johnreed 1st addendum to "johnreed Catch 22" - June 6, 2007

Kepler's laws are thought to be the consequence of Newton's universal
law of gravitation. I will show in this post that this is incorrect.
I
will show that Kepler's laws follow from the efficient, least action
motion, common to stable systems in our universe. I will show that
Newton's universal law of gravitation operates within, and in fact
co-
opts, this least action motion.

Isaac Newton defined centripetal force in terms of his second and
third law, to act at a distance, by setting his first law object on
an
imaginary circular path of motion, at a constant orbital speed. Note
a
perfect circle and perfect motion. Newton allowed the moving inertial
object to impact the internal side of the circle circumference at
equidistant points to inscribe a regular polygon. He dropped a radius
to the center of the polygon from each vertex (B) of the polygon to
describe any number of equal area triangles. "...but when the body is
arrived at B, suppose that a centripetal force acts at once with a
great impulse..."(Principia)

To argue for his supposition, Newton took the triangle base length,
toward the infinitessimal limit approaching zero. The base length,
and
the infinitesimal arc of the velocity driven and time consuming
trajectory of the moving inertial object, can then be represented as
arbitrarily close in length as desired. The velocity acceleration
vector (v/t), or (dv/dt) at the vertex (B), is by definition
consistent with the continuous and efficient curvature of the circle,
and is ultimately directed along the radius toward the center of the
circle and represented as centripetal acceleration (v^2/r). This
time-
space mathematical property of the perfect circle and perfect motion
serves as the assigned carrier for "inertial" mass, as the cause of
the defined centripetal acceleration and is designated as centripetal
force (mv^2/r). Note again that Newton used a perfect circle and
perfect motion to derive his supposition for a mass driven
centripetal
force from instantaneous acceleration where the only change in
velocity is direction.

Here the equal areas in equal times falls out of the perfect orbit as
a mathematical artifact of the efficient area enclosing circle itself
(See Take II). This efficient property of the circle is reflected in
the real elliptical orbits as Kepler's law of areas, where velocity
includes both magnitude and direction, such that the efficient area
enclosing property of the orbit is maintained [1].

Newton generalized the efficient equal areas in equal times property
of the supposedly mass driven perfect circular path, together with
his
centripetal force, to any curved path directed radially around a
point. "Every body that moves in any curve line... described by a
radius drawn to a point... and describes about that point areas
proportional to the times is urged by a centripetal force... to that
point." (Principia)

Newton extends the mass generated property to include the trajectory
of two bodies in elliptical orbit. "Every body, that by a radius
drawn
to the center of another body... and describes areas about that
center
proportional to the times, is urged by a force..." (Principia)

Newton ties his "least action" mathematical model for a supposed mass
driven centripetal force to gravity. "For if a body by means of its
gravity revolves in a circle concentric to the earth, this gravity is
the centripetal force of that body."(Principia). Note that Newton
accepts the resistance he feels and calls gravity, as a fundamental
given, (mass driven) force.

It is of special significance that Newton generalized Kepler's law of
areas to the entire universe as the carrier for his mass driven
centripetal force. "...because the equable description of areas
indicates that a center is respected by that force... by which it is
drawn back... and retained in its orbit; why may we not be allowed...
to use the equable description of areas as an indication of a center
about which all motion is performed in free space?" (Principia).

A circular orbit implies a centripetal force. However it does not
necessarily imply a mass generated centripetal force, nor does it
necessarily imply a centripetal force of the type we feel. The fact
that we can quantify the resistance we feel in terms of inertial mass
and call it gravitational force does not require that the earth
attractor act on the quantity of resistance we feel. The earth
attractor can just as well act on atoms.

