[Bogie_smiles (OP)]

A question regarding gravitational waves:

Einstein predicted gravitational waves, and they have been detected by several large-scale interferometers, LIGO and ESA for example. The basis of the application of the interferometer apparatus to the detection of massive gravitational waves traversing space is that there is detectible energy produced by the relative motion of massive objects to each other. That is to say that the amount of energy detected as gravitation wave energy by the interferometer would come from very massive events in space like the in-swirling death spiral of two blackholes, detected as the resulting energy passes the location of the interferometer itself (the location of the observation).

Though we can detect gravitational wave energy from very massive events, isn’t it logical that any relative motion between objects with mass in space will generate gravitational waves? An example would an apple falling from a tree; wouldn’t that event produce an extremely tiny and as yet unmeasurable amount of gravitational wave energy, based on the fact that there is relative motion between the apple and earth?

[Kryptid]

Yes, even small objects can release gravitational radiation when they accelerate (so long as they have a gravitational quadrupole moment, that is): https://en.wikipedia.org/wiki/Quadrupole#Gravitational_quadrupole

[Bogie_smiles (OP)]

As Kryptid points out via the link in his reply, an accelerated object emits gravitational wave energy (the equations to quantify the gravitational wave energy are provided in the link). So in regard to my example of an apple falling to earth, the apple is being accelerated by the gravitational field of Earth (and incidentally, the Earth is being accelerated toward the apple in the most insignificant way as well).


A related question comes to mind:

If accelerated objects emit gravitational waves, and gravity is said to have an infinite reach, is it fair to say that all space would contain gravitational wave energy, coming and going in all directions, from a potentially infinite history of the relative motion of celestial objects?

[Halc]

If accelerated objects emit gravitational waves, and gravity is said to have an infinite reach, is it fair to say that all space would contain gravitational wave energy, coming and going in all directions, from a potentially infinite history of the relative motion of celestial objects?

All space does contain gravitational wave energy simply because all space is near accelerating objects.  But gravity waves travel at light speed, so a given event can only reach as far as the event horizon, just like light.
Gravity on the other hand is a field and does not propagate at some speed, so gravity has no finite bound to its effect.
Information can be transmitted via gravity waves, but not via gravity.

[Bogie_smiles (OP)]

If accelerated objects emit gravitational waves, and gravity is said to have an infinite reach, is it fair to say that all space would contain gravitational wave energy, coming and going in all directions, from a potentially infinite history of the relative motion of celestial objects?

All space does contain gravitational wave energy simply because all space is near accelerating objects.  But gravity waves travel at light speed, so a given event can only reach as far as the event horizon, just like light.
Gravity on the other hand is a field and does not propagate at some speed, so gravity has no finite bound to its effect.
Information can be transmitted via gravity waves, but not via gravity.

Thank you, Halc, that is an appropriate clarification, and to reflect your points, I would amend my statement as follows:
 
“Since accelerated objects emit gravitational waves at the speed of light, and therefore gravity is said to have an ever expanding reach, it seems fair to postulate that all locations in space would contain fluctuating levels of gravitational wave energy that influence the relative motion of the surrounding celestial objects.”

That is still open to amendment, but I’m just saying that the influence that gravitational wave energy in space displays is an ever changing dynamic. It seems logical that there is a “mechanism” involved that governs that ever changing dynamic. I would refer to that mechanism as the “cause of gravity” which leads to the question, what is the mechanism at work when objects are accelerated by gravity?

The “mechanism” must have to do with the gravitational wave energy emissions from the massive objects themselves, so, are the gravitational emissions from massive objects the source of the “information” that governs the effect that the relative motion of celestial objects have on each other, i.e., the cause of gravity, and how do the mechanics of that influence work?

[evan_au]

the gravitational emissions from massive objects

By "massive objects" in this context, we are talking about neutron stars and black holes.
- In their last few milliseconds, we have seen orbiting black holes (initially just kilometers apart) convert the mass of the Sun into gravitational waves.
- Howevever, even the Earth on it's orbit for billions of years has been continuously radiating about 200W of gravitational waves. The mass is much smaller, and the distance is much greater. But this radiation is too subtle for us to measure using any currently conceivable method.
- It is thought that the Big Bang would have created gravitational waves at very high frequencies, and a team in China is actually searching for these "relic" gravitational waves.

So if you are looking for gravitational influences, there is nothing special about "massive" objects more than "non-massive" ones like the Earth.
- But if you are looking for one impetus that is more significant than the others, have a look at the Big Bang.
See: https://en.wikipedia.org/wiki/Gravitational_wave#Resonant_antennae

all locations in space would contain fluctuating levels of gravitational wave energy that influence the relative motion of the surrounding celestial objects.”
It seems logical that there is a “mechanism” involved that governs that ever changing dynamic. I would refer to that mechanism as the “cause of gravity”

I think you have cause and effect backwards.

