Orbit paths follow some pretty simple math.
If you know an orbiting thing’s position, speed, and direction, you can calculate its orbit path using basic undergrad physics using the equations for gravity and momentum. Space is great because the “assume no friction or air resistance” thing actually works.
Once you know the orbit path and speed, it’s easy to work out where the object was at any point in the past, and where it will be in the future, including the last time it would have been near Earth.
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