Gravitational effects between planets like these (picture)

[cosmicalstorm]

These wallpapers seems to be extremly popular, but I cant really enjoy them because I suspect life on a planet like that would be far from peaceful, but then again my knowledge about physics is very limited.

Does anyone know, roughly speaking of course, what would happen if you had two Earth sized planets that either orbited each other or at least passed each other this close frequently in their orbits?
Would it even be possible to maintain for any longer period of time?

Pictures:

[Kodiak]

I had always thought that these pictures showed earth-like moons orbiting much larger planets.

[Ariphaos]

Well we don't know the angular dimensions of those pictures - the angular dimensions of a planetary body don't change much when you look at it from ten to twenty miles further back with a telescope, but the landscape certainly gets a lot smaller in comparison.

So it's certainly possible for the planets to each be outside of each others Roche limits, though the dynamics of the first picture are highly suspect unless the big planet there is some sort of ice supergiant. In the second case, the third planet there needs to be orbiting the foreground planets.

[cosmicalstorm]

As I suspected it might be impossible to make any exact judgement from those pictures alone, I was just a bit curious.

Lets put it this way; would it be possible for two Earth sized planets to orbit each other at the distance that the Earth and the moon currently orbit each other?

[Junghalli]

These wallpapers seems to be extremly popular, but I cant really enjoy them because I suspect life on a planet like that would be far from peaceful, but then again my knowledge about physics is very limited.

A double planet that close would probably cause mega-tides. Then again, it would likely also tidally lock the two planets to each other, so that wouldn't be a problem (though the long day/night cycle might). Although there may be increased geologic activity due to tidal heating of the interior, like you get with some of the moons of Jupiter. On the plus side, that might actually be a good thing with a small planet, say Mars sized.

[GrandMasterTerwynn]

These wallpapers seems to be extremly popular, but I cant really enjoy them because I suspect life on a planet like that would be far from peaceful, but then again my knowledge about physics is very limited.

Does anyone know, roughly speaking of course, what would happen if you had two Earth sized planets that either orbited each other or at least passed each other this close frequently in their orbits?
Would it even be possible to maintain for any longer period of time?

They would tide-lock as they orbit around the system's common barycenter. Which means only one side of each planet would be able to see the other world. I would also expect the side of the planets facing one another to be vast expanses of ocean, with the odd chain of volcanic islands here and there; as all the volcanism would tend to be concentrated on the facing sides of each planet, resulting in broad, flat lowlands like the Lunar maria. (Of course, this means that all the mountains and subduction zones will be on the other side, and the other side will probably be barren desert.)

However, over the long term, a system of two planets of roughly identical masses will tend to be unstable. Gravitational peturbations from the parent star, and any significant gas giants in the system, will tend to make the double-planet's orbits increasingly eccentric, until one of the bodies is ejected from the arrangement, (either to be kicked out of the system or absorbed into the primary star,) or they merge into a single planet.

[Ariphaos]

As I suspected it might be impossible to make any exact judgement from those pictures alone, I was just a bit curious.

Lets put it this way; would it be possible for two Earth sized planets to orbit each other at the distance that the Earth and the moon currently orbit each other?

The pure Roche limit for such a situation - same density and radius - gives a value of about 125% of the planetary radius between the centers.

The fluid body solution doesn't seem to give that much greater a value - about twice the above. This only appears to be a serious problem in the first picture.

[Sikon]

For the opening post images, two earth-like planets orbiting each other is not a guaranteed assumption. It could be a terraformed moon orbiting a planet (as studies determined that merely lunar gravity could hold onto an atmosphere beyond a certain thickness for thousands of years if such was created in the first place, a reason enough lunar bases could even accidentally ruin the original vacuum). Or the satellite could even be an artificial hollow sphere with weak gravity but a practically invisible transparent dome keeping in its atmosphere.

The Roche limit for when a satellite would be broken apart by tidal stress applies only if there is little more holding together the satellite than its own gravity. Such a situation is approximately so with a collection of rock hundreds or thousands of kilometers in diameter, yet not so approached if considering artificial constructions with far higher tensile strength while also being smaller. An extreme example is how it isn't even the slightest issue to artificial satellites today in low earth orbit well below the conventional Roche limit.

However, in general, regarding Roche limits and the size of the planet seen in the sky:

For an initial illustration, Jupiter's moon Io has an orbital radius 2.9 times the diameter of its primary body, so Jupiter would appear about 40 degrees wide in the sky seen from Io's surface. I haven't precisely checked, but the artist making this image says he made it approximately to scale with software, thus showing how large Jupiter would appear in the sky if seen from Io (click for larger image):


From here.

Even that is far from the closest possible, though. The Roche limit for the system would permit Io to orbit without breaking apart as close as around 1.8 times Jupiter's radius, if its orbital radius was just 0.9 times instead of its actual 2.9 times Jupiter's diameter. (The internal tidal heating driving its volcanic activity would increase, though).

Such could have made Jupiter appear from Io's surface multiple times larger still than in the above image, if the moon had been instead in a closer orbit yet still beyond the Roche limit.

Indeed, it could appear far bigger in the sky than such as this image of the opening post:



For a satellite orbiting a planet of the same density, if a body is held together practically only by its own gravity (a large and weak satellite body, so to speak), the Roche limit is around 2.45 times the radius of the primary, 1.2 times the diameter of the primary.

If they are of different densities, it is proportional to the preceding times (rho_p / rho_s)^(1/3), where rho_p is the planet's density (such as 1.3 g/cm^3 for Jupiter, 3.9 g/cm^3 for Mars, 5.5 g/cm^3 for Earth), and rho_s is the satellite's density (such as 1.9 g/cm^3 for Ganymede, 3.5 g/cm^3 for Io, 8 g/cm^3 for nickel-iron asteroids).

For example, if a satellite body had double the density of its primary, it could orbit tens of percent closer than it could otherwise without breaking apart.