johnreed 1st addendum to "johnreed Catch 22" modified July 5, 2007

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.

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.

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 how important
our definitions and conceptual understanding of the words we use with
the applied mathematics, is. 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]. 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

Author's Note: In (2) we have the perfect orbit and perfect motion
where we allow our sensory quantity [m] (for resistance we feel), 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 the resistance we feel and quantify as mass
[m], as a controlling property of the least action orbits. 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 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].

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]). 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 is
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.

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 call this effort force. (The earth
attractor pulls on atoms and we pull back. We have assigned our "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 least action
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 solely in
terms of the least action measurements accompanying a resistance we
feel. 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 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] 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 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. 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 geodesic.

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

"johnlawrencereedjr" wrote in message
ups.com...
: 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.
:
: 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.
:
: 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 how important
: our definitions and conceptual understanding of the words we use with
: the applied mathematics, is. 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]. 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
:
: Author's Note: In (2) we have the perfect orbit and perfect motion
: where we allow our sensory quantity [m] (for resistance we feel), 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 the resistance we feel and quantify as mass
: [m], as a controlling property of the least action orbits. 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 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].
:
: 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]). 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 is
: 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.
:
: 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 call this effort force. (The earth
: attractor pulls on atoms and we pull back. We have assigned our "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 least action
: 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 solely in
: terms of the least action measurements accompanying a resistance we
: feel. 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 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] 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 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. 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 geodesic.
:
: 2) In the post "johnreed Catch 22" I have shown that inertial mass is
: "emergent" in the classical gravitational frame.
: johnreed
:


Comments:
a) Acceleration is instantaneous, "instantaneous acceleration" is as
meaningless as "quiet silence".
b) Forces act between two bodies, the Earth weighs 170 lb in my
gravitational field.
c) "velocity acceleration vector (v/t)"? What's that?
d) You do not appear to have considered equal masses M = m
or barycentres.
http://www.androcles01.pwp.blueyonde...AlgolOrbit.gif
e) Please clarify all definitions for completeness.
f) Ptolemy's, not "Ptolemies".

g 1)
"I will show that Kepler's laws follow from the efficient, least action
motion..."
g 2) "I'll leave it to the reader to show that Kepler's law of areas
proves...

That's called a copout.

On Jul 6, 12:43 am, "Androcles" wrote:
"johnlawrencereedjr" wrote in message

ups.com...
: 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.
:
: 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.
:
: 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 how important
: our definitions and conceptual understanding of the words we use with
: the applied mathematics, is. 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]. 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
:
: Author's Note: In (2) we have the perfect orbit and perfect motion
: where we allow our sensory quantity [m] (for resistance we feel), 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 the resistance we feel and quantify as mass
: [m], as a controlling property of the least action orbits. 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 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].
:
: 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]). 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 is
: 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.
:
: 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 call this effort force. (The earth
: attractor pulls on atoms and we pull back. We have assigned our "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 least action
: 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 solely in
: terms of the least action measurements accompanying a resistance we
: feel. 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 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] 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 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. 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 geodesic.
:
: 2) In the post "johnreed Catch 22" I have shown that inertial mass is
: "emergent" in the classical gravitational frame.
: johnreed
:

Comments:
a) Acceleration is instantaneous, "instantaneous acceleration" is as
meaningless as "quiet silence".
b) Forces act between two bodies, the Earth weighs 170 lb in my
gravitational field.
c) "velocity acceleration vector (v/t)"? What's that?
d) You do not appear to have considered equal masses M = m
or barycentres.
http://www.androcles01.pwp.blueyonde...AlgolOrbit.gif
e) Please clarify all definitions for completeness.
f) Ptolemy's, not "Ptolemies".

g 1)
"I will show that Kepler's laws follow from the efficient, least action
motion..."
g 2) "I'll leave it to the reader to show that Kepler's law of areas
proves...

That's called a copout.

Hello Androcles

What do you call this enumerated drivel? Do you really think it
qualifies for a seat at my table? Would you throw a Rosetta Stone in
the trash because it wasn't a perfect sphere or because you preferred
it to be another color?

