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Earth and Venus and very close to each other in mass and would both orbit around a point in space positioned almost perfectly in between the two.

Assume that this system is 1 AU from the Sun and the distance between Earth and Venus is the same as the distance between the Earth and the Moon. Would this system be stable in the long-term?

Both planets would very likely be tidally locked to each other, but I'm not sure if that would have any impact on stability.

PSA: I only used Venus and Earth because they're very close to each other in mass. What I'm really curious about is if a double planet consisting of 2 components very similar in mass can be stable in the long-term.

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    $\begingroup$ FWIW, using 384399 km for the semi-major axis, and grav params of Venus & Earth from Horizons, the orbital period of the Venus-Earth binary system (ignoring the Sun) is 1760541.5 seconds = 20.37664 days = 20 d, 09 h 02 m 21.5 s. The distances from the barycentre are 211790.3 km & 172608.7 km. $\endgroup$
    – PM 2Ring
    Dec 21, 2021 at 0:01

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It's certainly possible such a system could be stable in the long term. Barring the consideration of what exactly we're talking about (in terms of planets and stars) what you're describing is referred to as a hierarchical system. Effectively you have two bodies orbiting quite close to each other (in your case, two planets of similar Earth-comparable masses). Then they're both orbiting a star far enough from it that, from the perspective of the Sun, the binary planet system can be considered a single object of the combined mass of the two planets.

There are certainly star systems that have this same configuration (one potential example is HR 6819). The only difference is that you're dramatically reducing the mass of two of the "stars" so that they're now planets.

I will say that the real question is how did such a system form in the first place. You'd need a mechanism that allows these two planets to become gravitationally bound without accreting into a single planet. It's not impossible, but statistically unlikely.

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