Too cool, part 55: What are the odds?

Once again courtesy of Astronomy Picture of the Day, a few days back, we have a wicked conjunction:

first off, pretty decent image of sunspots, clearly taken with a solar filter. Getting the timing and focus down to capture the International Space Station so sharply against the sun’s face is a serious accomplishment in itself – I’ve been trying for this myself, several times over. But then Petr Horalek, of the Institute of Physics in Opava (Czech Republic) captured an aircraft at the same time, which virtually cannot be planned and probably wasn’t even timed – it was strictly luck. Definitely click on the links for the complete rundown and the larger version (click on the image at the APOD site, or here.) Why is the plane not as sharp as the rest? Because it was significantly closer than either the sun (~152 million kilometers distant) or the ISS (better than 400 kilometers distant,) likely being less than 10 kilometers distant itself – I can’t get any closer than that, because I don’t know exactly where or when it was taken. It’s still in focus enough to make out the pitot tube extending from the wing’s leading edge though, and no visible motion blur – the defocus characteristics seem the same on all sides, suggesting that the shutter speed was fast enough to limit the motion blur to trivial amounts (with none from the ISS either.) Petr Horalek estimates the chance of capturing these three objects together is about 30 million to one.

Can that be right? Let’s break it down. The sun is a relatively small target in the sky, being less that the width of a dime held at arm’s length (roughly 0.5 degrees,) so the chances of anything passing in front of it are small to begin with – the sky is 180° across of course. I semi-routinely use the ISS Transit Finder site to plot when the ISS and other manmade satellites may pass in front of the sun, and the path where this can be seen is usually around 8 km wide. The ISS itself is moving at a pretty good clip, so usually passes across the entire face of the sun in less than a second. A plane will cross it twice as fast or more, and while it’s larger from this viewing perspective, it’s also a lot closer and so the path where it will cross the face is much narrower. So while I wouldn’t bet heavily on the exact numbers, I can see where capturing them both is a matter of very specific timing and location. He’s also extremely lucky that the plane didn’t obscure the ISS, which would be just my luck.

Idly, I’ve been looking at that plane and trying to pin down what it is. Straight, unswept wings and no visible engine pods, plus exhaust distortion occurring right inline with the fuselage, seems to indicate a single-turbine internal engine, though it’s possible it was a single turboprop and the propeller is outside of the sun’s disk. There’s little else I can tell about it, and it’s not ringing any bells, but if I suspect I have it, I’ll let you know.