How Do NASA and other organisations make sure they are at the right spot to pick them up and that the astronauts don’t land in some war zone or remote hard to reach area?
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Well they know the speed on the planets and the space ship on each axis and they do a sorta complicated arithmetic using mechanical physics and the trajectory of projectiles to calculate when each body will be at a point where they can come in contact. Basically a lot of math and science brought about by their knowledge of the relativity of the planets and speed of everything so just taking the distance and the speed and finding the time and place.
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