# Surface waves on Dr. Miller's planet

In the movie 'Interstellar', the crew land on a water world orbiting a black hole. The gravity is greater than that of Earth and there are huge surface waves present in the ocean that they land in. Waves are generated through wind forcing, which is proportional to the square of the wind speed, on Earth. There did not appear to be a wind of the magnitude required for such large waves on Miller's planet in the movie so how were these waves generated? The increased gravity would also require a greater wind force to overcome the downward force too right? Could the close proximity to a black hole somehow generate such large surface waves?

Here are Kip Thorne's comments in Ch. 17 of The Science of Interstellar (note that when he refers to Miller's planet being "locked" to Gargantua, this refers to tidal locking in which the planet rotates at rate that always keeps the same face to the black hole, which minimizes the tidal stresses on the planet):

What could possibly produce the two gigantic water waves, 1.2 kilometers high, that bear down on the Ranger as it rests on Miller's planet (Figure 17.5)? I searched for a while, did various calculations with the laws of physics, and found two possible answers for my science interpretation of the movie. Both answers require that the planet be not quite locked to Gargantua. Instead it must rock back and forth relative to Gargantua by a small amount [snip Thorne's explanation of how Gargantua's tidal gravity will naturally provide a sort of restoring force back to its preferred orientation, explaining why the planet would rock this way] ... The result is a simple rocking of the planet, back and forth, if the tilts are small enough that the planet's mantle isn't pulverized. When I computed the period of this rocking, how long it takes to swing from left to right and back again, I got a joyous answer. About an hour. The same as the observed time between giant waves, a time chosen by Chris without knowing my science interpretation.

The first explanation for the giant waves, in my science interpretation, is a sloshing of the planet's oceans as the planet rocks under the influence of Gargantua's tidal gravity.

A similar sloshing, called "tidal bores," happens on Earth, on nearly flat rivers that empty into the sea. When the ocean tide rises, a wall of water can go rushing up the river; usually a tiny wall, but occasionally respectably big. ... But the moon's tidal gravity that drives this tidal bore is tiny—really tiny—compared to Gargantua's huge tidal gravity!

My second explanation is tsunamis. As Miller's planet rocks, Gargantua's tidal forces may not pulverize its crust, but they do deform the crust first this way and then that, once an hour, and those deformations could easily produce gigantic earthquakes (or "millerquakes," I suppose we should call them). And those millerquakes could generate tsunamis on the planet's oceans, far larger than any tsunami ever seen on Earth

The first explanation might correspond to the explanation Neil DeGrasse Tyson gives in the quote from Kieran Hunt's answer, but I'm not sure (presumably tidal bores on Earth don't remain at a fixed orientation relative to the Sun while the Earth rotates under them, since that would require them to travel at over 1000 kilometers/hour at most latitudes, but then the Earth isn't nearly tidally locked to the Sun so it's possible that what Tyson describes would be a type of tidal bore as well).

The theories of tidal pull, planet's rotation etc are good and promising, and almost explain the phenomenon that causes the great tsunami waves on Miller's planet.

But here is another theory: Because of the time slippage.

A planet that near to a black hole, if there is time slippage occurring (7 years per hour), this cannot be uniform all over the planet. The time dilation has to be more on the side facing the black hole than the other.

So, what happens to the water that moves into the dilated time zone? If one person is waiting on the far side of planet while another journeys across the surface to near side and all the way back to first person on far side, the one who journeyed may feel he travelled for only a year, but to the person waiting on far side outside the time affected time zone, the wait could be around 18 months - six months of time lost assuming the time passing is 1.5 times faster on far side than near side.

Now, the water going into slower time zone... It moves at its own steady pace towards the near side, but on far side, it's gonna look like the water is moving into the near side too quickly but never coming back from the other side. It's like, getting stacked towards the near side of black hole. So the sea level on the near side will be higher than far side. This explains why water was so shallow on far side where the astronauts landed, because the bulk of water is always on the far side, both because of tidal pull of black hole and time dilation.

