How is the Universe Expanding?

[vorlon13]

HOWEVER, as, for instance, our sun orbits our galaxy, it is radiating gravitational energy

. . . errmmm. . . is that a thing?  It sounds to me like something that isn't.  

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Distances are stretched through the expansion of space. It's as if space itself is stretched..You can think of it like ants walking on a rubber band that is being stretched.  
Two separate ants will move away from each other through the stretching, but the ants themselves keep their length because they are held together by forces which are not changed by the expansion of the rubber beand.
Likewise, in space, all objects which are held together by forces such as gravity or electromagnetism will resist this stretching and keep their sizes because their size is determined by these forces at work in or between them. Two distant objects which are not e.g. bound by gravitation will not have anything compensating the stretching of the space in between and their distance will increase.

Alex, if space is expanding, wouldn't the rate of separation of objects be a function of their original distance from each other?  I mean, if I put two dots 1cm apart on a rubber sheet and stretch it to 2x its original size, I'd expect them to be now 2cm apart.  But if I put them on opposite edges of a 1m sheet, I'd expect them now to be 2m apart-- a 100x difference in the apparent rate of separation even thought the original rubber "Universe" is expanding in exactly the same way both times.  But in the 1cm apart dots, it seems it wouldn't matter WHERE on the sheet they were-- near the middle or right up near the edge-- the apparent change in position relative to each other would be identical, no?

In other words, from one of those dots, I don't think I could necessarily figure out where the center of the rubber sheet was based on the changing relative position of any of the other dots.  So. . . how do they arrive at the Big Bang singulariy, rather than on a position that the Universe just expands forever and ever?

Once the gravitational wave detectors detected gravitational waves, the whole gravitational wave thing took on quite a bit of credence.

As for how long it will take the sun to spiral down into the core of the galaxy?  Be thinking a very long time.  I suspect your growing finger nails would get there first.  (sorry, I'm not going to do the math)