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Imagine, if you will, an Earth-like planet orbiting a Sol-like star. Now imagine that, from somewhere outside the solar system, a rogue planet, rocky and of roughly the same size and mass of the first planet, enters the solar system on a trajectory that eventually takes it so close to the first planet that they end up touching one another. What happens?

I was thinking that if both planets are spinning on their axes, they're going to rub against each other and potentially cancel each others' spin. Would their gravitational pulls eventually merge them into a larger rocky planet? How long would that take? If the Earth-like planet was inhabited, what would the inhabitants experience (after the panic subsided)?

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i.imgur.com/8N2y1Nk.gifv – King-Ink Jan 28 at 23:32
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What happens? Go outside and look up. – 2012rcampion Jan 28 at 23:33
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everybody dies. – Oldcat Jan 29 at 0:24
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When you consider that according to classic science, the meteor that killed the dinosaurs was only 9 to 12 miles across (or maybe even just 2.5 to 3.7 miles across), you can easily reason that a mass the size of a planet would probably kill you if it even only came close, and at some close enough point everything would die really, really fast. – ErikE Jan 29 at 1:42
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"what would the inhabitants experience (after the panic subsided)?" - Smug satisfaction that their panic was justified, judging by the answers... – colmde Jan 29 at 13:24
up vote 37 down vote accepted

Your planet is screwed.

As was mentioned in comments, the Giant Impact Hypothesis details a very similar situation, as Earth collides with another body of similar size.

In a somewhat direct impact, the centers of both bodies will collide and fuse, while excess material will be thrown off in one or more tails. Eiland et al. (2013) presented interesting models with one and two tails:

Alternatively, if the planets collide at a more oblique angle, a disk may form:

These are simulations that result in material being ejected into orbit, thus forming a moon. In a direct impact, this may not happen. However, your scenario will most likely lead to a glancing blow and a disk. Note that in the first simulation only, each planet is spinning in the opposite direction as the other.

See also Stevenson (1987) for a thorough theoretical treatment, which also explains how collision timescales differ based on different impacter masses:

That said, things might be different here. The incoming planet may be moving much quicker than the other body was in the Giant Impact Hypothesis, meaning that both bodies could be completely destroyed.

More cool (colorful!) simulation images can be found in Canup (2003).

As I mentioned here, death may come because of high temperatures, which will heat even some of the deep layers of both planets. Life can't run and hide underground.

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Good answer, and good choice of visuals from the Eiland paper! I was going to sketch something along those lines for my answer, but I probably can't improve on that in a reasonable time frame. – type_outcast Jan 29 at 0:53
    
@type_outcast If you were going to sketch something, you have my deepest respect. I'm terrible at drawing; computer simulations make everything easier. – HDE 226868 Jan 29 at 0:55
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Especially when it's someone else's computer simulations. – HDE 226868 Jan 29 at 1:01
    
I'm at a loss for which answer between these two is the one to select as "the answer." I'm down to flipping a mental coin. – J.D. Ray Jan 29 at 17:39
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+1: Also worth noting for the non-physic community here, that this kind of interaction between planetary masses produces an incredible amount of residual energy in the form of heat. So everything not hundreds/thousands of miles deep would burn and melt. IE., there's no riding this out in some hardened bunker. – RBarryYoung Jan 29 at 22:14

Everyone Dies

I assume the planets are on a "gentle" (shallow) approach to one another, which seems to match your description of "eventually takes it so close [that] they end up touching". There will be panic as the planets draw nearer.

Everyone will die; it's just a question of when and how.

Tidal forces

As the planets approach, their mutual gravitational acceleration (doubled!) will pull them together and accelerate them to even higher relative speeds. The first problem is, the gravitational acceleration will not be uniform: the "near" pieces of the planets will feel a stronger pull than the "far" pieces, and this effect will be very pronounced.

It will cause great earthquakes and incredible ocean tides (and tsunamis), which will obliterate anything within a few hundred kilometers of a coastline. It will also destroy key infrastructure.

The atmospheres of both planets will be easily affected, causing weather patterns of a far greater magnitude than anything we know as both atmospheres will be pulled toward the center of mass of the two planets.

Roche Limit

If anyone is still alive after all of the above, this last bit should do them in.

Edit: Fixed math (and included steps!) Thanks to MadBender for the catch!

The Roche limit is the distance (radius) within which a celestial body (like a planet) can no longer hold itself together via its own gravity, and is then pulled apart by the gravitational tidal forces I introduced, above. The Roche limit (d) for rigid bodies1 $\, m$ and $M$ (your twin Earths), looks like this:

$$d = R_m \left( 2 \cdot \frac{\rho_M}{\rho_m} \right)^{1/3}$$

$\rho_M / \rho_m$ is the ratio of densities of both planets. Since they are identical, their density ratio will be 1/1, thus:

$$d = R_m \left( 2 \cdot \frac{1}{1} \right)^{1/3} \approx 1.26 R_m$$ $$d \approx 1.26 \times 6\,371\text{ km} \approx 8\,027\text{ km}$$

As the two planets come within the Roche limit, the effects from the previous section will have already had catastrophic results, and started to elongate the planets. The difference is, that near the Roche boundary, gravity won't be enough to hold the planets together.

