Sally, you're failing to make the distinction between gravity and
'gravitational waves', which are two different critters.
No I'm not failing to make a distinction between them. I'm fully aware that
they would propagate outward from the oscillating source mass at C and I'm
aware of the distinction between gravity waves and gravity fields. I'm also
aware that they might be detected by small longitudinal changes in
dimensions of matter as they pass through it. So far, though, no experiment
has detected such waves. Presumably, current experiments are not sensitive
enough.

GW radiation
(if it's real) arises from oscillating masses or massive gravitational
events, and propagates as a longitudinal (compression-rarefaction) wave
(vis-a-vis EM radiation which propagates as a transverse wave, making it
subject to polarization).
As an aside, EM radiation contains two components, hence the name. I'm not
aware of more than one field component in the GW model, or the need for one.

GW radiation could more correctly be called a
'spatial acoustic pressure wave' in the fabric of space, propagating at
c. "Gravity-wave particles", or gravitons, would not be needed at all.
BUT if you believe space is functionally void (which
the mainstream almost universally does), then you do need the "messenger
particles"- flying photons, gravitons etc. to explain radiation thru
'nothingness'.
Yes, but...

There is at least one other option...we know that, at the quantum level, the
locations of particles can be "smeared" so that their position is not well
defined. One small modification to the math results in all particles being
smeared and having some minute chance of existing *anywhere*. According to
this view every particle is "smeared" throughout all of existence. They are
all touching and there is no such thing as "distance" and messengers are not
needed. The awkwardness of "action at a distance" through the void is no
longer needed.

Back to the distinction between gravity and GW
radiation- the distinction remains in place whether you believe in
void-space or the flowing-space model of gravity. Gravity remains a
centerward-bearing 'field', while GW radiation remains an outward-bound
flow of waves (or under void-space, "gravitons"). Don't feel bad- the
mainstream literature usually blurs the distinction, too, between
gravity and "gravity waves".
I don't feel bad, your paragraph is pretty much my understanding of the
concept.

In a previous reply to Bert, I suggested picturing the Earth-moon system
in side-on view to illustrate the pendulum idea. But since every
co-orbiting system presumably radiates GW energy, would not a
mechanically-frictionless pendulum also radiate GW energy? Though
miniscule, it would still represent a dissapative loss that will
eventually 'run down' the system. What do you think?
Yes, and if Bert had suggested that I may have agreed, but only after
allowing for a change in our original model to accept that specific
none-Newtonian dissipative feature. I was sort of skirting around the
subject of energy dissipation via GWs when I mentioned extreme accelerations
and masses falling into black holes a few posts back. I didn't pursue that
line of discussion at the time because we were still talking Newtonian
physics..at least..I was g. Bert...you reading this ?

It would seem to me that some of the energy of any object falling into a BH
would be radiated as a spike of gravitational energy. This would be more
like a gravitational shock wave than the continuous waves produced by
oscillating masses and I believe that if GWs are ever detected it will be as
these relatively strong single pulses long before GWs from orbiting masses
are ever detected.

Sally