how Astronaut landings can be calculated

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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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Orbital trajectories and the effects of air resistance are well known and very predictable.

Assuming that you are not in a spacecraft with wings, there is a predetermined point where you fire thrusters in the opposite direction to your motion to slow you down somewhat. That means your orbit starts to decay and intersects with the top of the atmosphere sometime after. That slows you down even more, generating a lot of heat as you compress the air ahead of you. As the atmosphere becomes thicker lower down you lo*o*se your remaining forward velocity and descend the last bit vertically under a parachute.

All those effects are known and can be factored into the calculation as to when, how long and how hard to do the initial reverse thrust burn to get fairly close to your desired landing spot.

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