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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https://spotthestation.nasa.gov/tracking_map.cfm
This is the ISS orbital tracker. If you separated from the ISS and burned retrograde (slowed down), your would begin to descend, and land somewhere along that path. How far along depends on how much you slowed down, and can be calculated.
Wait for the earth to rotate under the ISS until the path lines up with where you want to go, then burn retrograde the correct amount at the correct time.
The spacecraft can then use aerodynamic effects to steer inside the atmosphere as it falls back. The extent that it can do this is known as cross range capability. The Space Shuttle had a lot, because it had wings, but even capsules have a little bit
The blunt cone lifting body shape employed by the Apollo capsules and adopted by SpaceX, Artemis etc. can be flown with remarkable accuracy.
They have an asymmetric centre of gravity and thrusters that can rotate the capsule about that centre of gravity. This rotation allows the angle of attack of the blunt base to be varied to steer left or right, up or down. The Apollo capsules actually did two re-entries on return to Earth: an initial one to scrub off speed and then they would climb again, losing even more speed, before descending more steeply into the designated landing zone.
So it wasn’t so much a question of calculating where the capsule would land but one of having the Command Module Pilot fly the capsule to the required spot.
The blunt cone lifting body shape employed by the Apollo capsules and adopted by SpaceX, Artemis etc. can be flown with remarkable accuracy.
They have an asymmetric centre of gravity and thrusters that can rotate the capsule about that centre of gravity. This rotation allows the angle of attack of the blunt base to be varied to steer left or right, up or down. The Apollo capsules actually did two re-entries on return to Earth: an initial one to scrub off speed and then they would climb again, losing even more speed, before descending more steeply into the designated landing zone.
So it wasn’t so much a question of calculating where the capsule would land but one of having the Command Module Pilot fly the capsule to the required spot.
The blunt cone lifting body shape employed by the Apollo capsules and adopted by SpaceX, Artemis etc. can be flown with remarkable accuracy.
They have an asymmetric centre of gravity and thrusters that can rotate the capsule about that centre of gravity. This rotation allows the angle of attack of the blunt base to be varied to steer left or right, up or down. The Apollo capsules actually did two re-entries on return to Earth: an initial one to scrub off speed and then they would climb again, losing even more speed, before descending more steeply into the designated landing zone.
So it wasn’t so much a question of calculating where the capsule would land but one of having the Command Module Pilot fly the capsule to the required spot.
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