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by lamacase 1240 days ago
The equation is: if it isn't already in orbit, and it doesn't hit the atmosphere, then it flies past.

For an incoming object to start orbiting earth, it has to decelerate through active propulsion or aerobraking or something like that.
1 comments
graderjs 1240 days ago
Sounds like a nice heuristic but I don’t think that covers every case—and it’s not an equation. Sorry, wrong answer!!
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lamacase 1239 days ago
It does cover every case though. The solution for the orbit of a mass in a 2-body problem is always an ellipse! (Or a parabola/hyperbola for an escape trajectory). You can find the derivation here [1], it's not too complicated.

There is no way for an asteroid and the earth to interact gravitationally to change the asteroid's orbit from what it was coming in. Non-gravitational interactions (like hitting the earth/atmosphere) can do it.

Also, over many interactions and a long time you can have orbital capture in many-body situations, but there is no general equation for this (look up 3 body problem). This is how you get objects accumulating at Lagrange points for example.

TLDR: The equation you're asking for does not exist. Sorry, wrong question!!

https://en.m.wikipedia.org/wiki/Orbit

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