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Some time ago I asked a question about gravity on a hemispherical planet.

What would gravity be like on a hemispherical planet?

Would the water all boil away at first, quickly cooling the core of the planet? Would the ocean boil for centuries?

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DampeS8N
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    I think questions about hypothetical game situations probably aren't covered here. The moderators will most likely close this unless you can pose your question for a real physical situation. – Mark Rovetta Mar 13 '14 at 19:46
  • @MarkRovetta the fact that the information is for a game is irrelevant to the question. The situation, while itself being impossible, is also not relevant to the question. This boils down to water on the open core of the Earth. – DampeS8N Mar 13 '14 at 20:29
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    This question appears to be off-topic because it is about an unrealistic hypothetical situation. The Earth is nearly spherical due to physics and this question is asking about what physics tells us while ignoring the physics that made the planet nearly spherical in the first place. – Brandon Enright Mar 13 '14 at 20:35
  • I feel like this is a valid question. Sure, its hypothetical but it definitely uses real physics concepts and the answer might be able to be extrapolated to other (similar) situations. – dfg Mar 13 '14 at 20:55
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    @dfg If you want to go with that interpretation then the question is woefully underspecified as can be seen by the multiple interpretation offered as prospective answers flail around in search of what DampeS8n meant. But planetologists usually define a planet as having a number of properties including "self-gravitational roundness". – dmckee --- ex-moderator kitten Mar 13 '14 at 21:42

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It's impossible to discuss what would happen to the oceans because the planet itself wouldn't be able to exist in this scenario. Planets are round for a reason: any other shape is unstable for objects of their size and mass due to their self-gravity. Unless was it was a very small borderline planet you're cutting in half, it would break up pretty cataclysmically. Given enough time and no major interference from other nearby bodies, the planet would eventually reform into a new spherical planet with half the original volume.

  • Yes, I realize this. Consider this a thought experiment. In the game, magic holds the planet in the hemisphere shape. – DampeS8N Mar 13 '14 at 02:11
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    @DampeS8N, once you invoke "magic" all bets are off. Observe how it works: (1) I say "that's impossible because of such and such", (2) you say "but forget all that because magic does so and so, and (3) I say "WTF???" In other words, the question is by what laws does your magic "work"? If you can spell those out, it's not magic. If you can't, then your guess is as good as anyone else's which is to say, not good at all. – Alfred Centauri Mar 13 '14 at 02:17
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    @DampeS8N, you seem to have a common misunderstanding about what a "thought experiment" is. It doesn't mean you can just make up whatever rules you want. How can you expect a sensible answer if you do that? That's science fiction, not science. You cannot ask us to pretend the single most important force in planetary dynamics is "magically" altered and then ask what physics predicts. It's saying, "If physics as we know it were wrong, what does physics say would happen?" –  Mar 13 '14 at 02:22
  • @AlfredCentauri and dgh. Calm down guys. I'm asking about the core of a planet and an ocean. No magic there. I managed to get a good answer on the first question because someone accepted the premise. Don't worry about the shape of the planet. I'm interested in a water soaked open planetary core. – DampeS8N Mar 13 '14 at 03:02
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Well, this seems pretty easy to treat as a Fermi problem.

The heat capacity of magma (and rock in general, I suppose) is about $2\;\mathrm{kJ}/(\mathrm{kg}\cdot \mathrm{K})$.

The heat capacity of water is about $4\;\mathrm{kJ}/(\mathrm{kg}\cdot \mathrm{K})$, and it's latent heat of vaporization is about $2000\;\mathrm{kJ}/\mathrm{kg}$.

The total volume of the oceans is about $10^9\;\mathrm{km}^3$, so the total mass of water is about $10^{21}\;\mathrm{kg}$.

The total mass of magma/rock is, to a very good approximation, just the mass of the Earth, about $6\times10^{24}\;\mathrm{kg}$.

Assuming the oceans are at about $0^\circ\mathrm{C}$ (close enough), to boil them away would require:

$$\left(4\;\mathrm{kJ}/(\mathrm{kg}\cdot \mathrm{K}) \times 100\;\mathrm{K} + 2000\;\mathrm{kJ}/\mathrm{kg}\right)\times 10^{21}\;\mathrm{kg} = 2.4\times10^{24}\;\mathrm{kJ}$$

This would reduce the temperature of the magma by about:

$$\frac{2.4\times10^{24}\;\mathrm{kJ}}{2\;\mathrm{kJ}/(\mathrm{kg}\cdot \mathrm{K})\times 6\times10^{24}\;\mathrm{kg}} = \mathbf{0.2\;\mathrm{K}}$$

I'm assuming here that heat is rapidly conducted through the magma (relative to the rate of heat transfer to the ocean water). This seems more or less reasonable, and depends pretty sensitively on how water is flowing into the gap. The point is that there is plenty enough energy in the mantle to boil off the oceans.

How long it would take to boil away the oceans would depend how fast they're flowing into the gap between the hemispheres. It's also likely that the huge amounts of water vapour released into the atmosphere would wreak all kinds of havoc on the weather, and a lot of it would fall again as rain. The process of cooling the "flat" surfaces of your split planet would more or less reduce to the initial cooling of the surface of the Earth, and I guess proceed on similar timescales (though there is now significantly less heating in the mantle from the decay of radioactive isotopes, I think). What matters is how fast the vast amounts of energy stored thermally in the mantle can be transported away. You need the atmosphere to efficiently convect superheated air/steam out of the gap, and then efficiently dissipate the heat out into space (this probably works ok-ish, radiatively). It will still take a long time (geological timescales) to cool the flat sides of your hemispheres. A lot of estimation starts to break down now, because you need to know about things like pressure in the hemispheres, and because the hemispheres are not a stable structure, trying to treat them with physics breaks down at some point.

Kyle Oman
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  • The question and your answer both assume that the mantle and core would be similar to how they are now. The center of gravity of the Earth would shift, moving a large amount of pressure away from the former mantle and core to some new location. The question simply isn't answerable without tons of assumptions. – Brandon Enright Mar 14 '14 at 01:39
  • @Brandon Enright I went for the only part of the problem that seemed tractable - "could this boil the oceans". I think my last sentence sums up the rest. – Kyle Oman Mar 14 '14 at 06:23