If two identical balls are connected to the same very long rope, and one of the balls are floating in space and the other one is hanging above earth’s surface. What would happen?

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So my 7-year old asked me this and as much as I would love to be able to give him a proper answer, I couldn’t.

Does ball A (in space) float away, taking ball B (above earth’s surface) with it? Will the balls stay somewhat fixed or will ball B force ball A down?

In: Physics
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All of these outcomes are possible, depending on the exact location and speed of the balls. It is possible to set up the balls above the equator in such a way that they’ll just stay there – the lower ball hovering near the ground and the upper ball circling in orbit around Earth. You can then go up and down the rope to get into orbit and back at a fraction of the cost compared to rockets. This is the basis behind the concept of “Space elevator”. You can look it up and tell your seven-year old they’ve come up with a great idea independently. Technically the only setback is that we don’t yet have material strong enough for the rope, but we are kinda close to it, so it’s not unrealistic to hope that we will have it eventually.

Edit: somewhat expanded.

I was just trying to work it out and there are so many variables to take into account and assumptions to make that all those outcomes are possible. It all depends on how long the rope is, the height of the ball on earth, the height of the ball in space, whether they’re both moving at the earth’s angular speed, etc.

Ball A will be pull back to earth, because gravity will be acting on ball B stronger then Ball A and since they are connected ball B will drag A down

To put simply it a game of tug of war with Ball A just standing there with Ball B and earth pulling on the rope.

Edit: grammar

Assuming that “floating” means in orbit (otherwise, they just fall), they are “balanced” around the center of mass of the balls (half-way down the rope). One ball pulls “up”, and the other “down”, keeping the rope under tension. Congratulations – your 7 year old has intuited tides.

It’s a very interesting question.

Let’s say the rope is infinitely strong and will never break, to keep it interesting. And the rope also has almost no mass, to keep it simple.

The gravity on the lower ball would indeed be greater than the gravity on the higher ball. (There is always a little bit of gravity, even in space)

The difference in gravity on a long rope can actually be used to generate power.

It get’s complicated very quickly so not exactly ELI5:
https://en.wikipedia.org/wiki/Electrodynamic_tether

But the question is: do they float away or fall down?

If the balls and rope aren’t moving, they will fall down, regardless of the length of the rope.

If the rope is really really long, and the higher ball is hanging above the surface of Venus or Jupiter (planets or anything heavier than earth), they would both be pulled towards that other planet or the Sun.

If they are moving, for example the higher ball is flying around the earth from a distance and the lower ball is flying right above the earths surface, they might both begin to float further and further away from the earth and even escape and fly away like a very long and thin space craft. But it would have to be moving very fast.

If they move too slow, they will fall down.

Nothing happens I would think. Since there’s no gravity in space. The earth’s gravity would keep it right where it is. That would be my answer. It’s a lot like fluid in an astronauts brain when they return to earth. Most of the fluid that also cushions the brain from bumping your head concentrates to the base of the skull. Why? Because earth still has some gravity that affects the fluid versus no gravity in space.

Let’s make a few assumption to make this whole problem possible then lets just… Map it out?

First, we’ll assume that both balls have the same weight and that the rope is weightless (just to make things simpler). We’ll also assume that the rope is unbreakable. Earth ball (EB) is the one on the surface and Space ball (SB) is the one in space.

First thing, the earth has a gravitational pull. basically, anything that get close enough is attracted by the earth. The closer, the stronger the attraction. For now we’ll ignore the other big force that will matter. We’ll just focus on gravity.

Gravity is applying a force on both balls. EB is taking a stronger force than SB by virtue of it being closer to the ground. As long as EB does not rest on the ground it’ll try and get closer, giving part of its acceleration to SB. SB, unless really far away is also getting attracted but to a lesser degree. Since the rope is unbreakable, EB will be slowed down because it’ll be giving some of its acceleration to get SB moving. EB will thus be moving slower but still moving toward the ground while SB will be moving faster by stealing some of EB’s acceleration. Basically, if there is absolutely no other force at work, EB and SB are bound to both end up on earth.

