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So for my story I want to have a binary planetary system, where both planets are about the size of earth and are habitable by human people. I'm also thinking that they will be tidally locked to each other, which means their day will be the same amount of time it takes for them to orbit around their common center of gravity, about half way between the planets.

So my question is, how fast could they be going without going too fast where they would lose their stable circular orbit. I'm just trying to figure out what would be a reasonable length of a day in this situation.

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  • $\begingroup$ If they are tidally locked, central part of the hemisphere facing the other planet will always vary between dusk/night/dawn/eclipse cycle. $\endgroup$ – Cem Kalyoncu Sep 30 '16 at 20:51
  • $\begingroup$ The closer they are together, the faster they orbit about one another, and the more stable their mutual orbit about their sun is. So The question isn't how fast can they orbit, but rather how slow. $\endgroup$ – Alex S Sep 30 '16 at 21:15
  • $\begingroup$ So it depends on how close together they are. If very close together they could go faster, but would have more of an eclipse as well, if farther apart, slower but less shadow from the eclipse. Too close together though and they'd not be able to remain spheres and fall apart, too far apart and their days would be too long to maintain habitable temperatures. $\endgroup$ – VioletRain Sep 30 '16 at 21:34
  • $\begingroup$ I think you don’t understand orbits. The speed is determined by how close they are: the maximum speed is when they touch. Plug mass and radius into Newton’s laws of gravity to get the actual speed. $\endgroup$ – JDługosz Oct 1 '16 at 10:40
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Depends on the mass of the planets and the speed of the orbit. The larger the companion body, the more their gravitational pull will affect how long the days last. Essentially, a day and a "month" would last the same length for equal-sized tidally locked bodies.
For more info, I'd recommend checking out this videoabout terrestrial moons; they briefly cover orbital mechanics, and it can also apply to co-orbital bodies.

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  • $\begingroup$ I'm intrigued by the thought that the mass would affect the length of a day. If the Earth were tidally locked to the moon, both of us would have a day that lasted 28 of our current days, so it seems as though mass doesn't have an effect. $\endgroup$ – BrettFromLA Sep 30 '16 at 22:16
  • $\begingroup$ I was meaning mass relative between the two bodies, actually. If one body is smaller than the other, that could change the rotational mechanics. Similar to how the moon is tidally locked to Earth, yet we aren't locked to the moon. $\endgroup$ – Atlas the Worldbuilder Sep 30 '16 at 22:25
  • $\begingroup$ Right. That makes sense. I guess my point is that if the 2 bodies ARE tidally locked, they'll have the same length of day. $\endgroup$ – BrettFromLA Sep 30 '16 at 22:29

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