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Intrism comments on Harry Potter and the Methods of Rationality discussion thread, part 23, chapter 94 - Less Wrong
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Every single casting of Arresto Momentum ever was performed on a moving planet, which resulted in no issues. It's possible that casting from inside of a moving vehicle to outside of it might result in problems, but I strongly doubt that it'll do anything which would seem bizarre from the caster's frame of reference.
Of course. This suggests that the spell uses something as a reference. If it’s the caster, then casting Aresto Momentum on a tree while riding the TGV will cause the tree to suddenly start moving at a few hundred km/s. If it’s the planet, casting it on an object inside the train will have the same effect. Wizards might not use fast vehicles a lot, but even the Hogwarts train and the flying brooms are fast enough to be very dangerous with heavy objects.
(That said, I don’t think there are any examples, in canon or MoR, of the spell being used for anything other than falling objects. If it only does that, then it’s much less dangerous in normal life, especially in a society without high-speed elevators, and it makes a bit more sense, though the name is even sillier.)
You could probably make Arresto Momentum relatively safe by having it choose between the caster's frame of reference and the earth's (at the caster's position) based on whichever results in the spell doing less work. It's still dangerous, obviously casting it on someone else's moving vehicle would be a bad move, but it avoids making anything go "zoom" in a privileged frame of reference.
Eh, the spell probably just reads your mind and does whatever you actually want :-)
This is a great way of bringing a celestial body, e.g. Venus, on a transfer orbit which will put it in the same orbit as earth, but on the other side of the sun, as you'll only need to move the caster, not the planet itself. Such orbits are fairly stable on a human timescale, and colonization (plus terraforming) may begin then. Aiming the spell might be a little difficult, but is certainly doable (as amassed spell-casting will also do, there's no problem if several spells hit).