It's official. The universe is dying.

[Alex K]

I had hoped you wouldn't ask. The moon goes away due to friction but I think that only happend because it gets energy from earths rotation. A bound system with a kepler potential would usually come together and crash if it slowly loses energy. I think... The virial theorem says that smaller ~ less energy. Yes, it should shrink and the planets fall into what is left of the sun.

In a loosely bound planetary system like our solar system, would the loss of energy from gravity waves cause the system to collapse faster than expansion of the universe might tear it apart?

Excellent question. What I can say with certainty is that if dark energy behaves like a cosmological constant or a constant vacuum energy density, the expansion of the universe will approach an exponential expansion once matter and radiation are so dilute as to be negligible (this is almost already the case). In that picture the universe will remain in a similar rate of expansion as we have now

Scale ~ e^Ht

but then with a forever constant hubble parameter H which would be similar to the one now. The expansion forces felt by matter in this universe will. not be growing with this scale factor but more or less remain constant like H, so they should remain as weak as they are now and therefore remain irrelevant on the scale of the solar system.

A so called big rip scenario where the forces of expansion act on shorter and shorter scales require exotic forms of dark energy beyond an ordinary cosmological constant, something which provokes a faster than exponential expansion (maybe something like e^(t^2)). But there is no evidence for that yet.