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Can Two Earth-like planets exist next to each other and share atmosphere? How far apart can they be to do this?

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  • $\begingroup$ I think the gravitational force would cause them to collide $\endgroup$ – paparazzo Jan 3 '17 at 18:04
  • $\begingroup$ One question per question, please. $\endgroup$ – Mołot Jan 3 '17 at 18:32
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Not possible for Earth-like planet

The Roche Limit is the distance within which a satellite, held together by its own gravity, will be broken up by the differential gravitational pull of the planet it orbits.

The equation for it is $$d = 1.26R_{m}\left(\frac{M_M}{M_m}\right)^{1/3}$$ where $R_m$ is the radius of the satellite, $M_M$ is the mass of the planet, and $M_m$ is the mass of the satellite. (Note, this is the rigid body Roche Limit; you could use the fluid body approximation instead to get a factor of 2.46. The conclusions will be the same for either one.)

If your planet and satellite have the same radius and mass, the Roche limit is 1.26 times the radius of either. That means that the atmosphere of each of the two planets has to extend upwards by 13% of the radius of the planet in order for the atmospheres to merge.

For Earth, 13% of the radius is 828 km. The height of the atmosphere depends on what part you are measuring: Earth's a troposphere (the part with most clouds and weather) only extends up to about 20 km, stratosphere to 50 km and mesosphere to 85km. In any case, the International Space Station is at around 300-400km, so the atmosphere certainly stops well under 828 km.

So for the case of two Earths or Earth-like planets, the planets would cause each other to disintegrate under gravity before they shared atmospheres.

Possible for Titan - for a very short time

Titan's atmospheric layers are 40 km troposphere, 300 km stratosphere, and 500-600 km mesosphere. Titan's atmosphere is thicker and its gravity is lower allowing the atmosphere to extend up higher. 13% of Titan's radius is 334 km, so it is possible that two Titans could orbit each other while having their stratospheres merge.

However, that would not last long. The drag that the atmospheres would cause on each other would quickly cause the two objects to lose orbital kinetic energy, which would cause them to move towards each other as they orbited. And since these objects are only a Roche limit apart to start with, they don't have to lose much distance before they start tearing each other apart again.

So basically, even if you designed two planets with atmospheric thicknesses, masses, and radii to allow them to orbit each other outside the Roche limit while sharing atmospheres the act of sharing atmopsheres will cause enough drag to make the planets destroy each other.

So, in final conclusion, two planets cannot share atmospheres while you are planning to use real science.

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  • $\begingroup$ The touching atmosphere won't cause drag to the planet. Only low pressure parts of atmospheres will hit themself, that will cause maximally some local windy situations. Also, If planets will be same, the touching part will have near to zero gravity(equal g up and down), where nothing will be moving to cause any drag. The possible slow-down and catastrophy will be more significat from slap powers and solar wind etc. $\endgroup$ – Antoine Hejlík Jan 4 '17 at 12:39
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The Roche limit is the minimum distance some gravitationally bound object can orbit another one without being pulled apart by tidal forces.

For the Earth, and fluid satellites, the following approximate equation for the Roche limit is used:

$$d \approx 2.44 R \left ( \frac{\rho_m}{\rho_M}\right )^{1/3}$$

For two Earths, because the densities will be the same, this would be 2.44 times the Earth radius, or around 12.6 million metres. Next, one wants to calculate the distance at which there would be atmospheric sharing. One would have to find the radius at which there is an equipotential surface connecting one atmosphere with another.

But I am going to ignore that. This is because any atmospheric sharing is going to generate large amounts of friction which would sap orbital velocity. This would reduce the energy in the orbit and then lead to an in-spiral which then leads to the two planets colliding and destroying themselves.

If you want a binary planet system, however, they have to be at least 12.6 million metres apart. However, if you want a stable system, further is better, as there would be less chance of anything going wrong and causing an in-spiral.

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    $\begingroup$ If two same planets touch athmospheres, they do it around the central gravitational point, so it will be in nearly zero g. There will be no friction, gasses won't move against each other. They will be at dead point. $\endgroup$ – Antoine Hejlík Jan 4 '17 at 12:44
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Sure they can share an atmosphere....for all of about a few bright, painful seconds as they're colliding and turning into a cloud of dust and rocks.

But to have them close enough together that their atmospheres overlap and not crash together, you'd have to have them spinning around an extremely dense center point so quickly that the rotational force would tear them apart, and then unfortunately you're right back to your cloud of dust and rocks.

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