The Science of Interstellar

The outer balance point, by contrast, is stable: If Miller’s planet is there and gets pushed outward, gravity wins the competition and pulls the planet back in. If the planet gets pushed inward, centrifugal forces win and push it back out. So this is where Miller’s planet lives, in my interpretation of Interstellar.[31]

The Slowing of Time, and Tidal Gravity

Among all stable, circular orbits around Gargantua, the orbit of Miller’s planet is the closest to the black hole. This means it’s the orbit with the maximum slowing of time. Seven years on Earth is one hour on Miller’s planet. Time flows sixty thousand times more slowly there than on Earth! This is what Christopher Nolan wanted for his movie.

But being so close to Gargantua, in my interpretation of the movie, Miller’s planet is subjected to enormous tidal gravity, so enormous that Gargantua’s tidal forces almost tear the planet apart (Chapter 6). Almost, but not quite. Instead, they simply deform the planet. Deform it greatly (Figure 17.3). It bulges strongly toward and away from Gargantua.

^{Fig. 17.3. Tidal deformation of Miller’s planet.}

If Miller’s planet were to rotate relative to Gargantua (if it didn’t keep the same face toward Gargantua at all times), then as seen by the planet, the tidal forces would rotate. First the planet would be crushed east-west and stretched north-south. Then, after a quarter rotation, the crush would be north-south and the stretch east-west. These crushes and stretches would be enormous compared to the strength of the planet’s mantle (its solid outer layers). The mantle would be pulverized, and then friction would heat it and melt it, making the whole planet red hot.

That’s not at all what Miller’s planet looks like! So the conclusion is clear: In my science interpretation, the planet must always keep the same face pointing toward Gargantua (Figure 17.4), or nearly so (as I discuss later).

^{Fig. 17.4. The orbital motion and spin of Miller’s planet relative to distant stars. The red spot on the planet’s surface and the tidal bulge always face Gargantua.}

The Whirl of Space

Einstein’s laws dictate that, as seen from afar, for example, from Mann’s planet, Miller’s planet travels around Gargantua’s billion-kilometer-circumference orbit once each 1.7 hours. This is roughly half the speed of light! Because of time’s slowing, the Ranger’s crew measure an orbital period sixty thousand times smaller than this: a tenth of a second. Ten trips around Gargantua per second. That’s really fast! Isn’t it far faster than light? No, because of the space whirl induced by Gargantua’s fast spin. Relative to the whirling space at the planet’s location, and using time as measured there, the planet is moving slower than light, and that’s what counts. That’s the sense in which the speed limit is enforced.

In my science interpretation of the movie, since the planet always keeps the same face pointed toward Gargantua (Figure 17.4), it must spin at the same rate as it orbits, ten revolutions per second. How can it possibly spin so fast? Won’t centrifugal forces tear it apart? No; and again the savior is the whirl of space. The planet would feel no disruptive centrifugal forces if it were spinning at precisely the same rate as space near it whirls, which it is almost doing! So centrifugal forces due to its rotation, in fact, are weak. If, instead, it were nonspinning relative to the distant stars, it would turn at ten revolutions per second relative to whirling space and so would be torn apart by centrifugal forces. It’s weird what relativity can do.

Giant Waves on Miller’s 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, from the orientation on the left of Figure 17.6, to that on the right, then back to the left, and so on.

This rocking is a natural thing, as you can see by looking at Gargantua’s tidal gravity.