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Q&A

Tidal locking timescale assumption

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Is it safe to assume that any two binary planets of 0.5 to 1.5 Earth masses having mass ratios of 1:1 up to 2:1 would always have become tidally locked to one another long before any life could naturally arise on either or both of them?

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This post was sourced from https://worldbuilding.stackexchange.com/q/42692. It is licensed under CC BY-SA 3.0.

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As Wikipedia notes, $$t_{\text{lock}} \approx \frac{\omega a^6IQ}{3Gm_p^2k_2R^5}$$ where $a$ is the semi-major axis, $m_p$ is the mass of the primary, $\omega$ is the initial angular speed, and the other variables describe the secondary planet.

Clearly, these properties will vary based on the different initial setups. Even a change in $a$ by a mere factor of 2 will increase the timescale by a factor of 64.

This does lead us to the interesting question of whether or not there are "preferred" semi-major axes - that is, whether or not Earth-like binaries are more likely to have semi-major axes within some range. I would wager there are, stemming from the formation of the planets, but I don't have any hard facts on that yet. All of the other factors, though, should be easy to determine because we can figure them out by knowing the properties of terrestrial planets.

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