The orbits of objects under gravity can be viewed in Einstein's relativity as travelling in "straight lines" (a geodesic) on the curved surface of spacetime. As objects move on this curved surface, they are accelerated, and emit gravitational waves.

Now the universe is filled with moving objects - galaxies, stars, black holes, planets and apples, all moving under the influence of gravity. This motion is the effect of gravity.
- A these objects are emitting gravitational waves with different frequency, intensity, phase, location and inspiral rate. This radiation is the effect of motion in a gravitational field. 

If we had a sufficiently sensitive detector, we would detect a cacophony of gravitational waves from all these sources (including the Big Bang), creating a "white noise" of sources that are hard to distinguish.
- A Fourier transform will easily separate out the closer sources with different frequencies
- As the Earth moves around the Sun, the relative phases of the sources will vary, enabling separation of sources with the same frequency
- Waiting a bit longer,  sources which are spiralling inwards at different rates will separate in frequency, allowing them to be distinguished.

This cacophony is expected to be the limiting factor in the sensitivity of the eLISA gravitational wave detector.
See: https://en.wikipedia.org/wiki/Laser_Interferometer_Space_Antenna#Gravitational_wave_background

[Colin2B]

Since accelerated objects emit gravitational waves at the speed of light, and therefore gravity is said to have an ever expanding reach, it seems fair to postulate that all locations in space would contain fluctuating levels of gravitational wave energy that influence the relative motion of the surrounding celestial objects.”

I think there is a danger here of confusing 2 related but different things, the gravitational field and gravitational waves.
The gravitational field is due to a mass and gravitational waves are a propagating disturbance/oscillation of this field in much the same way that light is a disturbance/oscillation of the em field. The gravitational waves are not strong enough to influence the motion of celestial objects, but the gravitational field is.
Changes to a gravitational field (caused by a moving mass) propagate at the speed of light, but in a somewhat surprising way that means the force experienced by a test mass will always point to the current position of the moving mass rather than it’s position x light seconds ago. Below is a popsci article that explains what happens and below that I’ve compared it with a similar effect due to a moving charge.

https://medium.com/starts-with-a-bang/what-is-the-speed-of-gravity-8ada2eb08430

There are similarities between em radiation and gravity and comparisons can be made which help us to understand them better.
Let’s start with the field surrounding an electron. A test +ve charge will be attracted to the electrons position. We know that the electric field propagates at light speed, but if the electron is moving the test charge will move towards the current position of the electron, not where it was. In this way the field behaves in a similar way to gravity.
What is less well known is that if the electron changes velocity the test charge will move towards the position the electron would have been at had it not accelerated, until such time as the change in the field propagates to the test charge’s position. How does the test charge know where the electron will be? I can offer an analogy that shows that this behaviour of fields is not so mysterious.
Imagine a boat crossing a lake, the bow wave propagates away from the boat, but even at some distance from the boat the crests point to the boat’s current position (almost,  because waves in water don’t propagate exactly as do em waves). If the boat changes direction it will take time for the change to propagate to the observer, and until it does the bow wave will point to the predicted position of the boat had it not changed course.
In the case of the accelerating electron we know the speed at which the change propagates, because the change causes a discontinuity in the field which we detect as em radiation - light, radio etc (and if we have a quantum detector we can say we detected a photon).  We can describe the electron field at any point as being dependent on the history of both the position and derivative of position (velocity) of the electron.
A similar effect occurs with gravity. As @Halc pointed out, the force felt by the moon is directed to the current position of the earth rather than it’s historical position. This led early researcher to conclude that the speed of gravity was either instantaneous or extremely fast whereas it does not need to be for similar reasons as I have described for the electron.
It’s worth pointing out that the gravity situation is slightly more complex because there is a higher order effect which allows the masses to ‘point’ towards each other’s current positions despite both being in non-linear motion around a common centre of mass. This higher order effect is also why em waves are dipole and gravitational waves are quadrupole. It also means that gravitational waves cannot be produced by a simple acceleration of a single mass. However, the gravitational waves we have detected (which are analogous to the em radiation of the electron) show that the speed of propagation, and hence the speed at which gravity changes propagate, is as close to light speed as can be measured.

EDIT Whoops, @evan_au was posting as I was typing.

[Bogie_smiles (OP)]

Many thanks to @evan_au and @Colin2B for those great responses.