In your own mind you are a clever performer. We can suspect this of
anyone who calls himself "Androcles", but it is clear from your
actions that you intend to impress the observing readers with your
partially imagined acumen and skill. The thing is, the readers I
address are way more informed than you. To them any comparison of
what I offer here and what you offer here is as gold is to mud.

I am not trying to impress anyone Androcles. Even in an exchange as
insignificant as this my response is to your drivel alone, in support
of my intellectual platform. I am trying to communicate knowledge I
have gained. My entire platform 'may' be wrong. My arguments may be
elementary. Maybe symmetry analogs in different frames of reference
stretches the idea of invariance too far. Maybe our sensory quantity
"mass" causes the symmetric efficiency. Maybe mass is not just an
emergent quantity of resistance we feel and work against in the
classical frame. Maybe the universe is composed of little balls of
stuff that exchange little balls of force. Maybe mainstream physics
has it right and I have it wrong. I can only prove that the efficient
symmetry analogs exist and that our mathematical models in total,
depend on that efficient symmetry. This is the Rosetta Stone you must
address Androcles. Otherwise your enumerated drivel is merely the
performance of a rank amateur.

I trust that you have the mathematical training required to show that
any Kepler swept out area can be reduced to [2/rv]. If you lack that,
you lack the education required to read my post, much less comment on
it. I showed this, years and years ago in the post "johnreed Take II".
And don't even imagine that I have to conform to your hoakey idea of
what constitutes acceptable methods of argument. I have only one
requirement for my arguments. Namely communication. I'll leave it
thereafter to the new age Ptolemaic artist to do what he/she is
trained to do.

We can say that an object on a curved trajectory has a varying or a
constant speed. We cannot say that such an object has a constant
velocity. We can say that it has a constant varying velocity. A
varying velocity is acceleration. A continual change in direction is,
by definition, acceleration. In linear acceleration we can determine
an instantaneous velocity. In orbital motion the velocity is always
changing direction. Therefore it is always accelerating, by
definition. The reduction to infinitessimals does not make a circle a
square. It just lets us treat it as a square.

Outside of metaphors I try to use words in a more exact manner where I
find them inadequately used. I claim no perfection with regard to this
(or with regard to anything else). The arguments I have put forward in
my posts have never been addressed. I put this down to my failure to
adequately convey them. Its a complex bunch of work to do so, and it
only becomes clear and simple through hindsight. Hammering it out in
conceptually understood terms is a bear that I could only do a piece
at a time. From one direction and then another, and another and
another. And my present focus on gravity is secondary to my original
purpose, which was to conceptually understand atomic structure. It
turned out that our gravitational paradigm had to be modified as a
result. When I fully realized that, it put an entirely new face on the
work that lay before me. Isaac Newton was the giant of giants to me.
While I set out to unseat Einstein's photo electric effect
explanation, I never even imagined that it would lead to unseating
Newton's universal law of gravitation. I am almost certain that my
work would have ceased completely then (rather than the mere delay of
ten years), had the internet and world wide web not been made
available.

Considering the number of my posts since 1999, when one examines the
sparse response to them, one would think that they are ignored, or
rather not even read. When you also consider that they have no subject
line as a title other than johnreed take this and take that, one could
further support the liklihood that they are not read. I recognized
this possibility but I believed that my posts would be read if for no
other reason than to confirm in the readers mind the certain veracity
of his/her position that I was challenging. And of course while he/she
was looking to do one thing, I was busy at making it impossible to do.
So the reason my posts were read was immaterial. The end result is
unavoidable. Either I get corrected and learn or you get corrected and
learn.

The last post I read of yours was a clever representation of your self
imagined superiority over others. You had a list of newsgroup
participants that you claimed to have on killfile status. I noted that
I was listed in the group. Apparently this was just your duplicity
used in a manner that you think shows your brilliance. It seems that
your claimed killfile was non-existent. So what was its purpose in
being presented? I didn't really believe that you would not read my
posts. I believed that you would read anything I posted in the hope of
being able to publically discount it. It appears that my belief was
correct. Sam Wormley gets an A for presenting a current mainstream
supported position. But the drivel you put forward here is laughable,
not even in contention for an actual grade..

