How close to each other can Earth-mass planets plausibly form from the protoplanetary disk?

We occasionally get questions and answers that discuss how close to each other planets can be and still meet some criteria. For example, this answer to the question ''Habitable'' planet close to a star.

For the purposes of this question, I am not interested in answers discussing rogue planets which have been captured by the star. I am only interested in planets that form from a star's protoplanetary disk and remain gravitationally bound to that star.

I am also not interested in co-orbiting planets, such as anything at another planet's L4 or L5 point, or dual-planet pairs (not entirely unlike our Pluto and Charon). The planets I am talking about should each be in distinct orbits around the star, which differ in more than just phase.

Quite simply, given what we know about planetary formation and material density in a star's protoplanetary disk, what is the smallest difference in orbital radius where distinct, rocky planets similar in size to Earth can plausibly form?

I'm looking primarily for the formation of planets of similar total mass (let's say to within ±30% of Earth's mass), but bonus points if they can also plausibly have a similar composition (which, as also pointed out in a comment, I suspect is the easier part).

I realize that the answer will to some extent depend on the orbital radius of the planet that is forming, since there's more distance to cover around a circle and thus at least the potential for more material to go around the farther from the focal point you are. Therefore, let's limit this to final planets' orbits with radii of 0.5 to 1.5 AU from the central star. For simplicity, it is acceptable to assume that all orbits in the resulting system are perfectly circular, though if you want to do proper elliptical orbits, then go ahead.

The planets should ideally be able to hold together on their own over an astronomical timeframe. If you want to go down that rabbit hole, I suppose some such formed planets being ejected (or having their orbits changed to the point of, say, falling into the star) by perturbations from other planets could be acceptable, but it'd be a nice touch if the orbit is stable over the long term.

posted almost 5 years ago

Canina‭

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