Kepler's laws reflect efficient, least action motion common to stable
systems in our universe. Newton generalizes to the entire universe,
and co-opts, Kepler's law of areas, as the carrier for his mass
driven
centripetal force. Since Kepler's laws are required for Newton's mass
driven centripetal force, how is it we say that "Kepler's laws
require" Newton's mass driven centripetal force? That is: how is it
we
say that prior to Newton, Kepler's laws were entirely empirical and
that these empirical laws can be derived from Newton's universal law
of gravitation? The brief answer to this question shows the
importance
of our word definitions and conceptual understanding of the applied
mathematics. Consider:

1) F=GMm/r^2

We can see from (1) that Newton defined the gravitational force
between two objects as a function of the product of their mass where
the function is solely attenuated by the inverse of the square of the
distance between the masses. Note that [1/r^2] is an efficient least
action property. Note also that mass density here is a variable,
solely dependent on [r], and that the scale is set by [G], the
constant of proportionality, measured as a function of inertial mass.
Consider:

2) F=4pi^2mr/T^2

The right side of (2) reflects the efficient properties of perfect
circle and perfect motion orbits, where mass has been assigned to
apply by using the mathematical technique of multiplying both sides
of
an equation by one. The introductory text will set (1) equal to (2)
as:

3) GMm/r^2=4pi^2mr/T^2

Where on rearranging and simplifying we have:

4) T^2/r^3=4pi^2/GM

In (2) we have the perfect orbit and perfect motion where we allow
our
sensory quantity for resistance mass [m], a free ride. Then we use
(3)
and (4) to eliminate [m] from the derivation while including [m's]
empirical measurements and the measurements that accompany the least
action orbits, to define [M]. In other words, we assign as a
controlling property of the least action orbits, the resistance we
feel and quantify as mass [m]. Then we set the formulations
equivalent
where [m] divides out of the equation. We say this is to be expected
since all objects fall at the same rate. This is clearly functional
in
terms of time and space only folks. Not necessarily functional in
terms of the dynamics of planets, moons and stars... which must
include density as an attendant consequence, or cause of the
controlling attraction, rather than as a mere function of [r]. (If
the
reader has not yet referenced the endnote [1], it is necessary to do
so now.)

The introductory physics text will now offer that (4) shows that
Kepler's third law is merely a result of Newtons gravitational law.
And "... although this derivation uses perfect motion and perfect
orbits, it applies equally well to real orbits in real motion
provided
we use the average distance from the sun to the planet, for [r]."
paraphrased

The last paragraph is rather interesting. It states that the
derivation here uses perfect circles in perfect motion (where we have
the efficiency quotient as either [circumference/area] or [the
period/
area]) [1]. And then it states that the derivation applies to real
orbits as well, provided we use the average distance from the sun to
the planet for [r]. So that the efficiency quotient in the real orbit
case is: [2pir/pir^2] or [T/pir^2]. Clearly nothing has changed. They
each reduce to [2/r] or [2/rv].
Newton's centripetal force is defined within the parameters of a
perfect circle and perfect motion. A circle is efficient. Newton
connects this efficient property of the perfect circle in perfect
motion to its analog in time-space elliptical orbits. My analysis of
centripetal force as put forward by Isaac Newton revealed that the
law
of areas falls out of Newton's perfect circle and perfect motion as
an
efficient property, or artifact of the circle itself. Newton used
this
property of the real orbits to generalize his supposition for a mass
generated centripetal force, to the entire universe.

Kepler's laws have since been regarded as mere empirical facts, that
are a consequence of Newton's laws. True, it is not the law of areas
that is fundamental here. Rather, it is the principle the law of
areas
obeys. That principle clearly does not depend on mass. That principle
results in time controlled efficiency. We see it now as the universal
carrier for Newton's notion of a mass driven gravitational force.
When
Newton asked "...why may we not..." generalize the law of areas to
the
entire universe, as a carrier for his defined force, it almost seems
as though the subconscious half of his brain suspects something might
be wrong. Doing so will carry his idea of a mass generated
centripetal
force with it. Making it clear to me that the least action, time
controlled property of stable systems are used as the carrier for
Newton's idea for a mass generated force.

The introductory physics text approximates the orbits as circular and
notes that a circular orbit implies a centripetal force. It is
important to note again that while such an orbit implies a
centripetal
force, it does not necessarily imply a mass generated centripetal
force, nor does it necessarily imply any force of the type we feel
and
quantify in terms of the resistance we work against.

