"Heliocentrism"

Is the "heliocentric" idea this: we choose a coordinate system in
which angular momentum is minimized?

"Axel Harvey" wrote in message
om...
Is the "heliocentric" idea this: we choose a coordinate system in
which angular momentum is minimized?

I think it is a little more prosaic than that.
I suspect that the "heliocentric" idea in astronomy
means that the sun more or less physically occupies
the gravitational center of the solar system and that the
other bodies in the solar system follow in a variety of
orbits around it.
The fact that an earth centered coordinate system would not
minimize angular momentum was not the necessarily the
main consideration or driving force of the proponents.
It was considered more of a reflection of reality than
merely arguing over equally arbitrary coordinate
systems.

"Chosp" wrote:

I had asked:

Is the "heliocentric" idea this: we choose a coordinate system in
which angular momentum is minimized?

I think it is a little more prosaic than that.
I suspect that the "heliocentric" idea in astronomy
means that the sun more or less physically occupies
the gravitational center of the solar system [ ... ]
The fact that an earth centered coordinate system would not
minimize angular momentum was not the necessarily the
main consideration or driving force of the proponents.
It was considered more of a reflection of reality than
merely arguing over equally arbitrary coordinate
systems.

Thank you. In historical terms you are probably right, but I was more
curious about the concept than about the history. Given that
coordinate systems are more or less arbitrary, there might be good
reasons for preferring the one that minimized angular momentum (now,
for instance, rather than in the 16th century).

Not being a physicist, I don't even know that my first assumption was
correct. When we make the origin of a coordinate system coincide with
the barycentre of a physical system of orbits, DOES that, in fact,
minimize angular momentum?

I'm not sure what reflections of reality might mean to other people -
to me it seems that if you pick a model to reflect reality, there must
be a reason.

In article ,
(Axel Harvey) writes:
Is the "heliocentric" idea this: we choose a coordinate system in
which angular momentum is minimized?

I don't think so. Minimizing angular momentum would give a rotating
coordinate system (non-inertial) with roughly Jupiter's rotation
period.

A heliocentric system is one in which the Sun's linear momentum is
zero. A "barycentric" coordinate system makes the net linear
momentum of the entire solar system zero.

--
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA
(Please email your reply if you want to be sure I see it; include a
valid Reply-To address to receive an acknowledgement. Commercial
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"Axel Harvey" wrote in message
om...

Is the "heliocentric" idea this: we choose a coordinate system in
which angular momentum is minimized?


Copernicus assumed uniform circular motion, so momentum
wasn't the reason. It was chosen to simplify the model
and improve prediction by reducing the needed epicycles.

We choose ideas based on which better predicts the future.
Based on which allows us to find the higher points on our
perceived fitness landscape.

I'll let you in on a little secret. The same laws that create
the structure of the universe also govern the evolution
of biological systems.

Fitness and gravity operate under the same laws of
organization.


http://users.ox.ac.uk/~quee0818/comp...omplexity.html

http://www.santafe.edu/sfi/People/ka...Lecture-7.html


Jonathan

s

(Steve Willner) wrote:

I had written:
Is the "heliocentric" idea this: we choose a coordinate system in
which angular momentum is minimized?

I don't think so. Minimizing angular momentum would give a rotating
coordinate system (non-inertial) with roughly Jupiter's rotation
period.

A heliocentric system is one in which the Sun's linear momentum is
zero. A "barycentric" coordinate system makes the net linear
momentum of the entire solar system zero.

Thank you! So a ----centric system sets *linear* momentum to zero.
This answers my supplementary question, which was:

Not being a physicist, I don't even know that my first assumption was
correct. When we make the origin of a coordinate system coincide with
the barycentre of a physical system of orbits, DOES that, in fact,
minimize angular momentum?

Odd that so few people bothered to jump on my erroneous assumption.

"jonathan" wrote:

We choose ideas based on which better predicts the future.
Based on which allows us to find the higher points on our
perceived fitness landscape.

Nematodes and tigers may find it easy to discover the high points of
their fitness landscape, but humans with their impoverished instincts
need to think about it. There must be cases where the choice of a
coordinate system will simplify calculations, and the choice then is
made for mathematical reasons - when a different choice might lead to
equivalent correct predictions while creating unnecessary difficulties
of computation. (I am *not* referring to Copernicus here, just
suggesting a general idea.)

A propos, Albert Einstein and Leopold Infeld wrote in _The_Evolution_
_of_Physics_ (1938):

Can we formulate physical laws so that they are valid for all
C[oordinate] S[ystems], not only those moving uniformly, but also
those moving quite arbitrarily, relative to each other? If this can
be done, our troubles will be over. We shall then be able to apply the
laws of nature to any CS. The struggle, so violent in the early days
of science, between the views of Ptolemy and Copernicus would then be
quite meaningless. Either CS could be used with equal justification.
The two sentences, "the sun is at rest and the earth moves," or "the
sun moves and the earth is at rest," would simply mean two different
conventions concerning two different CS. Could we build a real
relativistic physics valid in all CS; a physics in which there would
be no place for absolute, but only for relative motion? This is indeed
possible!

