At what distance would binary planets not be tidally locked?

[Hainted]

Working on a story idea that involves binary worlds. To keep the math simple I'm assuming the planets to be Earth sized, and mass, orbiting a star identical to the sun. I managed to find someone to help with the first equations and discovered that based on the time it takes them to orbit each other (48 days) they would be 702,904.853km apart, and based on their year (432 days) they are 167,323,260km or 1.1 AU from the sun. I also discovered that a full "moon" would be 8 times brighter than our moon.

My question is Would 702,904.853km be far enough apart for them to rotate, or would they be tidally locked? Is it even possible for them to rotate and still be orbiting a common barycenter, and if so what would the distance be?

FYI I don't need the equations( I'm 2 decades out of school) but I don't need it explained like a 5yo either. Just looking at plausibility of this.

 

[Nugatory]

Is it even possible for them to rotate and still be orbiting a common barycenter, and if so what would the distance be?

Yes, it is possible. What matters is not the distance but the age of the system; the tidal lock develops over time. So for story purposes, you can have it however you want .

 

[Hainted]

Thanks, I'm not doing Hard SF, but I want to avoid making a complete fool of myself scientifically.

 

[astrostuart]

Yes I would say it would be probable that the worlds would rotate, but still may be synchronized if the system is very old.
Your distance is nearly twice the Earth moon distance of 384,400 km, but an Earth mass is roughly a little more than 8 times a moon mass, and since tides are raised to the cube of the distance, the tides on each world would be nearly the same (slightly more) as the moon raises on the earth.

You could still have the worlds rotate at different rates, or even make one world a little smaller and say it is synchronous and the larger one is not. About the only thing to watch out for is that smaller worlds are more likely to be synchronized by larger worlds.

 

[Hainted]

Synchronized as in Same rotation period (I.E. 24 hour day) or synchronized as in one orbit(48 days) equals one day/night period?