here’s an easy thought experiment.
imagine being on an airplane and dropping a cable to the ground, letting go completely. as you can imagine, the cable just flops to the ground because gravity pulls it down and nothing counter acts the gravity.
now imagine dropping one end and holding the other. if there were no air drag, the free end of the cable would move along the ground at the speed the airplane is moving. that’s because you have gravity pulling down and a counterforce (you pulling up) and the airplane pulling the whole cable “forward” along its flight path.
now, assume the cable is super strong, and it was attached to both the plane and the ground. of course the plane would eventually get pulled to the ground not because of gravity (lift counteracts gravity for the plane) but because the plane is traveling along an arc concentric with the ground curvature.
now imagine instead of a plane, it’s a satellite. satellites don’t hit the surface as they move because they’re actually “falling” *around* the earth. that’s what it means to orbit. the satellite is moving with a lateral speed faster than it’s falling, and in the case of a geo synchronous orbit the combined rate matches the rotational speed of the earth.
the latter case is how you’d have a cable extend straight up into space: something has to be pulling on it to contract gravity *and* has to be moving in a geosynchronous orbit (or rather the “center of mass” has to but that’s more technical)
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