[Tade0]

Not OP, but here's one instance over which I already had an internet fistfight with a person swearing by LLMs[0], meaning it should serve as a decent example:

> Suppose I'm standing on Earth and suddenly gravity stopped affecting me. What would be my trajectory? Specifically what would be my distance from Earth over time?

https://chatgpt.com/c/682edff8-c540-8010-acaa-8d9b5c26733d

It gives the "small distance approximation" in the examples, even if I ask for the solution after two hours, which at 879km is already quite off the correct ~820km.

An approximation that is better in the order of seconds to hours is pretty simple:

  s(t) = sqrt((R^2 + (Vt)^2)) - R

And it's even plotted in the chart, but again - numbers are off.

[0] Their results were giving wildly incorrect numbers at less than 100 seconds already, which was what originally prompted me to respond - they didn't even match the formula.