If you take a random trajectory through our solar system, your chance to pass this close to three planets is < 0.005%.
"The likelihood for such a perfect alignment of the orbital angular momentum vector around the Sun for Earth and 3I/ATLAS is π(5◦/57◦)2/(4π) = 2×10−3."
Sloppy sloppy work.
> In the following analysis we assume that 3I/ATLAS is on its current orbit but vary the time-of-entry into the Solar System (or equivalently the time of perihelion), assuming 3I/ATLAS could have come at any time into the Solar System, and happened to do so such that it came within the observed closest approaches of Venus, Mars and Jupiter. The probability of this is 0.005
So exact same trajectory, but analyzed over a long period of time. If it came any earlier or later, it would almost never get this close to exactly those three planets.
Go through the list, Mercury through Pluto, mentally saying "I find ____ interesting" and notice which one gives you an eye roll/chuckle/groan.
Are their trajectories uniformly distributed?
Since they are often small and dark, it's very possible we missed a few.
Hopefully we humans get a mission ready to go that will allow to go and have a look when a suitable one turns up with enough notice. Presumably one that isn't nailing though quite so fast as 3I/ATLAS (ʻOumuamua and Borisov were about half the speed each - about 30km/s). Annoyingly the speeds mean that really all you can do is a very fast flyby, unless you are incredibly lucky with trajectories, the object moves very slowly or we can ship a truly massive amount of "rapid" (e.g. not ion engines if you want to catch it this side of the heliopause) delta-v to orbit.
The rocket equation is really not on our side here if we wanted use chemical means. If you have a specific impulse of 300 seconds, you basically cannot get a 100kg probe to 30km/s delta-v without a slingshot. 100 tonnes of fuel gets you to about 20km/s, 2000 tonnes gets you to 30km/s. And a craft that holds 2000 tonnes of fuel probably masses more than 100kg.
Maybe the better bet is a really good sunshield and then everyone works on their cardiac health so they can see the intercept in 30 year's time, and even then it's a blink-and-you-miss-it flyby at over 20km/s: http://orbitsimulator.com/BA/lyra.gif
Or, hear me out, we built an orbital rail gun.
Using the Wikipedia example of a 1km, 5600g superconducting rail gun that launches at about 10km/s, we just need about a 10km gun to achieve 30km/s (length goes with launch speed squared).
Put it on the lunar surface for a roughly 2.5km/s penalty (I think, plus you obviously need to shoot it when the moon faces the right way).
No humans though, far too squishy. But you could launch a whole swarm of microprobes which could be a very effective distributed observation platform with a gigantic baseline.
If you haven't read it, the short story Maelstrom II by Arthur C. Clarke has a lunar rail gun in it. And the rest of the The Wind from the Sun collection is very good. The namesake solar sailing regatta story is great too.
That's a lot longer gun than I expected! Didn't the navy get to 6 km/s with a 5m barrel? That's a lot more than 5.6kg, of course.
> But you could launch a whole swarm of microprobes which could be a very effective distributed observation platform with a gigantic baseline.
For the beginning I'm going to assume each shot will end up vaporizing a significant fraction of the gun. Getting something to 30km/s once is certainly going to be much easier than doing it hundreds/thousands of times.