The overall mass stays the same, but the planets are literally torn to pieces. The atmospheres and oceans more or less go without a fight (see previous section), but the solid pieces will come bit by bit, and the (now very chaotic) motions will result in more impacts, which will continually pulverize the pieces until there isn't much left but a ring of debris around the star, almost certainly with no survivors.

What actually kills the remaining inhabitants is somewhat a matter of chance, but could be:

  • Direct impact or secondary impact forces
  • Suffocation/decompression as the atmosphere is pulled towards the center of mass but your tiny planetoid carries on a different trajectory. Or, the atmosphere simply gets thinner as the mass of your planetoid is too weak to retain it at sufficient density to support human life.

Other effects

  • The magnetic fields of both planets will combine, quite likely in a way that would reduce the effectiveness of the magnetosphere, allowing cosmic rays to bombard the inhabitants, causing an increase in radiation sickness and cancers, however I don't think anyone will live long enough for that.

Notes

  1. Of course the Earth isn't completely rigid. However, all of the liquid and gases would already have been pulled and squeezed into the gnarliest surf anyone has ever seen.
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Good answer. Given the amount of damage that earthquakes cause to humans, and how much smaller those are than anything like any part of the planet being sucked into space, I think it's pretty safe to say that practically any inhabitant will be churned to death before the planets start ripping away the atmospheres and oceans. – Dronz Jan 29 at 0:29
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Yikes, the image of living on a world mid-breakup due to the Roche limit as you outlined is terrifying! – evilscary Jan 29 at 9:50
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According to the formula from wikipedia (the one for liquid bodies), Roche limit for two Earths is about 15500 km between their centers (not 6.38 mil km) and 3000 km between their surfaces. The planets will disintegrate in the very last moments before collision – MadBender Jan 29 at 10:18
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Aside from any calculation, it should be intuitive that the moon (363000km away at perigee) hasn't broken up (in fact there's loose regolith on the surface) and therefore isn't inside the Earth's Roche limit. – Steve Jessop Jan 29 at 11:18
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OK, I've fixed the Roche limit section. @corsiKa Good question, and a complex one at that. I'll give that some thought and if I can sum it up in less than a hundred words or so, I'll edit my answer. And RBarryYoung, indeed, I'd imagine physicists would have been trying to warn people about Bi-Global Warming for decades, without avail. – type_outcast Jan 30 at 3:25

Total destruction

With the Earth's current orbit, the planet will have a velocity at infinity of between $12.5km/s$ and $72 km/s$, depending on the direction of which it hits. (It has an even higher velocity if it comes from outside of the solar system). Is this enough energy to destroy both planets into small pieces?

Assuming the other planet is similar to the Earth too, we can use gravitational binding energy to answer that question. The combined energy required to totally destroy them is $4.5 · 10^{32}J$. The energy added from the slowest impact is $4.7 \cdot 10^{32}J$. So both planets will be turned into molten gravel.

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This will be an inelastic collision, so molten gravel, please ;-) – Steve Jessop Jan 29 at 11:13
    
@SteveJessop Ok, I amend that. – Hohmannfan Jan 29 at 11:54
    
There's no reason to cap it at 72km/s as this is a rogue, not a body from within the system. – Loren Pechtel Jan 29 at 23:41
    
@LorenPechtel Why not? That is Earth's orbital velocity plus the velocity of a planet going in the exact opposite direction at solar system escape velocity – Hohmannfan Jan 29 at 23:44
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@LorenPechtel "To score a head-on hit it must have a velocity of it's own or it would hit the sun instead." Wrong. If it has a Vinf of zero, orbit is parabolic. It's possible for a parabolic orbit to have a non-zero perihelion. – HopDavid Jan 30 at 1:34

Answer for less science savvy readers:

If both planets are the same weight and size, and almost touch each other, it should be intuitive that at the point where they touch there is zero gravity, since the pull towards either planet cancels out each other. If it's not yet intuitive: imagine you are near where the 2 planets touch and you fall down - how can you tell towards which of the 2 planets you would fall? You can't.

The circumference of the earth is about 40'000 kilometers, and it rotates about once every 24 hours. So at the equator the speed due to rotation is about 40'000/24=1'666 km/h, and the one thing holding the planet together was gravity. Imagine swinging a ball on a long string at 1666 km/h and letting go.

Rocks (a.k.a. continents) and everything else, like air and water, will fall off of each planet, and either fly into space or bombard the other planet. For comparison, in an extremely strong tornado, air moves at 600 km/h and flattens buildings, now we have air, water, and mountains, moving at 1666 km/h and more. Once anything impacts the other planet, it becomes part of the other planet's surface. From there it will fly off again, for the same reasons it flew off from the first planet. No matter where you are, you either get squished or you get to see space - and probably get squished once you collide with other space rocks.

Time to start colonizing mars, and hope the debris doesn't impact too hard there. Maybe it would be safer to colonize a moon of one of the gas giants instead, because they are further away.

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