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I understand that for an hour on planet X to be 7 years on Earth, the planet X has to be really really close (I guess close enough to be absorbed) that point aside.

My question is: they are putting the bigger spaceship parallel to the planet while going inside using the smaller spaceship to save some time, but if the mothership is travelling parallel to planet X, there should not be any difference in time... I believe the below things would change in the story,

  1. smaller effect, the guy in mothership would not be 23 years older than others.
  2. major effect, basically earth is dead (if they had depended on ship return), because the mothership is also under the similar influence of the black hole as planet X.

Are my assumptions correct?

Peter Mortensen
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mido
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  • It was my understanding that the Endurance was orbiting outside of the gravity well, rendering it effectively immune to the relativistic effects. – phantom42 Nov 12 '14 at 16:03
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    I suspect not- Kip Thorne, who's an actual physicist, was executive producer and seems to have made sure it's all correct. He's even written a book on it: http://www.amazon.com/exec/obidos/ASIN/0393351378/ref=nosim/0sil8 – PointlessSpike Nov 13 '14 at 08:11
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    It was stated in the movie that the ship was far enough to not be affected by the gravitational time dilation – Huangism Nov 13 '14 at 15:22
  • @PointlessSpike - there are also books about "the philosophy of the Simpsons". This doesn't imply that there's anything philosophically interesting about the Simpsons. I haven't read Thorne's justification for the relativity issue, but given the staggering number of science and engineering howlers that he let through, I suspect it's probably not that impressive. – Jon Kiparsky Nov 17 '14 at 00:12
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    @Jon Kiparsky - If you read the book you may find that a lot of the things you think of as "howlers" have good explanations. As for the time dilation around a rotating black hole, I asked for exact formulas on this thread at physicsforums and got them from another poster, and in post #8 showed the formulas correctly reproduce the numbers Kip Thorne gives. – Hypnosifl Nov 17 '14 at 04:46
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    (continued) I also showed in that last post that while a planet in the innermost stable orbit at 1.000037636343GM/c^2 would only experience 1 hour for every 7 years* experienced by faraway observers, if a ship was parked just a little further out at 1.5GM/c^2, the ship would experience 1 hour for every 5.25 hours* experienced by faraway observers, so the difference is much smaller (for the black hole in the movie, GM/c^2 = 492.7 light-seconds, about the same as the radius of the Earth's orbit at its innermost point). – Hypnosifl Nov 17 '14 at 04:52
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    @Jon Kiparsky - I was just reading some more of The Science of Interstellar and I see Kip Thorne mentioned in ch. 19 that the Endurance was supposed to be in a parking orbit where its orbital velocity was 1/3 the speed of light, which according to the formulas here would indicate it was orbiting at around 9.338 * GM/c^2, at which point it would experience 1 hour for every 1.2 hours experienced by faraway observers. So the numbers he gives do seem to check out. – Hypnosifl Nov 18 '14 at 14:19
  • @Hypnosifl Interesting - but doesn't that imply a "magic lander"? By that I mean one that can land on a massive planet, maneuver on that planet, escape that planet's gravity, and then match orbits with a ship at 1/3 c? I'm not much of a physicist, but that seems unlikely. And assuming that we have that lander, why then did we see a classic multi-stage-to-orbit launch from earth at the start of the trip? Surely they could have just used that lander to get to the Endurance in the first place, no? – Jon Kiparsky Nov 18 '14 at 17:04
  • @Jon Kiparsky - Yes, it's true that even before doing a gravitational slingshot they'd need to get off the planet, and that wouldn't be possible for a lander that small with present technology, assuming the planet's gravity was similar to Earth's. But maybe with some near-future advanced propulsion technology like a nuclear thermal rocket it could be possible, I'm not sure. The use of multi-stage rockets at the start could be because they didn't want to waste the lander's own fuel, or because they wanted to get to the wormhole fast. – Hypnosifl Nov 18 '14 at 17:14
  • @Hypnosifl iirc, the gravity was 1.3g - "punishing" was the word they used - so yeah, I think we're requiring a fair bit of magic sauce there. Also, do we have any explanation for the light that's shining down on the surface of this planet that's orbiting a black hole? – Jon Kiparsky Nov 18 '14 at 18:18

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Time is slower on Miller's Planet because of gravitational time dilation from the black hole Gargantua.

The time dilation effect declines rapidly as one's distance from the black hole increases. According to this article, Gargantua is meant to be a rotating supermassive black hole, so the mathematics of just how rapidly time dilation falls off is extremely complicated. The bottom line is, being somewhat further out from the black hole -- say, twice as far away from Gargantua as Miller's World -- could reduce time dilation to negligible levels.

As mentioned by PointlessSpike in comments, the theoretical physicist Kip Thorne was an executive producer on the movie, and his book on the subject will discuss this in more detail.

Royal Canadian Bandit
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The time dilation is governed by the relative potential of the gravitational field, not by the gravitational force. The former generically scales like $\frac{1}{r}$ while the latter scales like $\frac{1}{r^{2}}$, so the time dilation factor falls off a lot more slowly than any percieved gravity.

Also note that the real situation is a bit more complex than this, because it is possible to have a nonzero potential in a situation where the force is zero (in the inside of a planet, for example).

Also note, the effect isn't an "on or off" thing. The guy in the ship would age less than the 23 years people in Earth did, but more than the people who went down to the planet.

Zo the Relativist
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At the black hole horizon, light travels away from the black hole at speed = zero, relative to the center(singularity). if light moves ten times slower, then it would take 10 times longer to reach it's destination. so if you are in 10 times slower light, time goes very slowly for you, and very fast for people in the 10 times faster light, they will age faster.

