Agreed; it's very serendipitous that you can basically light up a room with the gravitational energy that the sun/earth pair radiate out into space.

Light up 1 room with an incandescent bulb, or your entire flat with LED bulbs nowadays. I would be very interested in seeing some napkin math, based on power efficiency progress and "rate of technological innovation", that attempted to project when we could feasibly run the equivalent of our present-day human civilization purely off of gravitational waves/radiation.

Can I ask how you got there? G^4/c^5 makes sense, but the rest loses me.

(Eventually after all the typing below I think that I traced the 32/5 and (M1*M2)^2 * (M1 + M2) to (eqn 16) in Peters & Matthews 1963 maybe? (e=0, a->r) https://doi.org/10.1103/PhysRev.131.435 (stick sci-hub.se in front of that if you need to). The authors take an approach comparable to the textbooks below.)

Super-quick textbook review. Practically all of them start with the quadrupole moment and try to justify an energy which is quadratic in derivatives of that while still within a linear theory. Carroll and Mathtias Blau take slightly different-from-each-other paths through the transverse-traceless TT-gauge to P = dE/dt = -2/5 \frac{G^4 M^5}{r^5} (c=1) for a circular equal-mass soft binary. Wald uses the radiation gauge and so eqn 4.4.58 looks fairly different, and comes with the amusing Waldian line "A lengthy calculation (where many terms which integrate to zero are dropped) yields the final result,". Sigh. Blau's development looks a lot like MTW, but the latter gives us .... Exercise 36.6 ("Apply the full formalism ... to a binary star system with circular orbits. Calculate ... the total power radiated; the total angular momentum radiated ..."). Gee, thanks thick textbook. FWIW, 90 seconds of that (mostly trying to make sure both sides have the same dimension rather than extracting a power in watts because bad/lazy reasons and anyway I always think you had about the right order of magnitude) doesn't take me to anything like the form of your calculation.

Rather than flip through other textbooks, let me rely on my maybe-shaky memory and say that most of them, at least the modern editions, follow the TT gauge approach and come up with an equation in a form similar to Carroll.

What stands out here is that Earth-sun has a large mass ratio and noncircular orbit, and it's not really a binary system anyway, and so will defy these textbook schemes. Secondly all of these take P in the far field, because linearization. (Compare that with your edit).

I also got way off into the weeds wanting to work with chirp mass (rather than q=m_1/m_2) which is what GW obs data analyses use because extracting the individual masses is hard. I also know a bit about EMRI BHBs (extreme mass-ratio inspiral) and in those dissipation is dealt with differently from textbooks even for soft binaries (e.g. soft->hard roughly PN & perturbative methods, EOB, GSF, numrel) absolutely none of which is of immediate practical use here.

So that's some of what motivates my question about the origin of your calculation.

ETA: I think most of what happened here is that my brain reads equations as words, and I simply forgot that I could actually rearrange teh ltteres! TGIF :-)

I used a paper from 1968 ( https://doi.org/10.1098/rspa.1968.0004 ), and treating the centripetal acceleration due to orbital motion as uniform acceleration. It's good enough for the Earth-Sun system, but it'll fail in the case of something like close orbiting pulsars.