Consider:
In (1) where [M] represents the mass of the earth and [r] represents
the distance to the center of the earth from the earth's surface,
the
resistance we work against at the earth's surface is formulated as:

5) F=mg

We must exert effort to lift, to overcome the resistance of the
earth
surface inertial object. We quantify the resistance to our effort in
terms of mass [m], where the focus of the earth attractor can be
conceptually explained as an action on the atom. We call our effort
force. (The earth attractor pulls on atoms and we pull back. We have
assigned our quantified "pull back" to the entire universe and we
call
it gravitational force.) So that we set (1) equal to (5) as:

6) mg=GmM/r^2

Although we have defined two different formulations for a mass
generated force, when we set them equivalent in (6), mass [m] appears
to not be a part of the formulation. We see this again as a
consequence of the fact that all objects fall at the same rate.
Therefore the mass of the inertial object divides out of the
equation.
The fact of the matter is, that although mass is not acted upon by
the
earth attractor (see johnreed Catch 22), Newton has defined
gravitational force in terms of the local empirical measurements
accompanying mass [m]. This includes the gravitational constant [G].
The magnitude of [g] varies from location to location so that the
attraction between celestial bodies is defined in terms
proportionally
dynamic to the resistance we feel, using the similarity of
measurements accompanying least action motion. Then we simplify (6)
to
arrive at:

7) g=GM/r^2

To close for now, then, again consider [6]. Where when we divide
little [m] out, we are left with [7]. Note again that [G], [g], and
[1/
r^2] are empirical measurements that accompany least action
processes.
Note too that the law of areas is a consequence of a least action
orbit. So, when we divide [m] out, the result in [7] leaves [M]
proportionally hardwired to our empirical measurements that accompany
the least action physical processes involving [m] [endnote 2], and
extend to [M] via [1/r^2], also a property attendant to a least
action
process. In other words we have defined a universal gravitational
force in terms of the resistive properties of inertial objects (which
we qualify as and which we work against) that function "anonymously"
solely within least action parameters.

Endnotes
1) A circle is an efficient enclosure of area. That is, the circle
circumference is the shortest line length to enclose the greatest
area. Nothing is wasted here. Equal arc lengths from the same circle
will radially enclose equal areas, just as equal time intervals from
the same orbit will radially enclose equal areas. When we take the
efficiency ratio of the circle as the quotient [circumference/area]
or
[2pir/pir^2] and reduce it, we have [2/r]. When we take the quotient
of a circle's [arc segment length to its radially enclosed area] we
also reduce that to [2/r]. This is an efficient area enclosing
symmetrical property of the circle itself (see Take II). This is, on
the face, trivial and rather mundane, as it follows from the perfect
symmetry of the circle.

With the real world orbits this symmetric efficiency is retained in
terms of time and space. We have the efficiency ratio here as the
quotient [the period/the area enclosed by the orbit]. The reduced
quotient here when we take [r] as the average distance of the planets
from the sun, is [2/rv]. This is a real world orbit, time-boundary to
enclosed space analog, of the circle's length-boundary to enclosed
area, efficiency quotient [2/r] (see Take II). I'll leave it to the
reader to show that Kepler's law of areas proves that the analog of
the symmetry of the 'circle' efficiency, in the real orbits, is
maintained. All you need to show is that the efficient symmetry
quotient for any Kepler swept out area is [2/rv]. [Arc segment
interval length to radially enclosed area]. Just as in Ptolemies
model
it is the consistent efficiency of the orbits that enable the model
to
be as useful as it is. The same efficiency carries Newton's mass
driven centripetal force to the entire universe, as well as
Einstein's
mass-spacetime curvature, geodesic.

2) In the post "johnreed Catch 22" I have shown that inertial mass is
"emergent" in the classical gravitational frame.

