It's feasible. As a volunteer at the Spaceward Foundation (www.spacward.org) I fielded a question about this and did the math.
It is true that the climber will pull the ribbon to the west as it rises although the effect is small. The climber weighs 20 tons while the mass of the space elevator is 1,000 tons for the ribbon and 200-500 tons (depending on who you ask) for the counterweight. The SE will not spiral around the Earth. It will lean imperceptably toward the west.
This slight pull to the west creates a small horizontal force vector to the east that over the 7.5 days to GEO accelerates the climber to orbital velocity.
BTW, lifting stuff into space with the space elevator will slow the rotation of the Earth. After all, angular momentum must be preserved. The effect is slight because the mass of the Earth is huge compared to the space elevator and the climbers.
One thousand elevators operating continuously for 1,000 years lifting all payloads all the way to the top before releasing them would slow the Earth enough that we would have to add a leap second every 109 years.
Some may argue that we shouldn't permit any change. They need to remember that a) we add leap seconds routinely every few years, b) the length of a day is not a fixed constant because c) every time we have a major earthquake and a tectonic plate shifts up or down the length of our day changes and d) the moon is slowly pulling away from the Earth causing our days to grow longer.
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It's feasible. As a volunteer at the Spaceward Foundation (www.spacward.org) I fielded a question about this and did the math. It is true that the climber will pull the ribbon to the west as it rises although the effect is small. The climber weighs 20 tons while the mass of the space elevator is 1,000 tons for the ribbon and 200-500 tons (depending on who you ask) for the counterweight. The SE will not spiral around the Earth. It will lean imperceptably toward the west. This slight pull to the west creates a small horizontal force vector to the east that over the 7.5 days to GEO accelerates the climber to orbital velocity. BTW, lifting stuff into space with the space elevator will slow the rotation of the Earth. After all, angular momentum must be preserved. The effect is slight because the mass of the Earth is huge compared to the space elevator and the climbers. One thousand elevators operating continuously for 1,000 years lifting all payloads all the way to the top before releasing them would slow the Earth enough that we would have to add a leap second every 109 years. Some may argue that we shouldn't permit any change. They need to remember that a) we add leap seconds routinely every few years, b) the length of a day is not a fixed constant because c) every time we have a major earthquake and a tectonic plate shifts up or down the length of our day changes and d) the moon is slowly pulling away from the Earth causing our days to grow longer.