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?

1 Answer

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.

• The planets are tidally locked with one another. Jun 24, 2016 at 1:00
• I'm looking for an answer of yours and can't find it. It solves the time for collision of two bodies, in other words two bodies start at rest and fall towards their center of mass. I think that the question might have involved cosmological distances. I also seem to remember that there might have been an error in it and I mentioned it in comments, but now I can't find it at all. Any thoughts?
– uhoh
Feb 6, 2020 at 11:35
• I'm working on a numerical answer to this question but if you can find that equation for the time of two bodies falling towards each other go ahead and post it as an answer if you're interested.
– uhoh
Feb 6, 2020 at 12:43