>If you mark 2 points on a balloon with a marker and begin blowing it up, these two points would most certainly move away from each other. They would not, however, move away from each other near as fast as the expansion speed of the balloon itself.

For specific points it depends on where exactly they are in relation to each other. if they are on opposite sides of the balloon they would move apart at twice the rate of the expanding radius. If they were right next to each other they would barely move apart.

Let's move it to two dimensions to make it simpler here:

Assuming the angle between points a and b is 2Θ (you'll see why i chose 2Θ instead of Θ in a second) then I get the straight (not circumferential) distance between them is 2r(cosΘ), so as Θ approaches 90 from 0 (and thus the angle between the points approaches 180 from 0) you'll see that ab approaches 2r from 0

I have absolutely no idea how to post an integral here, but it's a fairly straight-forward first order one that shows for the entire circumference the mean distance is linear with r with a coefficient of 2π.

If those two points are on opposite sides of the sphere, the rate of expansion would be the same as the rate of expansion of the radius. Now, if these two points represented the only worlds with life on them and one of them is Earth, then we'd probably never know if the other exists. If there are several points throughout the sphere then there would be those close enough to confirm even as the sphere expands.

Joe you are the math man for sure
 

I have to hand it to you Joe you do your home work. Joe do you believe in creation or the big bang ? Can you give me the reason why ? I do like your post and even though I do not agree it is good to have you posting on this board. I will keep you in my prayers and until the last breath you are still in the game.
Isaac

>If those two points are on opposite sides of the sphere, the rate of expansion would be the same as the rate of expansion of the radius.

No, it would be double.

Oh, pardon me! I meant to say it is equal to the diameter's expansion. Got my geometry terms crossed for a moment.

Wanna quick way to end a thread? Bring Geometry into it! ;)