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I'm currently looking into writing a story or two set on twin worlds, which I came to find out in my research is apparently not a new idea (Double planets? Rocheworlds? Am I close?). But I want it to be as scientifically plausible as possible, so I'm here fact-checking. I guess my main question going forward is: is the description of my worlds, as they are, scientifically plausible, and if not, what should I change?

Specifically, these two worlds are very similar to our own Earth. To simplify things, let's say they have the exact same or relatively similar atmosphere and living conditions, so that humans and Earth-based life can live on it without much or noticeable acclimation. If you were to hop a ship from Earth and landed on one or the other, getting off the ship you would notice little to no difference than you would on Earth. Similarly, the short trip between each world shows little to no difference, although one has slightly more gravity than the other.

The only real difference between the two worlds themselves is that one is slightly smaller than the other, but by an almost negligible amount (a few thousand miles); the difference isn't as dramatic as, say, Earth and Mars orbiting each other, maybe Earth and Venus being the better comparison.
Let's also suppose that they are also far enough away from one another that they aren't dramatically effecting one another's gravity or tides, etc., but are still visible in one another's skies, prominent enough to be important to the culture of the other. I initially wanted them to be very prominent in one another's skies, but I suppose being as close as the moon is to our world would be too close: I'm curious as to how far away one would have to be and still be caught in the other's gravity (I suppose the smaller of the two would have to be the one caught in the bigger one's gravity? I plead ignorance on that one).

I'm in love with the idea that they broke off from one another in the same way the Earth and the moon supposedly did billions of years ago, in an impact event, and they slowly came to orbit one another (although this idea has recently been challenged, is my understanding). From what I've read, though, it might be more plausible that one formed naturally in the disk formation of that planet's solar system, and a rogue planet got caught in its gravitational pull. I like that idea less, but I'm not so proud I can't just get over it.

In my head, they have their own day and night cycles, just like Earth. They may not have identical hours in a day or days in a year, etc., but its similar. They same face of the planet is never quite facing the face of the other: it's not like the moon, which is locked to one side always facing us and the other always away. From what I've researched, though, it's probably more likely that the planets would be facing one another on one side constantly, and their day-night systems would be greatly affected by that. Again, not in love with that idea, but if it has to go, it has to go.

That's all I have for now. I would try to explain how they rotate one another better, but I can't: I'm terrible in that area, and I've forgotten a lot of the terms you use in describing this. Please let me know what your thoughts are.

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    $\begingroup$ What do you mean when you say the size difference is only "a few thousand miles"? The radius of the Earth is a little under 4000 miles. BTW, your twin planets orbit their common centre of mass (COM), and collectively orbit their star, so the length of a year for both planets is essentially the time it takes for the COM to complete an orbit. There will be a small variation if the year isn't a whole multiple of their "month" (the time they take to orbit the COM). $\endgroup$ – PM 2Ring Oct 12 '18 at 16:30
  • $\begingroup$ @PM2Ring Maybe I was being overly generous with "a few thousand miles." It's probably safer to assume that one planet is roughly Earth's size, and the smaller is roughly Venus' size. And seriously, thank you for that COM distinction/clarification, that was a huge help. $\endgroup$ – bsideswiped Oct 12 '18 at 16:36
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    $\begingroup$ I'm voting to close this question as off-topic because this question type is very common on Worldbuilding SE. Answers on Worldbuilding may also make alternative suggestions and be more useful to you in the context of writing a story. $\endgroup$ – StephenG Oct 12 '18 at 18:02
  • $\begingroup$ I think two Earths, 36000 km from eachother, both tidally locked to the other, could work. It would be stable. We would see the other Earth so big, like the Orion constellation, but we would have no way to visit them. The problem is that such constellations are produced extremely rarely by the known processes. $\endgroup$ – peterh Oct 13 '18 at 0:07
  • $\begingroup$ Look into Lagrange points. If two planets were co-orbital 60 degrees apart, their orbits would be stable, and each would see the other as a perpetual morning or evening star. It's hard to imagine a natural process ending in such a configuration though. $\endgroup$ – Mike G Oct 13 '18 at 19:00
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A couple thoughts:
Tidal lock depends on the age of the system, so you can have it or not as you wish, depending on how long they came to orbit each other -- which is to say, of course, orbiting a common epicenter very nearly halfway between the pair.
Depending on your whim, you might want the orbit plane to be in or 90 degrees out of the ecliptic, the latter leading to interesting effects on tumbling. I'd recommend staying in the ecliptic, which is more stable and allows each of the planets to rotate about an axis which allows night/day similar to Earth. Notice that there will be a dramatic bunch of total solar eclipses of decent length, on both planets in turn.

As to their spatial separation, take a look at Newton's Laws. Nearly any separation is allowed, though if they were very close they'd have suffered severe gravitational distortions (of shape) , messed up each others' atmospheres, and almost certainly have crashed together with horrific results.

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