(End of quotation).

(Axel Harvey) wrote in message . com...
Is the "heliocentric" idea this: we choose a coordinate system in
which angular momentum is minimized?

It is far more complicated than that but I have'nt seen you shy away
from these things before and perhaps you may see where errors built on
Newton's view snowballed in later centuries.

Newton's gravitational laws compliment Kepler's planetary laws however
Newton treats the Earth's variable orbital motion alone and dispenses
with the Earth's constant axial rotation within the variation in
orbital motion.He can then say -



"PHÆNOMENON IV.
That the fixed stars being at rest, the periodic times of the five
primary planets, and (whether of the sun about the earth, or) of the
earth about the sun, are in the sesquiplicate proportion of their mean
distances from the sun.

This proportion, first observed by Kepler, is now received by all
astronomers; for the periodic times are the same, and the dimensions
of the orbits are the same, whether the sun revolves about the earth,
or the earth about the sun. And as to the measures of the periodic
times, all astronomers are agreed about them. But for the dimensions
of the orbits, Kepler and Bullialdus, above all others, have
determined them from observations with the greatest accuracy; and the
mean distances corresponding to the periodic times differ but
insensibly from those which they have assigned, and for the most part
fall in between them; as we may see from the following table."

http://members.tripod.com/~gravitee/phaenomena.htm

Later scientists took this too far and shifted planetary longitudes
based on the 24 hour/360 degree equivalency to the sidereal value of
23 hours 56 min 04 sec to geocentric longitudes to suit the purpose of
justifying Newton's treatment of orbital motion and nothing could be
worse.

http://www.absolutebeginnersastronomy.com/sidereal.gif

The problem with the sidereal picture is that there is no equable
motion corresponding to 24 hours wrt to the Sun which is why the
Equation of Time was applied daily by astronomers.Newton could
correctly say that there is no observed equable motion corresponding
to the 24 hour/360 degree equivalency for the axial rotation of the
Earth.

"Absolute time, in astronomy, is distinguished from relative, by the
equation or correlation of the vulgar time. For the natural days are
truly unequal, though they are commonly considered as equal and used
for a measure of time; astronomers correct this inequality for their
more accurate deducing of the celestial motions. It may be, that there
is no such thing as an equable motion, whereby time may be accurately
measured "

Axel,there is a disaster in the making in there and especially the
decision to jettison the EoT bridge between the constant 24 hour day
and the natural unequal day or what amounts to the same
thing,jettisoning the relationship between absolute time and relative
time as Newton phrased it.With the Sun based Equation of Time format
which is a direct consequence of Kepler's second law,constant axial
rotation and variable orbital motion are combined in the natural
unequal day but the Equation of Time correction isolates axial
rotation by equalising the orbital variation,the following graphic of
Kepler's second law may be of use -

http://ircamera.as.arizona.edu/NatSc...res/kepler.htm

What is absent from the graphic is constant axial rotation within the
comparison or orbital motion,it makes all the difference because the
sidereal value imposes a clockwork picture on the Earth's orbital
motion where naturally the combined axial and orbital motion generates
a far more complex picture,one in which you cannot say the motion of
Earth around the Sun is the same as the Sun around the Earth.The
addition and subtraction of minutes and seconds which facilitates the
seamless transition from one 24 hour day to the next via the Equation
of Time determines that there is no equable combined motions of the
Earth around the Sun and subsequently it is a terrible error to
imagine that the combined motions of the Earth can be treated as a
single sidereal motion.

Newton ,while being aware of the Equation of Time and its components
never fully understood it,when he goes to tackle Flamsteed's data
based on the isochronos value he cannot make head nor tails of the
data and with good reason.

"Axel Harvey" wrote in message
om...
"jonathan" wrote:

We choose ideas based on which better predicts the future.
Based on which allows us to find the higher points on our
perceived fitness landscape.

Nematodes and tigers may find it easy to discover the high points of
their fitness landscape, but humans with their impoverished instincts
need to think about it. There must be cases where the choice of a
coordinate system will simplify calculations, and the choice then is
made for mathematical reasons - when a different choice might lead to
equivalent correct predictions while creating unnecessary difficulties
of computation. (I am *not* referring to Copernicus here, just
suggesting a general idea.)

A propos, Albert Einstein and Leopold Infeld wrote in _The_Evolution_
_of_Physics_ (1938):

Can we formulate physical laws so that they are valid for all
C[oordinate] S[ystems], not only those moving uniformly, but also
those moving quite arbitrarily, relative to each other? If this can
be done, our troubles will be over. We shall then be able to apply the
laws of nature to any CS.


