Soupspoon wrote:But it gets fairly close long before lim x→∞, in Space-Is-Really-Big terms, and a quick back-of-an-imaginary-envelope approximation with the starting conditions of "several thousand light years apart" it probably hardly matters for anything involving "very massive" masses. Whatever order of magnitude that should actually be.
Yeah, as I said above, Earth's escape velocity is 1m/s at about a tenth of a lightyear. Meaning anything falling (from rest) from a greater distance will have at most 1m/s of velocity by the time it reaches that point.
The difference in final velocity on impact, between starting at rest and starting at 1m/s from that distance, is about 45 microns
per second. And since said final velocity is 11.2 kilometers
per second, I'd say it's pretty safe to ignore that difference.
In other words, because the limit at infinity is easier to calculate than the precise value at some absurd distance, and because the difference it makes is parts per billion for a planet (and even less for something bigger like a star), and because the original question was about velocity and not time, it's safe to treat distances like a thousand light years as infinite, and just use the escape velocity in your calculations.
Unless stated otherwise, I do not care
whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
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