The new Google interface has provided me a much better guage of how my
posts are received. Since mid 2006 my posts have received 20 to 30
hits a day for the first month. By the 6th month thats down to from 3
to 10 hits a day. So I know I'm being read and I know that the only
attraction to the reader is the name johnreed in the title. This could
all be just the average life cycle of any post, but it shows that my
posts are not being ignored. Which means it all depends on my ability
to communicate. Once the subconscious half of our brains comprehend
it, it is a fait accompli.

You did have one comment that I found interesting and valuable. Why do
I write "Ptolemies" in the one case, and "Kepler's" in the other.
Totally unrecognized by me. I can only offer that to me Kepler is a
real owner and Ptolemy's ownership is shrouded in uncertainty. Which
is no valid reason. So thanks for that correction. If you want to
really get into my weak area just attack my punctuation. That brings
my SAT English score down to a high 14 all by itself.

I don't expect to modify the gravitational paradigm in my lifetime
actually. Its too deep set and ingrained as an a priori view. So deep
set that if I don't get it to you, I don't think you will ever get it.
If nothing else, I will at least leave behind some clues. I suggest
you put me on a real killfile status in order to avoid the possibility
of continually acting the buffoon, for posterity.
Have a good time.
johnreed

"johnlawrencereedjr" wrote in message
oups.com...
: On Jul 6, 12:43 am, "Androcles" wrote:
: "johnlawrencereedjr" wrote in message
:
: ups.com...
: : 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.
: :
: : 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.
: :
: : 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 how important
: : our definitions and conceptual understanding of the words we use with
: : the applied mathematics, is. 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]. 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
: :
: : Author's Note: In (2) we have the perfect orbit and perfect motion
: : where we allow our sensory quantity [m] (for resistance we feel), 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 the resistance we feel and quantify as mass
: : [m], as a controlling property of the least action orbits. 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 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].
: :
: : 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]). 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 is
: : 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.
: :
: : 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 call this effort force. (The earth
: : attractor pulls on atoms and we pull back. We have assigned our "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 least action
: : 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 solely in
: : terms of the least action measurements accompanying a resistance we
: : feel. 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 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] 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 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. 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 geodesic.
: :
: : 2) In the post "johnreed Catch 22" I have shown that inertial mass is
: : "emergent" in the classical gravitational frame.
: : johnreed
: :
:
: Comments:
: a) Acceleration is instantaneous, "instantaneous acceleration" is as
: meaningless as "quiet silence".
: b) Forces act between two bodies, the Earth weighs 170 lb in my
: gravitational field.
: c) "velocity acceleration vector (v/t)"? What's that?
: d) You do not appear to have considered equal masses M = m
: or barycentres.
: http://www.androcles01.pwp.blueyonde...AlgolOrbit.gif
: e) Please clarify all definitions for completeness.
: f) Ptolemy's, not "Ptolemies".
:
: g 1)
: "I will show that Kepler's laws follow from the efficient, least action
: motion..."
: g 2) "I'll leave it to the reader to show that Kepler's law of areas
: proves...
:
: That's called a copout.
:
: Hello Androcles
:
: What do you call this enumerated drivel?

I call it comments on your drivel. I expect you to address my
points if you find fault with them.


: Do you really think it
: qualifies for a seat at my table?

The fare at your table is inedible. I'll leave for the reader to see
you can't answer my points.


: Would you throw a Rosetta Stone in
: the trash because it wasn't a perfect sphere or because you preferred
: it to be another color?


Oh, is that what it's supposed to be, a Rosetta stone?

:
: In your own mind you are a clever performer.

Take a look at yourself in the mirror.



: We can suspect this of
: anyone who calls himself "Androcles", but it is clear from your
: actions that you intend to impress the observing readers with your
: partially imagined acumen and skill. The thing is, the readers I
: address are way more informed than you. To them any comparison of
: what I offer here and what you offer here is as gold is to mud.

So you cannot answer my points and resort to bluster.


