As far as I can make out from that post and the rest of your blog, you seem to reject Newtonian gravitation...

Reject Newtonian gravitation?

Why would I reject a meaningless concept such as “Newtonian gravitation?”

Newton did not know “Newtonian gravitation.” There is no “Newton’s constant of gravitation G” in the Principia. There are no equations in the Principia... “Newtonian gravitation” is an invention of Newtonian physicists.

My point is that if you want to understand the concept of force; look at its origins in Newton’s writings. Why? Because academic physics is a legal system. In legal systems, once a “law” enters the system, and it is canonized that law can never be removed from the system. The legal system of physics must remain consistent. This is the reason why Einstein’s Field Equations which claim to describe a nature without force has Newton’s constant of force G in them. Only in a legal system an equation denying force can have the unit of force in it.

As you can see from reading the comments in this thread by otherwise intelligent people they are utterly confused about what force is because they take the authority of physics as the absolute truth; and physics teaches nothing but the legal concepts of physics; in a legal system there is no right or wrong, or true and untrue, the truth table is not valid and there is no and/or; there is only legal and not legal.

Consequently, in a legal system, every concept comes in triplicates:

1. the letter interpretation of the law;
2. the spirit interpretation of the law; and
3. combination of letter and spirit interpretation of the law.

So, in physics it is legal to state

1. “force exists”;
2. “force does not exist”, and
3. “force existsnot”.

These are all legal statements in physics. If you try to conform your research on force to physics, you can only write a commentary on the concept of force in physics. The original article is a commentary on force in physics; it is a legal document.

...in favor of Kepler's laws of planetary orbits.

You see how much the Newtonian worldview is innate in your reasoning. You can only perceive nature in Newtonian terms. “Kepler’s laws” is the invention of Newton’s disciples who now call themselves physicists. Newton did not call “Kepler’s Rule” “Kepler’s Third Law.”

Kepler’s Rule is a rule, because it is a proportionality which ties the radius of an orbit to its period. Newton used Kepler’s rule to compute planetary orbits; this is what my blog is about. If you disagree; or you believe that my math is wrong, I cannot be happier to know that. But do not try to dismiss what I write by throwing Newtonian mythology at it.

How does your model account for the perturbations that are observed in three-body and more complex systems?

Again, you are using post-Newtonian notions invented by Newton’s disciples the physicists. You are assuming, when you write “three-body system”, that the world is Newtonian, and the three bodies in question interact according Newtonian occult force.

The world is not Newtonian.

Newton dealt with perturbations in the Principia in proposition III.13 http://science1.wordpress.com/2008/11/11/the-cause-of-saturn...
So the myth that “perturbation” is a dynamical phenomenon goes back to that proposition in the Principia.

What is perturbation and how does astronomy account for perturbations?

There is only 1 way to make orbit calculations in astronomy: define a model; make observations; subtract observations from the model to obtain residuals. This is it. There is no other way. This is how astronomical calculations are made. Anyone who claims otherwise is a charlatan.

The residuals are the perturbations. So for example: if your model is the Ptolemaic model; and you make a table of naked-eye observations, and take residuals you will find that your residuals are close to zero; Ptolemaic theory explains planetary orbits perfectly well for the naked eye observations.

Now take the residuals of Ptolemaic theory with the telescopic observations of planets and you will see sinusoidal “perturbations.” How do you account for these perturbations? You add new terms to your model to eliminate the perturbations. This is usually done with trigonometric expansions. There is no other way; you must add new terms to your model to account for perturbations. There is no Newtonian magic or occult force that explains these perturbations. This is where the hoax is.

So take a look at the proposition III.13 and you will see that Newton’s explanation is geometrical, not dynamical. This is why “Newtonian gravitation” is a hoax. Newton used Kepler’s Rule to compute orbits but he claimed to have used his dynamical force instead. http://science1.wordpress.com/2007/08/20/periodic-reminder-o...

For instance, right now there is a satellite called SOHO at the Sun-Earth L_1 Lagrangian point.
Why do you say that Newtonian gravity is a myth, when the existence of such an orbit violates Kepler's third law but is in perfect agreement with calculations according to the Newtonian model?

Can you tell me how Lagrangian point violates “Kepler’s Rule”? Can you compute Lagrangian points by using Kepler’s Rule only?

And conversely, can you compute Lagrangian points without using Kepler’s Rule? No you can’t. If you can let me know.

What physicists do, is to express Kepler’s Rule in Newtonian units such as GM http://science1.wordpress.com/2008/12/17/is-newtons-constant...
and they claim that because they used a conventional unit of their own invention and named it after their master Newton, they used Newtonian dynamical force in astronomical calculations. If this is not a hoax what is it?

Take a look at Lagrange’s original paper here: http://gallica.bnf.fr/ark:/12148/bpt6k229225j/f231 He states his goal as to calculate the orbit of three bodies by nothing but the distances between them.

This is the definition of Kepler’s Rule.

But Lagrange must still conform to Newtonian doctrines so he adds A, B, C as the “mass” of bodies A, B, C. But “mass” exists only to scale the calculations. Once you realize that mass in the Newtonian lingo is the constant term R03/T02; in other words, “mass” is the ratio of two lengths and it serves only to set the scale, you will see that Lagrange’s original equations do not concern themselves with Newtonian force; force terms exist only as cosmetic terms either eliminated or used as scaling units.

From Newton to the present day, physicists compute orbits by using Kepler’s Rule but claim to have used Newton’s dynamical terms. All we have to do is to look at the equations, ignore what Newton’s disciples write in their commentary; look at the equations.

Can you look at this calculation http://www-istp.gsfc.nasa.gov/stargaze/Slagrang.htm
and compute L1 by using Kepler’s Rule only?

Try it. All you have to do is to eliminate Newtonian labels G, M, m and F from formulas and use Kepler’s Rule directly: http://science1.wordpress.com/2011/04/10/computation-of-lagr...