event horizon to have such a large time dilation factor, see [this thread](http://www.physicsforums.com/threads/equation-for-time-dilation-of-body-in-orbit-around-kerr-black-hole.781691/), especially post #8 where I worked out the numbers given some equations that had been posted by stevebd1 in post #2.  
> **username_1**: @Hypnosifl You've shown in the past that you're very knowledgeable about black holes. Do you want to write up an answer for this question?  
> **username_7**: @HDE226868, "I'll write up the calculations either later today or possibly tomorrow", c'mon, it's never too late. I'm still interested!  
> **username_8**: "It couldn't have been a supermassive black hole; these form at the center of galaxies." Actually, if I remember correctly, it absolutely was an SMBH, at the center of a distant galaxy.  

---

### Answer by username_3 on 2015-08-12. Score: -1

If you are orbiting a 1-sun-mass black hole at 1 AU, gravity-wise it would be just like it is for us orbiting the sun. Gravity is gravity and mass is mass. The planets would have to have been captured after formation of the black hole or moved in from distant orbits. However, the accretion disk would be likely to be emitting lots of X-rays and not anywhere near enough visible light, so life on that planet would be pretty grim.


---

