12km/s is 85714 linguine/s!
Gonna go pasta fasta!
ESA's Solar Orbiter is to undertake a flyby of Earth, requiring a careful assessment of debris as it dips close to the orbit of the International Space Station (ISS) ahead of its main science mission. The flyby is due to take place on the 26 and 27 of November. The amount of debris on orbit was helpfully increased last week …
Given that these manoeuvres are all about changing energy and momentum I would have thought the Moon could be used instead of the Earth. This has the advantage that the number of things orbiting the Moon at any time is usually countable on the fingers of one hand at most.
the moon is much, much lower mass than the earth, so you'd get much less kick - additionally it's harder to target, the orbit of the earth is wobbling about the barycentre of the earth moon system, that point is still inside the earth - the wobble is about six thousand miles. The moon's solar orbit is also wobbling about that same barycentre - but that means that it's wobbling half a million miles.
"the moon is much, much lower mass than the earth, so you'd get much less kick"
On the other hand, you can get within a few kilometres of the surface for a faster kick, just need to avoid any tall peaks, either by staying above, or going through! Could be tricky, but great visuals :-)
Great visuals, very risky (a very small miscalculation will have unexpected lithobraking), but still a smaller kick than a comparatively safe fly past the larger planet. Of course that safety does depend on people not being complete idiots, and that state is depressingly common amongst decision makers.
You'd still be planning most of your maneuvers about the earth gravity well, but then you also have to plan it in such a way that you can get into the earth gravity well and slingshot around towards the moon at just the right time that you can THEN do a slingshot around the moon. Makes for a REALLY tricky maneuver. And when SO was launched nobody expected someone to do an ASAT test at that altitude (Because it also endangers the ISS and many other useful low earth observation orbits). By the time the ESA team would have known about the ASAT test debris they were already inexorably committed to making this maneuver at that altitude. They've probably got a proverbial window up there of only a few dozen square kilometers that they'll be aiming to fly through.
Yeah, at some point you've just got to throw your hands in the the air and go "Sod it. Done as much as we can.". Still, must be nice for the boffins to have almost real time comms with the kit briefly. May Eris, Goddess of Chaos smile upon the journey.