And what happens when the water on near side breaks free of the time dilation zone? Even smaller waves on the near side with small velocity are gonna become huge tsunamis when a torrent of water is released into the far side of the planet.

Now, this "torrent" or "packets of water" effect seems odd since the "pouring" of water back into faster time zone should be uniform.

This is where rotation of planet comes into effect. Sure, the planet is in tidal lock with black hole just like earth and moon.

This is proved (or rather suggested) by the fact that Miller's beacon was transmitting from only one side and Cooper and his team were so sure to keep the Space Station in wider orbit and send ranger down to planet and get back, as if the beacon is never gonna move into near side.

But just like earth and moon, where moon's near side keeps shifting back and forth a little, similar thing happens on Miller's planet.

Combine that, with the fact that its not an earth pulling moon but a giant black hole pulling a huge planet which makes the "swinging" more vigorous compared to that of moon, and to that, add the time dilation on two sides of planet and we get tsunamis generated every time the planet "shakes" with respect to the black hole and unleashes a huge wave into the far side. While the planet is not actually shaking (because that would cause "Millerquakes" which can explain tsunamis conveniently, yet there are so many other factors at play here), but instead of shaking, even small rotational anomalies causing the vector of gravitational pull to shift from side to side do cause sudden breaking free of large water amounts from near side into far side, and this happening all the time on both sides when such a shaking occurs, causes waves to form everywhere around a "vertical equator". This is why there were multi directional waves and swells on the planet.

I think this pretty much explains the waves.

Also, the time dilation of 1.5 times between surfaces is too much but that was done just to understand the theory. Even a time slippage of 1:1.05 will make big difference and cause a mile high waves.

I hope I'm not the only one who thought about that

• Except the "far side" has less GR time dilation but more SR time dilation. May 23 at 8:24

Neil deGrasse Tyson on the topic:

Initially, I thought, “OK, they have to throw in a wave… that looks gratuitous.” My second thought was, “Well, if it’s a tsunami, the wave actually needs water to be the wave, and they would see the water rush from around their ankles to feed this wave as it came by.” That’s how you know to run. In this, I would later figure out that both of those concerns were unfounded. The planet is deep in the gravitational well of a black hole, and the black hole would surely have very high tidal forces. Also, a “tidal wave” is misnamed—it’s actually a “bulge” of water fixed in space. The bulge is always oriented in the same configuration in space, so you on the solid planet rotate in and out of that bulge. You interpret it as a wave coming towards you and away from you, but what actually happens is you’re rotating from a high tide part of the water to a low tide part of the water. The fact that the waves came every hour or so meant that the planet rotates once ever two of those—because you have two high tides for every rotation. If I were to say that there was something unrealistic about that, it was how spiky the wave was. A tidal bulge would be smoother than that, and they would just rise up, float over the top, and rise back down the way a duck floats up and down as a wave goes under it. This is where they’re taking dramatic liberties to turn the wave into something more menacing, and I don’t have a problem with that.

Tl;dr - yes it's possible, but the waves wouldn't be nearly as steep.

I encourage you read Kip Thorne's The Science of Interstellar. Thorne, and his close Hollywood-producer friend were the instigators for creating the film at the very beginning. And it took over 10 years to materialize. Thorne became an executive producer, but also served as the consultant and science-policeman to see that matters were somewhat kept within the realm of feasible science. Miller's planet, and Gargantua, the black hole in which it orbits, is subject to high gravitational tidal forces. In his book Thorne offers all the assumptions and explanations regarding how the waves are driven by these tidal forces.

But in short, the surface waves on a planet are not all driven by wind traction. Most of the waves you are able to observe at sea or breaking on the shore are wind driven. Seismic events can cause abduction or subduction of the seafloor and create very high velocity, long wavelength soliton waves called Tsunamis (called tidal waves but not caused by gravitational tidal forces). But the slow period diurnal waves that take a full day to observe are driven by gravitational tidal forces (stretching and squeezing) from the moon. In the case of Interstellar these forces between Miller's planet and Gargantua are much larger than the forces generated between the Earth and its moon.