: I am not trying to impress anyone Androcles.

Just as well, you didn't succeed.


: Even in an exchange as
: insignificant as this my response is to your drivel alone, in support
: of my intellectual platform.

Answer my points, then, and cut the rhetoric drivel.


: I am trying to communicate knowledge I
: have gained.

Try English classes if you want to communicate drivel such as
"Ptolemies", I never learnt Gibberish.



: My entire platform 'may' be wrong. My arguments may be
: elementary. Maybe symmetry analogs in different frames of reference
: stretches the idea of invariance too far. Maybe our sensory quantity
: "mass" causes the symmetric efficiency. Maybe mass is not just an
: emergent quantity of resistance we feel and work against in the
: classical frame. Maybe the universe is composed of little balls of
: stuff that exchange little balls of force. Maybe mainstream physics
: has it right and I have it wrong. I can only prove that the efficient
: symmetry analogs exist and that our mathematical models in total,
: depend on that efficient symmetry. This is the Rosetta Stone you must
: address Androcles. Otherwise your enumerated drivel is merely the
: performance of a rank amateur.
:
"Maybe, maybe, maybe".
Got anything concrete without all the bull****?

: I trust that you have the mathematical training required to show that
: any Kepler swept out area can be reduced to [2/rv].

Hahahaha! Try dimensional analysis, v = dx/dt.
http://en.wikipedia.org/wiki/Dimensional_analysis
Areas are not measured in units of time, you are spouting drivel.

: If you lack that, you lack the education required to read my post, much
less comment on : it. I showed this, years and years ago in the post
"johnreed Take II".

In hypothetical sentences introduced by 'if' and referring to
past time, where conditions are to be deemed 'unfulfilled',
the verb will regularly be found in the pluperfect subjunctive,
in both protasis and apodosis.
-- Donet, "Principles of Elementary Latin Syntax"


: And don't even imagine that I have to conform to your hoakey idea of
: what constitutes acceptable methods of argument. I have only one
: requirement for my arguments. Namely communication.

You failed.

: I'll leave it
: thereafter to the new age Ptolemaic artist to do what he/she is
: trained to do.

Does that mean you'll shut up?

:
: We can say that an object on a curved trajectory has a varying or a
: constant speed. We cannot say that such an object has a constant
: velocity.

Did I say it did?



: We can say that it has a constant varying velocity. A
: varying velocity is acceleration.

Well, well. "A varying velocity is acceleration" - reed the great
communicator
and educator imparting his "knowledge", who claims areas are measured
in units of v (=dx/dt) and r.

: A continual change in direction is,
: by definition, acceleration.

Did I say it wasn't?

You obviously like the sound of your own typing, but you are a ****in'
boor and unable to communicate. Communicators can answer points
raised against them. Go eat at your own table and take your miserable
drivel with you.

The area swept is 2/rv... hahahahaha!
[rest of crap snipped]

On Jul 8, 5:26 pm, "Androcles" wrote:
"johnlawrencereedjr" wrote in message

oups.com...
: On Jul 6, 12:43 am, "Androcles" wrote:
: "johnlawrencereedjr" wrote in message
:
: oups.com...
: : 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.
: :
: : 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.
: :
: : 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 how important
: : our definitions and conceptual understanding of the words we use with
: : the applied mathematics, is. 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]. 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
: :
: : Author's Note: In (2) we have the perfect orbit and perfect motion
: : where we allow our sensory quantity [m] (for resistance we feel), 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 the resistance we feel and quantify as mass
: : [m], as a controlling property of the least action orbits. 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 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].
: :
: : 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]). 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 is
: : 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.
: :
: : 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 call this effort force. (The earth
: : attractor pulls on atoms and we pull back. We have assigned our "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 least action
: : 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 solely in
: : terms of the least action measurements accompanying a resistance we
: : feel. 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 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] 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 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. 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 geodesic.
: :
: : 2) In the post "johnreed Catch 22" I have shown that inertial mass is
: : "emergent" in the classical gravitational frame.
: : johnreed
: :
:
: Comments:
: a) Acceleration is instantaneous, "instantaneous acceleration" is as
: meaningless as "quiet silence".
: b) Forces act between two bodies, the Earth weighs 170 lb in my
: gravitational field.
: c) "velocity acceleration vector (v/t)"? What's that?
: d) You do not appear to have considered equal masses M = m
: or barycentres.
: http://www.androcles01.pwp.blueyonde...AlgolOrbit.gif
: e) Please clarify all definitions for completeness.
: f) Ptolemy's, not "Ptolemies".
:
: g 1)
: "I will show that Kepler's laws follow from the efficient, least action
: motion..."
: g 2) "I'll leave it to the reader to show that Kepler's law of areas
: proves...
:
: That's called a copout.
:
: Hello Androcles
:
: What do you call this enumerated drivel?

