Wouldn’t jumping off the top of a space elevator just put you in orbit? Or, if by top you mean the point where the space elevator anchors to its counterweight, in orbit around the sun.
OK, you’ve got space elevators wrong, and that’s OK.
The counter-weight doesn’t orbit the sun. It orbits earth. If it orbited the sun it’d rip the thing apart. It sits somewhere above a geostationary orbit, as a geostationary orbit is where the orbit point is always over the same point on the ground, which would be where your elevator is tethered.
The station part is somewhere below this. The higher it is the heavier or further out your counter-weight needs to be —and since it’s already impossible around earth no matter what, this needs to be as low as possible.
Because of this setup, your velocity (while below the geostationary line) is always less than the orbital velocity at that altitude. For example, the ISS orbits the earth 15.5 times a day. Our point on the space elevator cable stays at the exact same position over the ground, so it orbits 0 times. At the same altitude as the ISS you need to be moving the same speed as the ISS or you’ll fall down. It only doesn’t while attached to the cable because it’s being pulled by the counter-weight.
Basically, stuff dropped off a space elevator falls, unless it’s at geostationary altitude. It needs to be given some extra horizontal speed to stay in orbit.
Wouldn’t jumping off the top of a space elevator just put you in orbit? Or, if by top you mean the point where the space elevator anchors to its counterweight, in orbit around the sun.
OK, you’ve got space elevators wrong, and that’s OK.
The counter-weight doesn’t orbit the sun. It orbits earth. If it orbited the sun it’d rip the thing apart. It sits somewhere above a geostationary orbit, as a geostationary orbit is where the orbit point is always over the same point on the ground, which would be where your elevator is tethered.
The station part is somewhere below this. The higher it is the heavier or further out your counter-weight needs to be —and since it’s already impossible around earth no matter what, this needs to be as low as possible.
Because of this setup, your velocity (while below the geostationary line) is always less than the orbital velocity at that altitude. For example, the ISS orbits the earth 15.5 times a day. Our point on the space elevator cable stays at the exact same position over the ground, so it orbits 0 times. At the same altitude as the ISS you need to be moving the same speed as the ISS or you’ll fall down. It only doesn’t while attached to the cable because it’s being pulled by the counter-weight.
Basically, stuff dropped off a space elevator falls, unless it’s at geostationary altitude. It needs to be given some extra horizontal speed to stay in orbit.