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?

Question

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

Answer 1

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.