I call it comments on your drivel. I expect you to address my
points if you find fault with them.

: Do you really think it
: qualifies for a seat at my table?

The fare at your table is inedible. I'll leave for the reader to see
you can't answer my points.

: Would you throw a Rosetta Stone in
: the trash because it wasn't a perfect sphere or because you preferred
: it to be another color?

Oh, is that what it's supposed to be, a Rosetta stone?

:
: In your own mind you are a clever performer.

Take a look at yourself in the mirror.

: We can suspect this of
: anyone who calls himself "Androcles", but it is clear from your
: actions that you intend to impress the observing readers with your
: partially imagined acumen and skill. The thing is, the readers I
: address are way more informed than you. To them any comparison of
: what I offer here and what you offer here is as gold is to mud.

So you cannot answer my points and resort to bluster.

: I am not trying to impress anyone Androcles.

Just as well, you didn't succeed.

: Even in an exchange as
: insignificant as this my response is to your drivel alone, in support
: of my intellectual platform.

Answer my points, then, and cut the rhetoric drivel.

: I am trying to communicate knowledge I
: have gained.

Try English classes if you want to communicate drivel such as
"Ptolemies", I never learnt Gibberish.

: My entire platform 'may' be wrong. My arguments may be
: elementary. Maybe symmetry analogs in different frames of reference
: stretches the idea of invariance too far. Maybe our sensory quantity
: "mass" causes the symmetric efficiency. Maybe mass is not just an
: emergent quantity of resistance we feel and work against in the
: classical frame. Maybe the universe is composed of little balls of
: stuff that exchange little balls of force. Maybe mainstream physics
: has it right and I have it wrong. I can only prove that the efficient
: symmetry analogs exist and that our mathematical models in total,
: depend on that efficient symmetry. This is the Rosetta Stone you must
: address Androcles. Otherwise your enumerated drivel is merely the
: performance of a rank amateur.
:
"Maybe, maybe, maybe".
Got anything concrete without all the bull****?

: I trust that you have the mathematical training required to show that
: any Kepler swept out area can be reduced to [2/rv].

Hahahaha! Try dimensional analysis, v = dx/dt.
http://en.wikipedia.org/wiki/Dimensional_analysis
Areas are not measured in units of time, you are spouting drivel.

: If you lack that, you lack the education required to read my post, much
less comment on : it. I showed this, years and years ago in the post
"johnreed Take II".

In hypothetical sentences introduced by 'if' and referring to
past time, where conditions are to be deemed 'unfulfilled',
the verb will regularly be found in the pluperfect subjunctive,
in both protasis and apodosis.
-- Donet, "Principles of Elementary Latin Syntax"

: And don't even imagine that I have to conform to your hoakey idea of
: what constitutes acceptable methods of argument. I have only one
: requirement for my arguments. Namely communication.

You failed.

: I'll leave it
: thereafter to the new age Ptolemaic artist to do what he/she is
: trained to do.

Does that mean you'll shut up?

:
: We can say that an object on a curved trajectory has a varying or a
: constant speed. We cannot say that such an object has a constant
: velocity.

Did I say it did?

: We can say that it has a constant varying velocity. A
: varying velocity is acceleration.

Well, well. "A varying velocity is acceleration" - reed the great
communicator
and educator imparting his "knowledge", who claims areas are measured
in units of v (=dx/dt) and r.

