I don’t understand this:

If Newton’s force has been proved to be unphysical and non-existent by physicists themselves why are we still bound by 18th century derivations involving force?

The only answer to this can be that Newton’s occult and non-existent force has pedagogical value because it is simpler to teach than General Relativity.

But does this justify experimental observation of the Newtonian occult and non-existent force in class with a Cavendish pendulum? If physicists proved Newtonian force to be unphysical how do they measure it in a physical experiment? Can you measure an unphysical force that exists only pedagogically in a physical experiment?

I say no. To me this suggests a bureaucratic habit. Schools continue to teach the Cavendish lab because they always have. This cannot be allowed to happen in an experimental science such as physics.

The other pedagogical advantage is, as physicists put it, “Newton’s laws and Newton’s mechanics work well in the solar system and in systems moving much slower than the speed of light.” In other words, Newton still works in its domain.

This claim is based on the assumption that

is Newtons law or Newtonian mechanics or, when it’s written as a function of coordinates, Newton’s equation of motion.

I don’t see any terms that make

a Newtonian expression.

As I’ve shown in my previous post

is Kepler’s rule written with a conventional unit.

We know that even though G is called Newton’s constant it has no Newtonian content. G is Newtonian in name only.

G is a unit conversion factor that appears in various places in physics, for instance, in Einstein’s equations. The fact that G appears in Einstein’s equations does not make Einstein’s equations Newton’s equations. We don’t say Einstein’s equations are Newton’s laws or Newton’s equations because G appears in them.

I’ve shown here that G is what is now called the Gaussian constant of gravitation k^{2}

This substitution was made in the late 19th century. Therefore G added nothing new to Kepler’s rule.

The substitution

is a cosmetic and political substitution, a mere name change, effected by British physicists to claim ownership of astronomical constants by expressing k^{2} in British units and in a British/Newtonian name.

G is not a constant of nature without which physics will fail to work. On the contrary dropping G from equations or setting it to unity will have no effect in physics. It doesn’t matter if G is written or not because G is a political symbol not a constant of nature. Physics is independent of political symbols.

And mass M is defined as the constant term in Kepler’s rule

G and M always appear as a single constant in astronomy, so, one of them or even both must be decorative.

GM is physicists’ polemical solution to fix the unit term in Kepler’s rule cosmetically as a Newtonian constant of nature

Physicists defined the constant term in Kepler’s rule as GM and have been enforcing it as a true constant. This way of branding geometric elements or mathematical objects in order to own them has always been the method used by physicists.

In this case renaming k^{2} “G” and naming G “Newton’s constant of universal gravitation” did not make R_{0}^{3}/T_{0}^{2} physical or Newtonian because

The fundamental quantity is Keplerian constant R_{0}^{3}/T_{0}^{2}.

k^{2} and GM are specific unit conventions that physicists at various times asserted as true units.

k^{2} and GM are only conventional units because any astronomical quantity that can be computed with k^{2} and GM can also be computed without them by choosing any unit for R_{0}^{3}/T_{0}^{2}.

And this is what Newton did. Newton did not use k^{2} or GM or any named unit but he used his own unit for R_{0}^{3}/T_{0}^{2}.

Unit means that a given distance is kept constant and other distances are counted with that distance which is kept constant as a unit.

G is a conventional defined unit created by converting k^{2} into British units which was then established by propaganda as a true constant of nature.

Physicists reject this historical evidence because they consider experimental evidence stronger than historical evidence. But historical habits can only be refuted by historical evidence. Historical habits cannot be refuted by physical experiments. And experiments physicists use to measure G are historical and professional habits and not true experiments.

All Cavendish type experiments apparently measuring the value of G are circular experiments.

How can the true nature of G be decided one way or the other?

To summarize:

I say that G is a conventional unit defined in the 19th century and I offer historical evidence.

G was not observed in an experiment first. It was not discovered. G was defined to replace k^{2} then used as the value of R_{0}^{3}/T_{0}^{2}.

Then I show that physicists’ claim that G was first measured by Cavendish in 1798 and later with ever increasing precision in countless Cavendish type experiments of many sizes and shapes is wrong.

Cavendish experiment and all Cavendish type experiments claiming to measure G are circular. Physicists already know the value of G and build an oscillator that will oscillate with a natural period to give the known value of G. The rest is error analysis.

So if I put 10 peanuts in a bag, shake it, and count the peanuts, there will be 10 peanuts. Nothing of value can be derived from a circular experiment. In Cavendish type experiments physicists find what they put into the experiment.

I also noticed that physicists always offer the consistency of physics as proof that the branded labels of physics such as G are true and physical and natural quantities.

I reject this type of argument by authority.

The most that physicists will concede is that in simple circular orbits Kepler’s rule may be good enough but when perturbations must be included then Newton’s force and mass must be used.

To this I reply that Newton used Kepler’s rule in proposition III.13 to compute perturbations of Saturn’s orbit by Jupiter.

This makes sense because physicists themselves recognise that force is unphysical and dismiss it. If force is unphysical it can no longer be used as an explanation. But physicists keep using force as an explanation because force remains a valid professional habit.

No force terms ever appear in the operational formula which is Kepler’s rule and Kepler’s rule does not contain force.

Instead of starting directly from Kepler’s rule physicists write force terms and eliminate them to obtain Kepler’s rule. Strange behavior that appears to be a ceremonial professional habit devoid of any scientific content.

My proposition is that Newton’s laws, Newtonian mechanics and Newton’s equation of motion, Newton’s constant, Newton’s force and Newton’s mass are not needed and are not used in astronomy in practice.

If so, why do they exist?

How can physicists claim to measure in experiments the occult force they themselves found to be unphysical?

Can we establish an independent committee to define clear standards of evidence to find out if G is a defined unit marketed as a true constant of nature to save Newton’s authority or if it is a true constant of nature measured in true experiments?

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If G were a “constant of nature” not merely a conventional unit by physicists we could compute astronomical orbits without using G as is done here.