# Interstellar relativity

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?

• 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: amazon.com/exec/obidos/ASIN/0393351378/ref=nosim/0sil8 Nov 13, 2014 at 8:11
• It was stated in the movie that the ship was far enough to not be affected by the gravitational time dilation Nov 13, 2014 at 15:22
• @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. Nov 17, 2014 at 4:46
• (continued) I also showed in that last post that while a planet in the innermost stable orbit at 1.000037636343*GM/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 1.5*GM/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). Nov 17, 2014 at 4:52
• @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. Nov 18, 2014 at 14:19

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.

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.

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.

• 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. Jan 22, 2015 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 Jan 22, 2015 at 23:29
• 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? Jan 22, 2015 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. Jan 23, 2015 at 1:16
• 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. Jan 23, 2015 at 4:36