Kaptain K’s statement attempted to claim that Newton’s first law was not valid for two globes connected by a cord and rotating about their common center of gravity. To the best of my knowledge gravitational radiation has not been detected directly. The evidence for that radiation is indirect: e.g. an eight-hour period of a binary pulsar system observed to be decreasing by 75 microseconds per year. If that system existed and began its rotation 15 billion years ago, it would have lost only about one one-thousandth of its angular velocity by now.

So when he says that Newton's globes would lose angular velocity via gravitational radiation, his claim that therefore Newton's first law doesn't apply to his globes seems like hair-splitting of some hairs that are already very, very fine. For all we know a similar argument might be made against Newton’s first law really applying to linear motion of a body. A more fundamental refutation of Kaptain K’s claim follows.

The laws of angular motion are analogs of Newton’s three laws of linear motion. Here is the first law for rotating motion. A body in rotation will continue to turn about a fixed axis with unaltered angular velocity unless acted upon by an external torque-producing force.

Note that the first law for rotating motion does not restrict the shape of the body in rotation. That body could have a rigid dumbbell shape, or could have a wire-like section connecting the two globular ends. Thus, there is no reason that Newton’ globes and cord would not be subject to the same law.

In A JOURNEY BEYOND THE UNIVERSE the existence of gravity waves and gravitational radiation arises without recourse to relativity theory. Let us examine their relationship to Newton’s globes. In order to support wave motion a medium must present a finite, non-zero impedance to the generation and propagation of the wave. That impedance represents a real, physical force to be worked against in those processes. Both zero impedance and infinite impedance preclude any energy transfer. The impedance of free space is a well-understood and quantified property (377 ohms) for electromagnetic radiation. The force associated with the impedance of space for gravitational radiation would have to act against the globes’ motion in order for energy transfer to result in the generation of gravity waves. That force is certainly external to Newton’s globes; and therefore, Newton’s first law (in the form of its analog for angular motion) remains valid for Newton’s globes and cord..

On 2002-07-18, in reply to my asking where the angular momentum lost by Newton’s globes would reappear for conservation, Kaptain K wrote:
The question is deeper than a superficial reading of it might suggest. Certainly anything carried away from the globes must be carried by gravitational radiation. Since the energy transported by the wave will be related to the amplitude of the wave, we can look to the amplitude for the energy. The angular velocity of the globes will appear as the frequency of the wave. How will the wave carry the angular momentum?

Think of the question in reverse. Assume a gravity wave detector aimed at a right angle to an approaching gravity wave front. When the wave passes through the detector we would expect the detector to oscillate in the propagation direction of the wave. The magnitude of the oscillation would be proportional to the amplitude of the wave. The frequency of the oscillation (with a compliant detector) would be that of the wave. The wave has given up some of its energy in moving the detector. How would the wave transfer the corresponding quantity of angular momentum to the detector? In other words, how would the wave produce torque on the detector?

Although both quantum mechanics and wave mechanics preclude the continuous loss of energy to which you refer, they do not preclude the balancing of electrostatic attraction by centrifugal force in the allowed orbits. If the quantum number is greater than 10,000 for the electron orbiting the hydrogen atom, the frequencies of the emitted light calculated by quantum mechanics and classical mechanics differ by only 0.015%.
Perhaps there has not been a response because the questions were put too obliquely. Let me reframe the issue in a direct form and address it to the ‘centrifugal-force-is-not-real-camp’ whose members include DaveC, jumbo, Kaptain K, ljbrs, Ring, and Wiley. Do you still claim that centrifugal force is not a real force? If you answer yes, then what forces compressed the spring? If you are undecided, let us know the nature of your dilemma. Maybe we can help you resolve it.