Yesterday, I wrote about a new study that indicates that free-floating planets in the Milky Way may outnumber planets orbiting stars, and even be more numerous than stars themselves. It's an amazing result! The most likely scenario is that these planets formed in solar systems similar to ours, but got ejected due to gravitational interactions with other planets in the system. These planets get literally tossed out into space, wandering the galaxy forever*.
This made me wonder: if these numbers are correct, how likely is it that such a rogue planet might actually be close by on a cosmic scale? And given the kind of topic I like to write about, are we in any danger from a close encounter with one of these galactic nomads? These wandering planets are so dark and distant they are currently essentially impossible to detect using regular techniques, so we don't know if any are in our galactic neighborhood or not. The only way to get a grip on how close one might be is to look at it in a statistical sense: on average in the galaxy, how many of these planets are there per cubic light year of space? Then we can fiddle with the number a bit to see how far away one of these planets could be. Let me be clear up front about something. No doubt there will be people who may want to claim these rogue planets might explain Nibiru or Planet X or the Mayan apocalypse. These people are wrong (again, and as usual). As you'll see, the math absolutely does not support such a claim at all. So if you hear someone talking doomsday, send 'em here. And I might as well address the TL;DR crowd: the conclusions I draw here are that a) on average, a rogue planet may be closer than I would've initially guessed, but 2) not nearly close enough to be a concern in any way. OK then, got it? Onward to the math!