: A continual change in direction is,
: by definition, acceleration.

Did I say it wasn't?

You obviously like the sound of your own typing, but you are a ****in'
boor and unable to communicate. Communicators can answer points
raised against them. Go eat at your own table and take your miserable
drivel with you.

The area swept is 2/rv... hahahahaha!
[rest of crap snipped]

Ah Androcles... I share with you the joy and smug vindication you must
have felt at noting my hastily written and poorly worded sentence
above. Surely your projected status as a grand wazoo can no longer be
challenged. Nevermind the referenced context and nevermind the fact
that the quotient [2/rv] cannot be interpretted as a static
representation for area. So to insure that we don't throw the baby out
with the bath water, I humbly submit the following corrected
sentence:

"I trust that you have the mathematical training required to show that
the efficiency quotient of any Kepler swept out area can be reduced to
[2/rv]."

You will have to reread the original post if you fail to understand
what is meant here by "efficiency quotient."
Have a good time.
johnreed

"johnlawrencereedjr" wrote in message
oups.com...
: On Jul 8, 5:26 pm, "Androcles" wrote:
: "johnlawrencereedjr" wrote in message
:
: oups.com...
: : On Jul 6, 12:43 am, "Androcles" wrote:
: : "johnlawrencereedjr" wrote in message
: :
: : oups.com...
: : : 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.
: : :
: : : 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.
: : :
: : : 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 how
important
: : : our definitions and conceptual understanding of the words we use
with
: : : the applied mathematics, is. 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]. 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
: : :
: : : Author's Note: In (2) we have the perfect orbit and perfect motion
: : : where we allow our sensory quantity [m] (for resistance we feel),
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 the resistance we feel and quantify as mass
: : : [m], as a controlling property of the least action orbits. 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 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].
: : :
: : : 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]). 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 is
: : : 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.
: : :
: : : 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 call this effort force. (The earth
: : : attractor pulls on atoms and we pull back. We have assigned our
"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 least action
: : : 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 solely in
: : : terms of the least action measurements accompanying a resistance
we
: : : feel. 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 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] 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 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. 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 geodesic.
: : :
: : : 2) In the post "johnreed Catch 22" I have shown that inertial mass
is
: : : "emergent" in the classical gravitational frame.
: : : johnreed
: : :
: :
: : Comments:
: : a) Acceleration is instantaneous, "instantaneous acceleration" is as
: : meaningless as "quiet silence".
: : b) Forces act between two bodies, the Earth weighs 170 lb in my
: : gravitational field.
: : c) "velocity acceleration vector (v/t)"? What's that?
: : d) You do not appear to have considered equal masses M = m
: : or barycentres.
: : http://www.androcles01.pwp.blueyonde...AlgolOrbit.gif
: : e) Please clarify all definitions for completeness.
: : f) Ptolemy's, not "Ptolemies".
: :
: : g 1)
: : "I will show that Kepler's laws follow from the efficient, least
action
: : motion..."
: : g 2) "I'll leave it to the reader to show that Kepler's law of areas
: : proves...
: :
: : That's called a copout.
: :
: : Hello Androcles
: :
: : What do you call this enumerated drivel?
:
: I call it comments on your drivel. I expect you to address my
: points if you find fault with them.
:
: : Do you really think it
: : qualifies for a seat at my table?
:
: The fare at your table is inedible. I'll leave for the reader to see
: you can't answer my points.
:
: : Would you throw a Rosetta Stone in
: : the trash because it wasn't a perfect sphere or because you preferred
: : it to be another color?
:
: Oh, is that what it's supposed to be, a Rosetta stone?
:
: :
: : In your own mind you are a clever performer.
:
: Take a look at yourself in the mirror.
:
: : We can suspect this of
: : anyone who calls himself "Androcles", but it is clear from your
