"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."
I also misread that. The 0.005% is in relation to this:
> 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.
isnt the chance only for those specific three planets, not any three planets? there are 56 ways to choose three planets from the 8 (sorry pluto) in our solar system, so the probability of passing that close to any three planets is 56x greater
Given mass distribution of our galaxy is decidedly anisotropic I would expect the answer to be a resounding "no". The ((5/57)/ (4 Pi)) implicity assumes uniform incoming trajectories - I think. There's an odd mixing of radians and steradians in this formula, if the "4 Pi" represents the total solid angle of a sphere.
ATLAS was expanded in 2022, and this object was discovered by the new telescope in Chile - the more we look the more we find. With more survey telescopes coming online (Vera Rubin just recently, Nancy Grace Roman and Xuntian coming soon to name a few), I suspect we'll start seeing quite a few more of these.
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
> 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
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.
> 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
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.