Author's afternote:
The reader's indignation runs high with this post. I can understand
that. It challenges the very foundations of physics as we know it. I
am only the messenger and if the message is valid, personal attacks
on
me serve no purpose. If the message is invalid, then again, the
message should be attacked, not the messenger. The proper questions
to
consider are: Are my arguments valid or invalid? And if they are
valid, are they significant or insignificant? I note the following:

Argument 1: Isaac Newton defined a mass generated centripetal force
in
terms of his first law object moving along a perfectly circular
trajectory at a uniform (perfect) speed. I show that this is true
directly from The Principia

Argument 2: The law of areas falls out of a perfectly circular
trajectory and uniform speed as a property or artifact of the
efficient area enclosing circle itself. I see this as self evident
but
I have explained it in the first footnote.

Argument 3: Kepler's law of areas is an efficient symmetry analog of
the circle. I show this by first showing that the efficiency quotient
of the circle reduces to the efficiency quotient of any radially
enclosed area of the circle. Then I show that Kepler's law of areas
proves the analog case for the real orbits.

Argument 4: Isaac Newton connects this efficient property of the
circle to its analog in the real orbits.and uses Kepler's law of
areas
to carry his idea of centripetal force to the entire universe. I show
that this is true directly from The Principia.

Argument 5: I show that our mathematical derivation of Kepler's laws
from Newton's universal law of gravitation ultimately rests solely on
least action motion. The fact that all objects fall at the same rate
also shows that mass operates solely within least action motion,
"anonymously".

Argument 6. I show that setting the quantity we work against and call
weight [F=mg], equal to Newton's universal law of gravitation [F=GMm/
r^2] co-opts the least action properties attendant to an anonymous
object in motion, and proportionally renders these properties solely
in terms of the resistance we work against and call force.

Collateral arguments presented in earlier posts:
1. We can perform no experiment such that we can absolutely determine
that mass and not the atom, is acted upon by the earth attractor. I
leave it to the reader to think of one.

Consequently, all our measurements and experiments. All our ideas and
notions can be explained satisfactorily in either case. Therefore any
property of matter we measure in terms of mass cannot be used as a
logical argument to unseat or discredit my work. The properties we
measure can be seen to result from either case. This includes angular
or linear momentum, which includes equal and opposite behavior and
the
conservation of momentum. This includes centers of mass, centers of
gravity and barycenters, which can be seen as a point on a time-space
trajectory. This includes weight on the earth and elsewhere. The
measurement of all these things and any related measurement would
come
out the same whether the earth attractor acts on mass or on atoms.
Whether mass is a universal causal property or merely an emergent
quantity that we work against. (Actually this is not completely true.
If the earth attractor acted on mass we could not peel ourselves from
the surface of the earth. All objects would not fall at the same
rate.
Nor could we even exist. So far however our collective knowledge has
not yet provided this conscious awareness.)

2. The mathematics fits the stable universe because the mathematics
easily represents the least action motion attendant to stable systems
in the universe. I have argued this case in the broadly stroked 5
part
post "Mathematics and the Universe: Why They are so Well Matched." I
will argue this case further in my post on spiral galaxies and the
large scale structure of the universe.

I believe that I have presented arguments that warrant an address.
However I do not require this. I need no verbal interaction with
others to continue my work. However, if the reader wishes to
critically comment on aspects of this post it is more than welcomed
by
me. I would request, in such a case, that if the reader uses any
current mainstream conclusions to discount, out of hand, my argument,
to please explain the logic behind it. In other words, please bring
more to the table than a mere listing of present mainstream
conclusions that are based solely on the aspects of the current
paradigm that come into question as a result of my original principle
arguments.

I don't suggest that I can dictate the terms of the argument a reader
brings to the table here. I only ask that it be on point. If it is
shrouded in indignation it probably will not be on point. And if its
"only" point or points serves to support that
continuing the discourse. Recent experience has confirmed this. I do
not enjoy being called a liar nor do I enjoy being called derogatory
names, by foul mouthed, socially inept rumpkins, baring their
imaginary fangs, while wearing their "wanna be bad ass" capes, within
the safe security offered by their mother's womb.
johnreed