The problem is that, lateral traveling light still travels sideways very fast even if it doesn't travel away from the black hole very fast.

That means that your body is turned into spaghetti, as explained by Steven Hawkins in his book, movement around the BH is 100000ds times faster than up down movement. Which makes entry of coherent matter into a black hole nonsensical.

In fact, the earth would be the size of a peanut if it was lodged on the edge of a black hole, as it would be so compressed by gravity, in terms of compression of matter by gravity. All the neutrons and the protons would be thoroughly disassembled and turned into a space plasma and it would be very hot and magnetically bizarre and fusioning, Chemical Elements would not exist near event horizon.

So, I suggest that being in a place where time is 7yrs of times faster than on earth, means that gravity would be so huge already, that the guy would be deformed by the gravitational disparity on the radial and angular axis.

Up to you to answer if you can enter a black hole, seeing as you would turn into cobwebs of spaghetti and compressed to the size of a grain of dust a few nanometers wide, and then reconstitute yourself again upon exit.

An interesting thing about singularities is that time is nearly infinitely slower there, as nothing can move anywhere fast there... and that 1000 big bang to cosmic-lights-out timescales could occur in 1 second of earth time at a high enough compression of mass. however there is no valid science yet to say if matter starts to resist compression beyond a certain size, although it is theorised both pro and against.

Ampfni France
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    This is incorrect, spaghettification is a consequence of tidal forces--if you're falling in feet first, then if the gravitational pull on your feet is much stronger than the gravitational pull on your heat, you'll be stretched into a long spaghetti-like mass. Tidal forces would be deadly at the horizon for a black hole with a mass comparable to that of a star, but for a much larger "supermassive" black hole you'd be OK at the horizon, see my answer here, especially the quote from Neil DeGrasse Tyson. – Hypnosifl Jan 22 '15 at 23:03
  • That's an informal/incorrect statement by Stephen Hawkins. The compression of matter near the event horizon of any black hole is so great that nothing can survive, if the atoms in your body are compressed into one Angstrom or so (the Schwartzchild Radius of a human) then you would achieve fusion of your chemical elements by that stage. black hole event horizon compression is far greater than steller compression of matter, you could survive it less than being on the sun's surface. Thanks for the Spaghetti information :P – Ampfni France Jan 22 '15 at 23:29
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    I've read many experts besides Hawking (not Hawkins) and Tyson say that the passage through the event horizon of a supermassive black hole would be quite survivable. Do you have any expert source of your own for the claim that there is a huge "compression of matter near the event horizon of any black hole", or is this an idea of your own invention? – Hypnosifl Jan 22 '15 at 23:38
  • Also, the whole idea of lateral velocity of light being high while radial velocity is small seems to assume that "velocity" has some absolute meaning, but in general relativity the velocity of anything can only be defined in terms of some spacetime coordinate system for assigning position and time coordinates to points on a particle's path. Around a black hole, in some coordinate systems the radial velocity of light goes to zero at the horizon, but in others like Kruskal-Szekeres coordinates light has a constant radial velocity. – Hypnosifl Jan 23 '15 at 01:16
  • Hi, The time disparity in the film implies that light is travelling at 1/220,000th the speed that it does in the rest of space time, so to escape the black hole's gravity again, the craft would have to travel at 119,999/220,000 of light speed. – Ampfni France Jan 23 '15 at 04:36
  • Hi, The time disparity in the film implies that light is travelling at 1/220,000th the speed that it does in the rest of space time, so to escape the black hole's gravity again, the craft would have to travel at 119,999/220,000 of light speed. (243567). Thanks for the great clarification, I understand. It's my assumption the matter is compressed and subject to massive forces that produce quasars at the boundary and fusion. I'll have to understand that. Also have to think of radiation levels near the radius. – Ampfni France Jan 23 '15 at 04:56
  • The orbit of the parent solar system around Gargantua would be very fast as well, if time is advancing at similar speed there than it does on the surface of a neutron star. 1/200k of our own time implies a similar sized body orbits at about 200 k times faster than in our solary system. I didnt think that matter would stay coherent at that kind of orbital frequency. – Ampfni France Jan 23 '15 at 05:07
  • I think you're jumping to conclusions a little about how the speed of light relates to time dilation--basically there are two ways of measuring time dilation, one is the rate a clock is ticking relative to the time coordinate of whatever coordinate system you're using, another is the rate that people far away from the black hole would see a clock ticking visually when light from different ticks reached them. The first will depend on what coordinate system you choose, while all coordinate systems will agree about the second type, even those like Kruskal-Szekeres with a constant light speed. – Hypnosifl Jan 23 '15 at 14:19
  • Also, there are coordinate systems like Eddington-Finkelstein coordinates where the speed of a light ray depends on its direction--in the "ingoing" version of these coordinates, light falling radially inward toward the horizon has a fixed coordinate speed, but light emitted very close to the horizon and traveling radially outward starts off traveling very slowly, only picking up speed as it gets further away from the horizon--see the second diagram here. – Hypnosifl Jan 23 '15 at 14:27
  • Finally, the reason quasars shine brightly is thought to have to do with the intense magnetic fields around them created by charged particles falling into the quasar--see the discussion of relativistic jets here. In The Science of Interstellar, physicist Kip Thorne discusses this in ch. 9, and he says he imagined the black hole in Interstellar was a very old one that hadn't swallowed any new stars for millions of years, so the magnetic field could have mostly "leaked away" and the jet died off, making it safe to get near. – Hypnosifl Jan 23 '15 at 14:35