If I tied a rope to earth and have it unsecured 420mi out in space. Will it stay straight up or will it sway?

Question

A answer will help me provide some facts for a statement I want to make conserning a hypothesis I want to prove. Nothing public just for myself.

Answer 1

Exactly how it will fall and sway depends how you do it, really, except for the fact that it will do both and won't stay straight up in any case. To orbit the earth and avoid falling back down, an object must revolve around it at a speed that varies with the object's distance from the earth. Since your rope would have to orbit at all distances from the earth between the surface and 420 miles from it, it would have to travel at a different speed at each point along the rope. That is not sustainable, since the period of orbit also varies according to radius from the earth. Different parts of the rope would have to take different times to go once around the earth. Most notably, the geosynchronous infinitesimal section of rope would be at odds with the rest of the rope that would need to actually move with respect to the earth to stay in orbit. The rope would have to break at all points and have its atoms go their separate ways in order not to have any of it fall. You must remember that no matter where you go, there is gravity in space. Zero gravity is an illusion, and even an astronaut doing a spacewalk is accelerating almost as quickly toward the earth as if he were falling off of a building. The astronaut just doesn't necessarily move toward the earth, even though gravity is pulling him in that direction, because he is in orbit.

As a side note, let's imagine what would happen to a rope in space, attached to nothing at either end. Even in stable orbit around a body such as the sun, nonuniform forces would act upon it to change its shape. Radiation pressure from the sun and other radiant bodies would torque it and make it spin (photons and other particles bounce off of it and impart momentum to it). Gravity from other objects that move with respect to it will exert forces that are nonuniform across its length. It is more or less destined for a life of dynamism, however minute.

By the way, the two "top contributors" are each slightly physics-clueless in their own way. For example, things don't acquire negative gravitational attraction to the earth at 46,000 miles. Also, if it were rigid, it would stay straight for all intents and purposes even if it had a large mass. Think space elevator.

Answer 2

You're talking about a space elevator, obviously. The basic concept is that the centrifugal force of going around the Earth every 24 hours will hold up the top end of the rope. Once in place, satellites could be carried up the rope by a climber and released into orbit about 35,000 km up.

Many companies are working feverishly to develop the technology to make it possible. Some think the first one may be built within the next ten or twenty years; others think it should never be built because of the potential for catastrophic failure. View animations of several failure scenarios at http://www.mit.edu:8001/people/gassend/spaceelevator/breaks/index.html.

Helmut is correct, though the exact length depends on several factors, like how much mass is connected to the top end. If there is no counterweight tied to the top end, I think it needs to be more like 60,000 km.

The main obstacles are materials and power delivery systems.

If the rope were made of kevlar (the best available material so far) and only 1/2 cm thick at the bottom, the thickest part (at geostationary orbit height of 35,000 km) would need to be about 8 meters thick, just to hold up its own weight. Theoretically, single-walled carbon nanotubes should be strong enough to do the trick, but nobody is able to make them yet.

NASA has been conducting annual contests for a couple of years and awarding prizes to the makers of the best climbers.

Actually, they're talking about a ribbon, rather than a rope, because a ribbon will suffer less from micrometeor impacts. My own #1 misgiving is the impossible task of cleaning up the mess when the ribbon breaks and wraps completely around the equator in the tops of rainforests with tree branches sticking thru the slits in the ribbon.

Answer 3

How can the rope stay straight in the atmosphere without being tied to some point in space. A rope is not like a light beam or line of sight to be unaffected by earth's atmosphere. Only if the rope has zero mass and enough rigidity, can it remain straight and in that case, it behaves like a beam of light (without the scattering that the light undergoes). In that case, how long the rope is doesn't matter. It remains straight.

Answer 4

As the earth rotates in its orbit, the rope would slowly wrap around the earth. Of course, the fact that the earth's gravity would tug at the rope would also cause the rope to fall back to earth (even if the rope didn't burn up in the atmosphere).

Answer 5

If it were strong enough and extended about 46,000 miles into space, it might stay up and straight. A mere 420 miles would fall back to Earth more or less in a line west of the anchor point.