Janus and Epimetheus are in small, comparable mass objects in very close orbit to Saturn, so they can develop resonances like this with relative ease as compared to planets at a distance from Earth’s orbit to the Sun. Long term this likely not a stable configuration but then Saturn is a highly dynamic system to begin with; it has over 270 satellites, a complex system of rings, and the planet itself has a mean density that is less than liquid water. It’s a weird and wild place.
The impact of the hypothetical Theia into the primordial Earth would have been a violent event for them to not just merge into a single body, instead producing Luna from ejecta at the edge of orbital stability about Earth’s sphere of influence, indicating that Theia must have been in an highly eccentric, overlapping orbit coming from the outer solar system 9or possibly even an extrasolar object although that is considered unlikely).
I don’t see how that could happen. In most cases, the two bodies and their overall rotation will all have angular momentum in the same direction. Energy dissipation from tidal forces will separate the two bodies, because if the angular momentum from the rotation is lost, it has to go into the orbit. And orbits gain angular momentum as they separate. Which is why the Moon is slowly moving away.
There are a few other ways for the angular momentum to dissipate, but they aren’t significant on a planetary scale. Gravitational waves are only significant at the neutron star/black hole level, and light pressure effects are only significant for small, irregular bodies.
It’s my understanding that the Moon is moving away now, but eventually would become tide locked and start spiraling in instead until it reached the Roche limit and breaks up. It’s just that it and Earth will be immolated by the Sun first as it dies, so it doesn’t matter.
That would have to be an exceptionally long-term process, again because there are few places for the angular momentum to go to. Gravitational waves would do it eventually, but the universe would end first, not just the Sun. Same for light pressure effects, dust, etc.
Two Earth-sized bodies would become tidally locked fairly quickly but I don’t know of any rapid process after that where they can shed the remaining angular momentum and spiral into each other.
Does angular momentum have to be lost, though? As the bodies get closer, they just co-rotate faster around the center of gravity thus maintaining the total angular momentum of the system.
As for total energy: the faster the co-rotation, the greater the kinetic energy. But at the same time the bodies are getting closer, so gravitational potential energy decreases.
Admittedly this is a somewhat tricky problem and I need to think about it some more…
No, the orbital velocity is determined by the masses and the distance between them. For one mass much larger than another (like an artificial satellite), the velocity is just v=\sqrt{\frac{GM}{r}}. And angular momentum is just rmv. Substituting v you get \sqrt{GMm^2r}. Which means that angular momentum scales proportionally to \sqrt{r}, holding everything else constant.
It gets a little more complicated with non-negligible masses, elliptical orbits, etc., but the basic principle is the same. And anyway, orbits tend to circularize over time for energy-related reasons.
So what does this lead to in the case of a double planet (a la Rocheworld or Summertide)?
Let’s set up a clear gedankenenexperiment. Two exact copies of the Earth in size and composition, co-rotating, stably in the short term, around a barycenter, with a separation of 3 Earth radii between their centers. No other gravitational influences.
I would think at that separation they would be tidally locked (though there might be a bit of libration)? At least let’s start with that assumption.
How does this system evolve over the long term?
PS: of course there are a lot of potential questions about how, or even whether, such a system could come about in the first place. But as I said: this is a gedankenenexperiment…
I’m about 90% certain they’d immediately merge into one planet. The tidal forces would be immense–a point on the near side of one body would experience 4x the force as one on the far side. So they’d immediately elongate, and that would be a self-reinforcing effect, until the two bodies touch, at which point all hell would break loose, so to speak. Their splatting together would send debris all over and I’m not sure how it would evolve, but most likely a bunch of stuff would fly off and the rest of it would behave chaotically until it settled down into a sphere.
I don’t know about Rocheworld but it looks like the position has been delicately arranged so that the planets touch gently. I’m not sure if this is stable, even if it’s actually in equilibrium (think of a pencil balancing on its point). My inclination is that it’s not stable; that some small perturbation would grow until again the whole thing breaks down and it mostly turns into a sphere. Maybe it’s possible that the small but non-zero strength of the crust could hold those perturbations in check; normally we ignore that (it’s part of the definition of the planet), but maybe in a case like this it could be an influence.
Overall, though, I don’t know. This isn’t a case where I can apply basic Newtonian physics and come up with an answer. If the other planet was 60x the radius away, as the Moon is, I think they’d just become tidally locked pretty quickly and then be stable.
That close together, they might tear each other apart, and at the very least would have extremely distorted shapes. If they did tear each other apart, then you’d have a chaotic spinning debris field, that would eject objects (and hence angular momentum) until the angular momentum of the remains were low enough to settle into a single rapidly-spinning world.
Even if farther away (the current Earth/Moon distance, which note is 32 Earth diameters), the issue is that larger mass of the companion will destabilize the axial tilts much quicker than the Moon will, causing all sorts of climate havoc when they do.
Well, there are lots of problems. Even if you make the planets out of scrith, the regions between the two planets get almost no sunlight. Having a third ice-cap on the side of your planet is going to make things weird.
Contact binary stars are a relatively commonplace type of star; these form curious elongated shapes where the stellar material more-or-less fills the Roche Lobe.
To demonstrate that planets can’t form into similar binary configurations, you’d need to show that there is something intrinsically different between close-orbiting planets and close-orbiting stars.
One significant difference is that there is a vastly higher range of densities in the stars compared to a planet. On Earth it’s about 4x. For a star, it’s thousands of times. So a contact binary is much more like two planets orbiting outside of their Roche limit, but where you’ve added enough atmosphere so that they merge. Interesting but not quite the same thing.
The proposal was two equal-sized planets only 3 radii apart (i.e., only one radius between the surfaces). The tiny angle from the ecliptic won’t make much difference. The Moon doesn’t eclipse on every pass because it’s small and far away.
For someone at the darkest spot, the other planet will take up 60 degrees of the sky (compared to 0.5 for the Moon). So ~4 hours of eclipse every day, assuming a 24 hour rotation. And those happen to be the prime daylight hours as well, basically 10 am to 2 pm. That’s a dramatic reduction in light.
Even if you imagine the co-rotating plane is 90 degrees to the ecliptic so each planet sees the other as being in a polar orbit about itself you still get eclipes & climatic issues.
That plane is aligned w the fixed stars. So as they both progress together around their solar orbit, sometimes one is sunward from the other and vice versa.
The real Earth may be a mess, but that place would be very unhealthy to the biosphere.
If they even held together at all over a timescale of mere centuries, much less millions of years.
