Twin Planet Scenario

[Mouse]

Ok. I've been toying with this for about 5 years now, and I still don't know if the situation is feasible.

I'd like to know what you think.

Ethran and Errispa are twin worlds. Ethran is fractionally smaller than Errispa, and is tidally locked on Errispa (Errispa is not tidally locked to anything). Both worlds orbit their star(s) as one planet, but spinning around each other on an axis that is somewhere in the space between them.

Here is a purely arty view of the way I imagine Ethran would look from somewhere in space near Errispa's horizon:

MAP OF ETHRAN (low res).JPG

And here are the questions I simply can't answer, because I'm not an astrophysicist. I'm not even a mathematician. But I do need to know how ridiculous this setup really is before I finish the first book

1. How close would 2 approximately Earth sized planets be able to orbit one another without eventually colliding or throwing one or both of them out of orbit? (I'm looking for as close as possible here)
   
   
2. Would the heat generated by the gravitational egg-shape distortion of the tidally locked Ethran be sufficient to prevent the deep freeze you would normally expect in the permanent eclipse zone? (I have assumed in the image above that there would be a vast amount of volcanic activity there, and that the surface and atmosphere would be warm enough for water and life, but I really don't know if this is possible)
   
   
3. Would Ethran's atmosphere bulge and the pressure be relatively high on the face locked to Errispa, and would it be drawn away by the slightly larger Errispa very slowly over time? (not necessarily to Errispa, but just torn away and wasted into space as a result of the proximity of the two worlds)
   
   
4. If the answer to the above double question is 'yes' and 'yes', would the dwindling atmosphere and lower atmospheric pressure over the rest of Ethran cause an 'ice world' catastrophe to occur, such that all but the tidally locked face of Ethran became frozen solid and uninhabitable? (as is shown above by the encircling wall of ice that traps the Iris Ocean)
   
   
5. Finally - as Ethran's core cools and the planet's mass solidifies and becomes less and less plastic in nature, would Ethran be torn apart, and the remaining fragments fly off into space (being much less in mass but still orbiting Errispa at the same speed as before)?

Thank you - to anyone who has enough free time to bend their mind around this for me

[kacey]

I don't know anything about astrophysics so I can't help you there but this map looks really neat!

[Mouse]

Thank you Kacey

Its the first Finished Map I ever uploaded, but I think it was before your time here

I wasn't confident enough to ask these questions and be prepared for a good scoffing back then, but I am now

[Azélor]

How close would 2 approximately Earth sized planets be able to orbit one another without eventually colliding or throwing one or both of them out of orbit? (I'm looking for as close as possible here)

Any object that is orbiting closer than the roche limit of the planet will be crushed by the gravitational pull.
That's how Saturn got the rings. One planet got too close and started to disintegrate.
https://en.wikipedia.org/wiki/Roche_limit
The limit changes depending on the material. Since water is "softer" than rock for example, it will get pull away sooner.


I take Venus orbiting around Earth as an example using Universe sandbox. It is a physic simulator, not perfect by it gives a good idea.
The combined distance of their respective roche limits is about 23 000 km (I think I messed this part cause in my second test it was around 60 000km). And at that distance, Earth's gravity is too strong for Venus to keep a stable orbit.
It crashes after a few days only. Like when you fail in Zelda majora's mask (if you played it). The crash was to be expected since the distance was more than 10 times smaller than the Earth-Moon distance.

At about 70 000 km, it look stable. I'm a little skeptical about the numbers here, it might need to be fuhrer away to prevent Venus form losing her atmosphere
I don't know if Earth can avoid being tidal locked, the pull of Venus is extremely strong at that distance. The tidal pull exerted on each planet is considerable.
Venus has an elliptical orbit and speed is not constant because of the pull from Earth.

It take 1.5 days for Venus to make 1 revolution around Earth.

Would the heat generated by the gravitational egg-shape distortion of the tidally locked Ethran be sufficient to prevent the deep freeze you would normally expect in the permanent eclipse zone? (I have assumed in the image above that there would be a vast amount of volcanic activity there, and that the surface and atmosphere would be warm enough for water and life, but I really don't know if this is possible)

Probably not. Europa is the closest example of this. Despite the gravitational pull, it is buried under a thick layer of ice.

Would Ethran's atmosphere bulge and the pressure be relatively high on the face locked to Errispa, and would it be drawn away by the slightly larger Errispa very slowly over time? (not necessarily to Errispa, but just torn away and wasted into space as a result of the proximity of the two worlds)

At 70 000 km that seems likely to happen but I don't have the specific numbers.

