Books always say Saturn has such low density it could float in water. But a planet with an ocean big enough to put Saturn in would have so much gravity it would rip Saturn apart and the materials would merge into one planet. Saturn floating never makes any sense 😜
Ok, bigger problem here. The radius of curvature on this ocean suggests the planet is thousands of times bigger in diameter than Saturn. But even if it were just 3 times bigger diameter than Saturn it would erupt into nuclear fusion and become a star. Here’s why... 
3/ In the gravity of a planet, the heavy stuff sinks to the core. That’s why terrestrial planet cores are metal, and giant planet cores are rock & ice. (Sources: uh.edu/~jclarage/astr…, solarsystem.nasa.gov/resources/677/…)
4/ But in this ocean world where Saturn floats, the surface is liquid water, so everything below the ocean is at least as dense as water. Let’s assume the planet is as light as possible. So everything is as light as the surface. It’s water, all the way down. Density=1000 kg/m3.
5/ So if its radius is just 6 times bigger than Saturn’s (I mistakenly said 3 before), then its mass is 178,600,000,000,000,000,000,000,000,000 kg, which is 94 times the mass of Jupiter.
6/ A body that is only about 75 times the mass of Jupiter will have high enough temperature and pressure in its core to undergo sustained nuclear fusion. Usually a body that size will be made mostly of hydrogen. This body is all water. Will water allow fusion? Yes, because...
7/...at those conditions, the molecules are slamming into each other with such energy that oxygen atoms can’t hang onto their hydrogen. The water molecules in the core completely ionize. So it is a hot plasma of 2/3 hydrogen and 1/3 oxygen. The hydrogen atoms will undergo fusion.
8/ The energy released from fusion will work its way out from the core. The surface will reach temperatures in the range of 2000 K (only about 1/3 the temperature of the sun, but still pretty darned hot). The water will boil and turn to vapor. There cannot be an ocean that big 😢
9/ As Saturn falls down toward this boiled-away ocean, tidal forces will rip it apart. At the same time, the high flux of radiating energy from the star will boil Saturn into gas. The vaporized stream of matter that once was Saturn will merge into the atmosphere of the star.
10/ So the killjoy conclusion is that, not only can Saturn not float in a big ocean, but an ocean big enough to float Saturn like shown in the picture cannot even exist. I suppose there’s a third problem...
11/ If we pretend the ocean doesn’t erupt into nuclear fusion as a star, and we pretend somehow Saturn’s gravity holds it together despite the much larger tidal forces from the much larger gravity of the giant ocean planet, then how...HOW...do we get Saturn down into that ocean?
12/ Because the potential energy of Saturn above the ginormous ocean would be So Huge, that as Saturn fell down it would accelerate to tremendous speed, hitting the ocean at the planet’s escape velocity as a minimum. Let me calculate how fast that would be...
13/ I’m going back to the original picture. The radius of that ocean planet is maybe 1000 times bigger than Saturn. Assuming it is water all the way down, then (ignoring relativity for now) the impact velocity of Saturn on the ocean *would* be 1.38 million kilometers per second.
14/ But that’s non-physical since it is faster than light. Need to re-do with relativistic energy. Standby...
15/ As I suspected. If the picture is correct, and the radius of the ocean world is that large, then it would collapse into a black hole. A diameter of 1000 times the mass of Saturn, all water, would be more than 400,000 times the mass of the sun.
16/ But again, assuming it doesn’t turn into a star or collapse into a Black Hole, then how fast will Saturn fall into this ocean? And will it survive? Inquiring minds want to know!
Doing the relativistic calculation now. (It has been a long time since grad school. Patience 🙏)
Doing the relativistic calculation now. (It has been a long time since grad school. Patience 🙏)
17/ Again assuming I didn’t make an error, Saturn will “land” in this giant ocean at 14.4% the speed of light. That’s 43,200 kilometers per second.
Will Saturn survive? Well, there *will* be a splash, to put it mildly. A shockwave...
(Image:NASA/Don Davis)
Will Saturn survive? Well, there *will* be a splash, to put it mildly. A shockwave...
(Image:NASA/Don Davis)
18/ I’m no expert on relativistic impacts. I assume the physics is super exotic. Maybe an astrophysicist can weigh-in, here.
In the milder planetary collisions we see in a solar system, this is what a shockwave from impact does...
In the milder planetary collisions we see in a solar system, this is what a shockwave from impact does...
19/ The shockwave travels down into the target body but also up into the impactor. This is a compression wave. As this wave reaches the opposite side of the impactor, it reflects and changes from a compression wave to an “un-compression” wave that goes back down. What does it do?
20/ For a rocky impactor, like an asteroid, this “un-compaction” wave breaks every molecular bond in the rock, vaporizing the asteroid. I assume a relativistic impact of a gas giant is even more exotic, but I think we’re safe to assume Saturn will be completely obliterated.
21/ By the way, I said “un-compression” wave then “un-compaction” wave, but the real term is “rarefaction” wave. The shock wave rarefies the material as it passes through. Because rocky material behaves nonlinearly, it breaks every molecular bond turning the rock into gas.
22/ But that’s for a relatively slow impact of an asteroid on a planet like Earth, where the velocity is about 18 km per second. A comet impact on Earth will be 30 to 50 km per second. Saturn landing in that gigantic ocean is 43,200 km per second!!! So no, it won’t survive.
23/ Other than that (and the size of the waves, the rings not melting and missing some features, and the sunlight falling on Saturn and on the waves from opposite directions), the picture is 100% accurate. 😉
A cosmologist weighed in:
Another good point!
Good point! We should search the ocean bottom for planet cores in case any planets were floating in Earth's oceans any time in the past.
