: I got to thinking that, scientifically speaking, how would one work? How
: people are transported from one end to another, and how the space end
: would align perfectly in respect to the ground.

: Science fiction? Or can it realistically be done with the right things?

The closer a satellite is to it's parent body the faster it has to orbit. Low earth orbit sats do several orbits per day. Higher ones take longer.

So, when you think about it... it's clear that there must be a height where it takes exactly one day to go round the world. If you are going round in the same direction that the earth spins... then your sat stays stationary above the same spot on the earth. (If it's orbit was perfectly circular and on the same plane as the equator)

So let's imagine a sat in geostationary orbit taking a day to orbit. Let's draw an imaginary line from the earth's center and through the sat and on out into space.

Now imagine another sat on the same line but 100 miles lower. How fast would that be going?

The circumference of a circle is pi R squared. R is smaller so the distance traveled is smaller so the lower satellite is traveling slower than the first. Given that it needs to be traveling faster to stay in orbit... it is clear that it would fall out of the sky in a fairly short time.

The converse is true of a sat on the line but 100 miles higher than the first.

Imagine that we tie the three sats together. The lower sat tries to pull the collection down. The higher tries to pull it up. You can see that the two pulls could cancel each other out and you have a line that is being pulled from both ends. The line is under tension.

Materials are generally stronger under tension that they are under compression. If you pull on a string it naturally straightens out. If you compress it then it can kink up in any number of ways so you have to reinforce the sting to try to prevent bending.

It's easy to visualize how much tension is on the line at different places along the line. For example if we take a point a foot from the bottom of the line and the line is in equilibrium then we can see that there will be the weight of one foot of line tugging downwards and one foot worth of force pulling it upwards. That is not a lot of force.

The maximum tension is at the geostationary point. You have the weight of all the line below this point and all the line above that point.

So... we need to taper the line. It is thickest at geostationary and thinest near the ends.

It turns out that we could use almost anything to make our line... it's just that weaker materials need to be very much thicker at the thickest point than strong materials need to be.

It may be that we could make the line out of wet toilet tissue but the maximum thickness may exceed the width of the earth ;-)