If the answer to the above double question is 'yes' and 'yes', would the dwindling atmosphere and lower atmospheric pressure over the rest of Ethran cause an 'ice world' catastrophe to occur, such that all but the tidally locked face of Ethran became frozen solid and uninhabitable? (as is shown above by the encircling wall of ice that traps the Iris Ocean)

Lighter gases all get suck up, Helium and Hydrogen first because they are lighter. Heavier gasses remain closer to the surface at a lower density. The atmosphere could resemble the one on Mars regarding the atmospheric pressure. You would have a considerable variation of temperature between night and day. Parts that are always in the dark becomes much colder than Antarctica or Siberia coldest temperatures. It's hard to tell exactly because there are too many fuzzy details but as a reference, the lower temperature on Mars are at about -140 Celsius while they are at -280 on Mercury. The absulute zero is -283, if I remember correctly and it is impossible to go lower since there is no energy left.

Finally - as Ethran's core cools and the planet's mass solidifies and becomes less and less plastic in nature, would Ethran be torn apart, and the remaining fragments fly off into space (being much less in mass but still orbiting Errispa at the same speed as before)?

I'm not sure I understand. I don't think the cooling of the core will have a big impact. I'd be more worried about a weakened magnetic field and increase of radiations received from the star at that point. It takes so long for the core to cool that the star might die before all of this gets too serious. Going into the supergiant mode. Eradicating all forms of life, likely bumping the planets out of orbit or simply destroying them in the process.

[Mouse]

Wow! thank you so very much for your thoughts, Azelor

I was hoping you might say something, and this has given me a lot of information to think over.

Thank you!

[waldronate]

I'm very confused by what the map is showing. It looks like the sort of bullseye that is described for a planet that is tidally-locked to its sun. If you have something like the Earth-moon system, with one partner locked to the other and both going around the star, you'd see Errispa would see phases of Ethran, but Ethran would have the normal complement of climates expected of any world, not a bullseye. The bullseye forms on a world when the world is tidally locked to the sun; being tidally-locked to another body is irrelevant.

According to Wackypedia, the Roche limit calculation for fluid bodies (planets are basically fluid over long time scales) is 2.44*planetRadius*(planetMass/satelliteMass)^(1/3). Since your planets are approximately the same size, this pretty much reduces to 2.5 times your planetary radius. Note that this is the distance where things are actively breaking apart and that the bodies will be very distorted at that point. To reduce distortion and improve stability, you should probably go at least 10 times that amount. There would be lots of crust stress (meaning lots of earthquakes and volcanoes), especially if the orbits are more than just slightly elliptical. For a 6 300km radius on bodies of similar mass, the destruction distance is about 2.5*6 300=15 750 km. Ten times that would be 157 500km (half the Earth-Moon distance). The Earth is about 6 300/1 700=3.7 times larger than the Moon, and the 150 000km distance is 150 000/385 000=.39, so simple, not-correct math would indicate that Ethran would appear 4/.39=10.25 times larger in the sky than the Moon does from Earth.

[Mouse]

LOL! Oh my! All those figures

You are another from the small group of people who seem to know astronomical stuff that I was rather hoping would comment, Waldronate - and thank you so much

I completely get your point about the bullseye thing, so I had better say right now that at least some of it is down to God-like Tech present on the surface in that area (it has to be if Azelor is right about the ice world scenario - like Europa), and the reason this powerful entity has taken up just there is because the atmosphere is more dense than anywhere else on the planet (I think that bit is still true after considering Azelor's input).

As for the numbers - the story depends rather heavily on the planets being as close as possible, yet in a stable orbit. While some crust stress would be part of the story, I think I will need at least a certain amount of stability.

So, Earth radius being 3,959 miles (call it 4,000 for numbskulls like me), and both planets being around that size, the bare minimum distance on the brink of mutual annihilation is 2.5 x 4,000 = 10,000 miles. Have I got that right?

10 x that distance is about 100,000 miles, which actually compares with Azelor's estimation of 70,000 miles quite well.

Its not as close as I wanted them to be for the sake of the story, but I can adapt it

Thank you so much for all your help

EDIT: oops - just noticed that Azelor's figures were in kilometres, not miles, but I still think that between you, you have answered the question as to how close they could be.

[Diamond]

I'm so glad we have some math-heads here who enjoy this kind of thing and are willing to help the rest of us. Calculations of this magnitude feel like they'll make my eyes explode.

[Mouse]

LOL! D - some of that stuff I read last night when I was looking at your tidally locked problem turned my brain to mush!

[Azélor]

the atmosphere is more dense than anywhere else on the planet

If the place is really cold, the air pressure is higher and so is the density. The reasoning is sound to me.
But it also makes the atmosphere inner. On Earth, the troposphere (the layer of the atmosphere where we live) is twice as thick at the equator than it is at the poles.
If Mt Everest was located at either poles, people would not be able to survive the ascension without much more advanced equipment.