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Would A Wide Rope Reach From Earth To A Geostationary Satellite?

If you want to reach from a geostationary satellite to earth using a rope does the rope's thickness matter?

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Photo: Laplander (Flickr)

It's difficult to imagine a long rope reaching from a geostationary satellite to earth. Do you know why? Because it is impossible to do... even with a very thick rope!

We’ve been having some fun with physics imagining ourselves sitting in a geostationary satellite. That’s a satellite that orbits the equator at the same speed as the earth turns, so it’s always over the same spot of land, 22,500 miles up.

Could you let down a rope and pull up some supplies?

The answer was no, because no rope is strong enough to support its own weight at that distance. Before you even get a chance to tie something to the rope, it would snap — from trying to support thousands of miles of rope!

Well, what could you do? Maybe you could have the rope gradually become wider as it goes up.

Would a wider rope work?

Think of it this way. A one-inch-wide rope would break with a certain weight, but a two-inch-wide rope could hold that weight.

Why not figure out what the maximum possible weight is at every point along the rope, and have it be just a little bit wider than the breaking width?

This all sounds good but what are we forgetting?

Think for a second. Yep — every time we widen the rope, we also increase its weight. Any benefit we gain in being able to hold what’s under a certain section of rope would be cancelled by the added strain of holding that section.

Aside from that, to reach all the way to a geostationary satellite, the rope would have to be thickened so much that it wouldn’t really be a rope any more. It would wind up being about three hundred feet wide at the top, even if the bottom end were a tiny thread.

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