Question involving space travel and the expansion of the universe

[anonymous3]

From what I understand, the expansion of the universe means that sub-lightspeed travel is sort of like running on a treadmill and eventually the expansion wins out and you'll never get anywhere.

So, my question is,

Take a point in the universe, and imagine a sphere expanding from that point at, say, 80% the speed of light, how much of the universe will that sphere envelop before the expansion of the universe gets the upper hand and the sphere gains nothing but vacuum space?

 

[gneill]

From what I understand, the expansion of the universe means that sub-lightspeed travel is sort of like running on a treadmill and eventually the expansion wins out and you'll never get anywhere.

So, my question is,

Take a point in the universe, and imagine a sphere expanding from that point at, say, 80% the speed of light, how much of the universe will that sphere envelop before the expansion of the universe gets the upper hand and the sphere gains nothing but vacuum space?

For a rough approximation apply Hubble's Law and determine the distance at which the speed of recession is 80% the speed of light. Your sphere won't catch up to anything that starts out beyond that distance.

 

[Drake711]

well your expanding sphere will immediately start gaining empty space unless the point starts in a black hole because the universe as a whole contains mostly empty space. If you mean when will the sphere start gaining totally empty space the answer is never because the edge of the universe is expanding faster than the speed of light. There are no pockets of empty space in the observable universe because energy and time homogeneously fill each other which is probably why something can't reach 0 Kelvin and why you can't ever have a true vacuum.

 

[Naty1]

For a closely related discussion, see post #8 here.


https://www.physicsforums.com/showthread.php?p=4210303#post4210303