That is how it works, yes. The Earth-Sun system emits gravitational waves and is losing energy.
Or more notably, the binary pulsar, which won its discoverers the Nobel Prize.
But one can still posit a rapidly occurring event far away that changes the mass of a large object, and ask a meaningful question about how long it takes the gravitational effect to propagate. For example, the sun exploding, or a fast-moving massive object colliding and merging with it.
My own simplistic way of looking at it is that the speed of gravity has no material constraint, just like light in a vacuum has no material constraint, unlike the propagation of wave energy in a substance which is governed by the physical properties of the substance. But, it still has to obey the relativistic laws that define the nature of simultaneity and causality in spacetime, just as light does, which includes any kind of effect or information. Thus, if the sun suddenly exploded, the earth would feel the lessening of gravity and start to fly off into space at precisely the same time that we saw the event, about 8.3 minutes after it happened. Until then it would continue serenely in its usual orbit, because from our reference frame, the sun was still there!
If the Sun exploded, it’d take longer than that to feel the effects, because the Sun’s mass isn’t changed. If the explosion were spherically symmetrical, then the change in gravity would happen right as the spreading debris from the explosion passed us (with some of it probably hitting us in the process), and since that’s matter moving, it’d have to be slower than c.
Wouldn’t the change in gravitational influence from the matter moving towards us affect us earlier than the change for matter moving away?
For simplicity’s sake, say we have an object 1ly away with mass M affecting us with a gravitational pull of F. It is very large, we’re very small and we are in effect in a circular orbit.
The object explodes into two parts with direction directly towards us and directly away, and a speed of 0.1 c. At the time two seconds (as observed by us) after the explosion we will observe, and experience the gravitational pull of, the two parts as being 1.182ly away and 0.778ly away, for a total gravitational pull of:
F/(21.182^2) + F/(20.778^2) = 1.184F
Are we neglecting the dynamics of explosion, though? The Sun is stable because of thermal/gravitational balance. For it to explode, it would have to become unbalanced, which means it would have to compress: all explosions are preceded by compression. This would change the profile of the gravity well, to a very small degree, over, probably, a relatively long period of time compared to the interval of the explosion. The Earth would experience a very subtle reduction in solar gravity, causing it to move very slightly outward prior to the explosion event.
If the explosion were spherically symmetric, then it woudn’t matter. Outside of a spherically-symmetric mass distribution, the gravitational field (curvature, metric, whatever else you care to matter) depends only on the total mass. The gravitational field of the Sun is the same as the gravitational field of a one-solar-mass black hole (in fact, the Schwarzschild metric was originally developed to describe the gravitational field of stars; the theoretical prediction of black holes came when someone noticed that the metric got weird for very small objects).
Oh, and Triskadecamus, I’m not sure what SLUGGO is supposed to be an acronym for, but the next working gravitational wave detectors will be KAGRA and LIGO India. Or possibly GEO, but I have my doubts that they’ll ever get anything useful out of that one. LIGO India will, as the name implies, be the same design as LIGO Hanford and LIGO Livingston, just placed on the other side of the world (there are significant advantages to spreading them out). There were at one time plans for another one in Australia and possibly somewhere in South America, but the funding didn’t materialize. KAGRA (in Japan) is a different design, and in many ways better than LIGO, but it’s new enough that it’s taking them a while to get all the details worked out (just like it did for LIGO).
It does appear to matter if the sphere is changing shape and gravity has a finite speed though. You couldn’t integrate over the actual shape of the mass, since the gravitational influence of the various bits take longer the further away they are, and since the bits are now moving, the apparent shape they form in aggregate is no longer spherical.
Neither do I 
!
But it would be nifty.
Southern Latitude Undersea (help me out here) Graviton Observatory?
Tris
C’mon, these are the same folks who gave us strange quarks and a galaxy named Snickers!
Southern Latitude Undersea Geolocating Graviton Observatory?
Naah, no way geolocating is actually be a part of it.
Space Laser Unified Granularity Gravitational Observatory
or maybe the memorial
Stephen’s Lachrymose Ululating Gryphon …
OK, now you’ve got me wondering about this, too: The closer half of a star collapsing should be indistinguishable from the entire star collapsing, at least for a few moments when you can’t yet tell whether the far half is collapsing… but one of those is spherically symmetric, and the other isn’t. I think that the key lies in the forces that are causing (or preventing) the star to collapse: Not just mass but also pressure is a source of gravity, and so the effect of those forces might compensate for the changes from the mass.
Oh, and the U in “Sluggo” could plausibly be “underground”. One of the improvements in KAGRA is putting it deep underground to help isolate it from potential noise sources. And given the value in having instruments spread across the globe, “southern latitude” is pretty good for SL. So now we just have one extra G to account for.
Got it, we just make sure it’s all on the Gawler Craton, in Austrailia!
Southern Latitude Underground Growler Graviton Observatory.
Do they need another one there?
Tris
If we build it, they will . . . groan.
“So why is the facility underwater?”
“We needed a U.”
“Underground?”
:smack:
Heh!
I wouldn’t put it past some physicists. When Alpher and Gamow published their groundbreaking paper on the Big Bang, they invited Hans Bethe in as co-author, just so the author list would be αβγ.
The way I heard it, Alpher was not happy that Gamow invited Bethe to join the paper, since the gimmick would naturally lead to Alpher (the most junior by far) being overshadowed.
Cite https://www.npr.org/templates/story/story.php?storyId=4505414
“Not surprisingly, Alpher took exception. He feared that crediting Bethe would diminish how the rest of world perceived his own contribution to the research. Alpher’s name was already overshadowed by Gamow’s co-authorship, because Alpher was the young Ph.D. student and Gamow the famous physicist, and adding Bethe’s even more eminent name would only make things worse for him. Alpher had done more than his fair share of the work, and now it seemed that he was going to receive only a tiny fraction of the credit.”