Distance and orbital period for terrestrial binary planets This article, http://phys.org/news/2014-12-binary-terrestrial-planets.html, suggests binary planets could orbit each other at a distance of only three planet radii. For two earth-like planets, that is approximately 12,000 miles. Does this distance seem accurate? How long would it take for these planets to orbit their barycenter?
The formula for orbital period is $$T= 2\pi\sqrt{\frac{a^3}{G \left(M_1 + M_2\right)}}$$

For your example, $a=19000000$ metres, and $M_1 = M_2 = 6e24$

Which gives an orbital period of just over 5 hours.

Whether such an arrangement is likely depends on the nature of the the formation of the binary planet, and how the orbital period and rotation rates are affected by tides.