Ladder paradox?

Question

There is an escape velocity to leave earth. 8 km per second.

But if we build a gigantic ladder, we can slowly climb to outer space, so escape velocity will be 1-2 feet per econd.

Answer 1

You're comparing apples to oranges.

Escape velocity talks about the velocity you START with, assuming no other force is added afterwards.

When you climb a ladder, you push with your foot on each rung.

It would also be possible, in theory, for a rocket to escape very slowly. The biggest reason this wouldn't be practical is the weight of the fuel.

Climbing a ladder would have the same problem; it would take so long that the amount of food and water you'd need to carry would be so great you never could move in the first place.

Answer 2

My theory of division by zero has a corollary that says paradox does not truly exist. Your ladder paradox is not a paradox because it is impossible. You are not able to build such a ladder. It is like asking, "If I drank all the water in the world, would it clear up my acne?" The question is irrelevant because it cannot be done.

It is quite all right if you disagree with me on this point -- Just build the gigantic ladder and prove me wrong. We can discuss it further then.

But even if you did build your "gigantic ladder," how would that be a paradox? Wouldn't it just redefine esape velocity? By the definition of escape valocity, would you need to keep climbing past Jupiter (or whatever) at 1-2 feet per second? (Or, "per econd"?)

Interesting...

Barjesse37

Answer 3

One thing to keep in mind is that your velocity would not simply be 1-2 ft/sec. Change your frame of reference and you'll see that your linear velocity increases quite a bit as you move further and further out on the ladder (and you slow the rotation of the Earth a tiny, tiny bit.) I haven't done the math, but at some point you would reach 8 km per second, if you didn't get knocked off by space junk first.

Answer 4

That's an interesting thought - not only would the escape velocity be 1-2 feet per second, but the climb would get easier and easier the higher you go.
Unfortunately, it's only a thought experiment - in reality, you would need to take so much equipment with you to survive the high altitude environment that you would probably never make the first few rungs.
Never the less, it's an interesting thought.

Answer 5

Someone had a similar idea that could work someday if the materials science gets good enough.

Put a big station up in geostationary orbit. Hang a cable down to earth.

Run stuff up and down the cable to make space launch much, much cheaper.

Trouble is, building a cable that long that doesn't collapse under its own weight is a problem. Even pure carbon nanotube fibers probably won't be enough.

Never say never though. It could happen theoretically.