But there are other forces. The first one is gravity from other astral things. Stars, planets, comets, moons, etc. It’s simply impossible to evaluate. So we will acknowledge their existence, but ignore them.

There is though one other force that we CAN take into account somewhat reliably. Centrifugal force. The earth is spinning. Centrifugal force apply to both balls again. but this time, the further you are from the center of rotation, the more acceleration you get. So this time, SB is getting a lot of force whereas EB isn’t getting much. it’s actually low enough that gravity is by itself enough to hold EB from its own centrifugal force. But since SB is much further out, it’s likely that SB will take a stronger centrifugal force than gravity will pull. SB will try to leave for space. In it, it’ll try to drag EB.

And that is the result. Basically, the further the ball, the stronger the centrifugal force pulling balls away. The closer the ball, the stronger the gravity pulling balls closer. Which mean that the real question become… How long the rope is? If the rope is long enough, centrifugal force will apply enough energy to SB that it’ll drag EB away. If the rope is short enough, gravity will overpower the centrifugal force and EB will drag SB back. If the rope is just the right length, gravity and centrifugal force will simply counter each other leaving the balls somewhat where they are

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I’ll assume you’ll want to explain these concept to your child. You’ll probably want to simply try and explain what centrifugal force is by tying a ball on a rope. Show him that the ball always fall toward the earth. That’s gravity. Then start spinning the ball on a rope. That’s centrifugal force. If you do it properly, the ball will rise despite gravity. Proof that it’s powerful enough to counter gravity. I have no idea how to make him correlate the rope length with the gravity force since in our little test, we’re willingly exaggerating the force for demonstration.

It depends on the rope and just where in space the ball is floating.

The big problem is that if you are just as high up as the International space station, you would need a 400 km long rope to reach the ground.

Any normal rope that long would rip apart under its own weight, but you could probably make one from Kevlar or something that might work.

But there is another even bigger problem the ISS and the space ships flying to it may look like they are just floating in space, but they are actually moving very quickly compared to the ground beneath them.

Objects that high fly sideways at speeds that would be 22 times the speed of sound here on earth.

So what would happen that the drag of the weight of the rope and the lower ball and the air resistance of the lower ball and the part of the rope in atmosphere would either slow down the upper ball until it fell down from orbit or it would simply snap the rope under the strain.

Even if you could keep the rope from snapping you would still have to deal with the upper ball being slowed down by the air resistance of the lower ball and the lower ball being speed up by being dragged by the one above.

It is something that would be very destructive to anything around it.

One way to escape that problem of one part going very fast is to simply take the upper ball and take it much much higher into an obit where it always was above the same patch of ground.

This way you would have no speed difference between the ball near the ground and the one in orbit.

This sort of construct is more or less what we call a space elevator and it would work the way you would want it to. You have a rope that you could climb up to get to the the ball floating in space.

The problem is that instead of a few hundred kilometer long the rope would now need to be 36 thousand kilometer long.

We don’t really have any material that could be used to make a rope that long. Some think that some sort of fancy carbon nanotube fibers could work for this and some tricks that involve tapering one end and some other stuff.

We can’t build anything like that yet, but it is a serious idea that could work in theory.

Either Ball A would fall to earth (and burn up in the atmosphere) or the string would break.

One of the major problems with space elevators is the length of the string is so long that even our lightest and strongest strings would break under their own weight.

The very long rope would break and the ball in space would burn up, if it was still inside the atmosphere, or fly off into space.

The reason is ball at the end of the rope would have to move much faster than the ball close to the surface just to keep up.

Well to stay in space you would have to be in orbit and I could imagine because ball A is several times faster than a bullet to do that and ball B being completly still, the rope would just rip. If it was undbreakable though ball A would just pull it with it slowing itself and ball B down because of air resistance. Eventually there would just be an obstacle like a mountain which would bring both to a stop. That’s atleast what I would think that would happen