The problem with this statement is that one can't apply a model of
reality universally if a coordinate system is used. The structure
of the universe and of life is due to dynamic ...and...non-linear
processes. Which cannot be mapped with the use of linear
equations. In reality the input does not predict the output
as any equation seeks to do.

Coordinate systems seek deterministic answers, there
are none. It is the entire concept of objectivity that is
the core problem with establishing a universal theory.

What is needed is a relative approach, where the ...methods...
used are transformed from completely objective to completely
subjective depending on the observer. It is critical that
the observer is included by subjectively deciding the frame of
reference before proceeding with the analysis.

For example, if an object of study were treated by the
observer as an isolated system, then ecosystem or
holistic methods would be used. If the same object
is defined by the observer to be a component of
a larger system then classical objective methods
would be used on the object.. If the object is somewhere
in between then the observer would need to make
a judgment and mix methods appropriately.

In addition by using behavior (output) as the object of study
as opposed to part properties(input), one can move between
disciplines with ease. To accomplish the dream quoted
above, a subjective and behavior driven mathematics
is needed. This is now called complexity science, a universal
mathematics that provides a common scientific language
to all of reality. A psychologist can compare notes with
a biologist or a politician. This allows the commonalities
of all the various disciplines to be seen with ease.

Those commonalities found would define the axioms of
science.

Since no object is truly isolated, the more one objectifies
the more one simplifies. And since objective methods
tend to start from the smallest scale and extrapolate out
to the whole, objective and repeatable methods define
the most error filled and limited possible method of
understanding when dealing with complex dynamic
systems...with life.

To accomplish the quoted goal we must simply and
rigorously ....inverse...all the frames of reference we
have been taught to follow. All of them.

Then start over from scratch.


Jonathan

s




The struggle, so violent in the early days
of science, between the views of Ptolemy and Copernicus would then be
quite meaningless. Either CS could be used with equal justification.
The two sentences, "the sun is at rest and the earth moves," or "the
sun moves and the earth is at rest," would simply mean two different
conventions concerning two different CS. Could we build a real
relativistic physics valid in all CS; a physics in which there would
be no place for absolute, but only for relative motion? This is indeed
possible!


Yes it is. The earth revolves around the sun for the same reason
life evolves, for the same reason sun shines, and the same
reason market systems self-tune.

Because they all stand poised at the subcritical supracritical
boundary between their static and chaotic forms. At the phase
transition between order and chaos.


Fourth Law Stuff
http://www.santafe.edu/sfi/People/ka...tigations.html

Some complexity links
http://users.ox.ac.uk/~quee0818/comp...omplexity.html
http://necsi.org/cxworld/index.html
http://www-chaos.umd.edu/
http://www.psych.lse.ac.uk/complexity/
http://cnls.lanl.gov/Conferences/Annual-2003/CNLS03AC/
http://feynman.princeton.edu/~steinh/


Jonathan

s




(End of quotation).

I am not aversed to telling people how it is that you abandon Newton,
because the moon does not spin on its center of mass gravity
as it should , and Einstein would falter if you mentioned the
tides, and he would mumble something about gravitons,
and then Feynman would begin to throw pillows at
Hawking who would begin the head nodding process.

All the while, frame dragging is the cause of the tides,
and if you examine that gravity waves are a form of dark energy,
that ALL elements emit, then you can see, that the push
from the gravity waves, is what affects the tides, and
GR and SR are still valid in all reference frames,
and the principle of equalivalence, is preserved.



"Axel Harvey" wrote in message om...
"jonathan" wrote:

We choose ideas based on which better predicts the future.
Based on which allows us to find the higher points on our
perceived fitness landscape.

Nematodes and tigers may find it easy to discover the high points of
their fitness landscape, but humans with their impoverished instincts
need to think about it. There must be cases where the choice of a
coordinate system will simplify calculations, and the choice then is
made for mathematical reasons - when a different choice might lead to
equivalent correct predictions while creating unnecessary difficulties
of computation. (I am *not* referring to Copernicus here, just
suggesting a general idea.)

A propos, Albert Einstein and Leopold Infeld wrote in _The_Evolution_
_of_Physics_ (1938):

Can we formulate physical laws so that they are valid for all
C[oordinate] S[ystems], not only those moving uniformly, but also
those moving quite arbitrarily, relative to each other? If this can
be done, our troubles will be over. We shall then be able to apply the
laws of nature to any CS. The struggle, so violent in the early days
of science, between the views of Ptolemy and Copernicus would then be
quite meaningless. Either CS could be used with equal justification.
The two sentences, "the sun is at rest and the earth moves," or "the
sun moves and the earth is at rest," would simply mean two different
conventions concerning two different CS. Could we build a real
relativistic physics valid in all CS; a physics in which there would
be no place for absolute, but only for relative motion? This is indeed
possible!

(End of quotation).