: : actions that you intend to impress the observing readers with your
: : partially imagined acumen and skill. The thing is, the readers I
: : address are way more informed than you. To them any comparison of
: : what I offer here and what you offer here is as gold is to mud.
:
: So you cannot answer my points and resort to bluster.
:
: : I am not trying to impress anyone Androcles.
:
: Just as well, you didn't succeed.
:
: : Even in an exchange as
: : insignificant as this my response is to your drivel alone, in support
: : of my intellectual platform.
:
: Answer my points, then, and cut the rhetoric drivel.
:
: : I am trying to communicate knowledge I
: : have gained.
:
: Try English classes if you want to communicate drivel such as
: "Ptolemies", I never learnt Gibberish.
:
: : My entire platform 'may' be wrong. My arguments may be
: : elementary. Maybe symmetry analogs in different frames of reference
: : stretches the idea of invariance too far. Maybe our sensory quantity
: : "mass" causes the symmetric efficiency. Maybe mass is not just an
: : emergent quantity of resistance we feel and work against in the
: : classical frame. Maybe the universe is composed of little balls of
: : stuff that exchange little balls of force. Maybe mainstream physics
: : has it right and I have it wrong. I can only prove that the efficient
: : symmetry analogs exist and that our mathematical models in total,
: : depend on that efficient symmetry. This is the Rosetta Stone you must
: : address Androcles. Otherwise your enumerated drivel is merely the
: : performance of a rank amateur.
: :
: "Maybe, maybe, maybe".
: Got anything concrete without all the bull****?
:
: : I trust that you have the mathematical training required to show that
: : any Kepler swept out area can be reduced to [2/rv].
:
: Hahahaha! Try dimensional analysis, v = dx/dt.
: http://en.wikipedia.org/wiki/Dimensional_analysis
: Areas are not measured in units of time, you are spouting drivel.
:
: : If you lack that, you lack the education required to read my post,
much
: less comment on : it. I showed this, years and years ago in the post
: "johnreed Take II".
:
: In hypothetical sentences introduced by 'if' and referring to
: past time, where conditions are to be deemed 'unfulfilled',
: the verb will regularly be found in the pluperfect subjunctive,
: in both protasis and apodosis.
: -- Donet, "Principles of Elementary Latin Syntax"
:
: : And don't even imagine that I have to conform to your hoakey idea of
: : what constitutes acceptable methods of argument. I have only one
: : requirement for my arguments. Namely communication.
:
: You failed.
:
: : I'll leave it
: : thereafter to the new age Ptolemaic artist to do what he/she is
: : trained to do.
:
: Does that mean you'll shut up?
:
: :
: : We can say that an object on a curved trajectory has a varying or a
: : constant speed. We cannot say that such an object has a constant
: : velocity.
:
: Did I say it did?
:
: : We can say that it has a constant varying velocity. A
: : varying velocity is acceleration.
:
: Well, well. "A varying velocity is acceleration" - reed the great
: communicator
: and educator imparting his "knowledge", who claims areas are measured
: in units of v (=dx/dt) and r.
:
: : A continual change in direction is,
: : by definition, acceleration.
:
: Did I say it wasn't?
:
: You obviously like the sound of your own typing, but you are a ****in'
: boor and unable to communicate. Communicators can answer points
: raised against them. Go eat at your own table and take your miserable
: drivel with you.
:
: The area swept is 2/rv... hahahahaha!
: [rest of crap snipped]
:
: Ah Androcles... I share with you the joy and smug vindication you must
: have felt at noting my hastily written and poorly worded sentence
: above. Surely your projected status as a grand wazoo can no longer be
: challenged. Nevermind the referenced context and nevermind the fact
: that the quotient [2/rv] cannot be interpretted as a static
: representation for area. So to insure that we don't throw the baby out
: with the bath water, I humbly submit the following corrected
: sentence:
:
: "I trust that you have the mathematical training required to show that
: the efficiency quotient of any Kepler swept out area can be reduced to
: [2/rv]."
:
: You will have to reread the original post if you fail to understand
: what is meant here by "efficiency quotient."
: Have a good time.
: johnreed
:

e) Please clarify all definitions for completeness.

Oh wait, it is considered drivel to politely ask for clarification.

Let's try this instead, maybe it will communicate if I use different words.
What the **** are you ranting about, ****head?