| Topic: |
Science > Physics |
| User: |
"John Baez" |
| Date: |
24 Oct 2004 07:06:49 PM |
| Object: |
Lagrange Points |
If you like physics and astronomy, check out my new improved
webpage on "Lagrange points" - those orbits where a small third
body can stay in equilibrium rotating along with two more massive
ones:
http://math.ucr.edu/home/baez/langrange.html
Watch a movie of Trojan asteroids, read about the rare Mars
Trojans and the one known Neptune Trojan, see a movie of the
crazy horseshoe-shaped orbit of the asteroid 3753 Cruithne,
read about the search for alien spacecraft at the earth-moon
Lagrange points, and learn what was *found* at these Lagrange
points! Read about the mysterious missing extra moons of the
Earth: Lilith and Kleinchen! There's some nice math here, too:
Neil Cornish's updated version of Lagrange's proof that orbits
at L4 and L5 are stable.
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| User: "Narasimham G.L." |
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| Title: Re: Lagrange Points |
25 Oct 2004 11:22:01 AM |
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(John Baez) wrote in message news:<clhg2p$n4p$1@glue.ucr.edu>...
If you like physics and astronomy, check out my new improved
webpage on "Lagrange points" - those orbits where a small third
body can stay in equilibrium rotating along with two more massive
ones:
http://math.ucr.edu/home/baez/lagrange.html
Watch a movie of Trojan asteroids, read about the rare Mars
Trojans and the one known Neptune Trojan, see a movie of the
crazy horseshoe-shaped orbit of the asteroid 3753 Cruithne,
read about the search for alien spacecraft at the earth-moon
Lagrange points, and learn what was *found* at these Lagrange
points! Read about the mysterious missing extra moons of the
Earth: Lilith and Kleinchen! There's some nice math here, too:
Neil Cornish's updated version of Lagrange's proof that orbits
at L4 and L5 are stable.
Respected Sir,
Gravity, electrostatic and magnetic fields exert forces spatially by
the same Inverse Squared Law. We can see lines of magnetic force using
iron filings. Are there similar demonstrative physics experiments of
moving poles or charges that simulate gravity, convincingly showing
relative locations of stable points L4 and L5 among motions of the
three bodies? It may perhaps be more instructive than fictitious
computer games and animations.
.
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| User: "Uncle Al" |
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| Title: Re: Lagrange Points |
25 Oct 2004 11:54:19 AM |
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"Narasimham G.L." wrote:
baez@galaxy.ucr.edu (John Baez) wrote in message news:<clhg2p$n4p$1@glue.ucr.edu>...
If you like physics and astronomy, check out my new improved
webpage on "Lagrange points" - those orbits where a small third
body can stay in equilibrium rotating along with two more massive
ones:
http://math.ucr.edu/home/baez/lagrange.html
Watch a movie of Trojan asteroids, read about the rare Mars
Trojans and the one known Neptune Trojan, see a movie of the
crazy horseshoe-shaped orbit of the asteroid 3753 Cruithne,
read about the search for alien spacecraft at the earth-moon
Lagrange points, and learn what was *found* at these Lagrange
points! Read about the mysterious missing extra moons of the
Earth: Lilith and Kleinchen! There's some nice math here, too:
Neil Cornish's updated version of Lagrange's proof that orbits
at L4 and L5 are stable.
Respected Sir,
Gravity, electrostatic and magnetic fields exert forces spatially by
the same Inverse Squared Law.
Except for magnetism.
We can see lines of magnetic force using
iron filings.
There are no lines of magnetic force. You are viewing an artifact.
Are there similar demonstrative physics experiments of
moving poles or charges that simulate gravity, convincingly showing
relative locations of stable points L4 and L5 among motions of the
three bodies? It may perhaps be more instructive than fictitious
computer games and animations.
"Az di bobe vot gehat beytsim volt zi geven mayn zeyde."
Do you have three grandfathers?
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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| User: "Narasimham G.L." |
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| Title: Re: Lagrange Points |
26 Oct 2004 03:44:17 AM |
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Uncle Al <UncleAl0@hate.spam.net> wrote in message news:<417D2FBB.7CC3563D@hate.spam.net>...
"Narasimham G.L." wrote:
baez@galaxy.ucr.edu (John Baez) wrote in message news:<clhg2p$n4p$1@glue.ucr.edu>...
If you like physics and astronomy, check out my new improved
webpage on "Lagrange points" - those orbits where a small third
body can stay in equilibrium rotating along with two more massive
ones:
http://math.ucr.edu/home/baez/lagrange.html
Watch a movie of Trojan asteroids, read about the rare Mars
Trojans and the one known Neptune Trojan, see a movie of the
crazy horseshoe-shaped orbit of the asteroid 3753 Cruithne,
read about the search for alien spacecraft at the earth-moon
Lagrange points, and learn what was *found* at these Lagrange
points! Read about the mysterious missing extra moons of the
Earth: Lilith and Kleinchen! There's some nice math here, too:
Neil Cornish's updated version of Lagrange's proof that orbits
at L4 and L5 are stable.
Respected Sir,
Gravity, electrostatic and magnetic fields exert forces spatially by
the same Inverse Squared Law.
Except for magnetism.
We can see lines of magnetic force using iron filings.
There are no lines of magnetic force. You are viewing an artifact.
Please correct this if and where in error: In a pure magnetic
dipole(elecromagnetics) and in a pair of opposite
charges(electrostatics) forces act on any point as per Inverse Squared
Law, with a constant angle between the forces, and so the lines of
force are circles through the poles/charges. Imaginary lines of Force
and Equipotential lines are given by the complex variable function
using bipolar co-ordinates z = i a coth[(zeta+ i eta)/2]..
I thought that what we learnt in school with a bar magnet and oriented
iron filings was in principle just this, a visualization of lines of
magnetic force.
The lines of force may be seen fictitious or real, but a force causing
the push along the fictitious (man invented) lines is real...
Accelerations,velocities and and so the integrand displacements are
all real in this sense, like paths taken by planets around the sun.
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| User: "Uncle Al" |
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| Title: Re: Lagrange Points |
26 Oct 2004 10:55:47 AM |
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"Narasimham G.L." wrote:
Uncle Al <UncleAl0@hate.spam.net> wrote in message news:<417D2FBB.7CC3563D@hate.spam.net>...
"Narasimham G.L." wrote:
baez@galaxy.ucr.edu (John Baez) wrote in message news:<clhg2p$n4p$1@glue.ucr.edu>...
If you like physics and astronomy, check out my new improved
webpage on "Lagrange points" - those orbits where a small third
body can stay in equilibrium rotating along with two more massive
ones:
http://math.ucr.edu/home/baez/lagrange.html
Watch a movie of Trojan asteroids, read about the rare Mars
Trojans and the one known Neptune Trojan, see a movie of the
crazy horseshoe-shaped orbit of the asteroid 3753 Cruithne,
read about the search for alien spacecraft at the earth-moon
Lagrange points, and learn what was *found* at these Lagrange
points! Read about the mysterious missing extra moons of the
Earth: Lilith and Kleinchen! There's some nice math here, too:
Neil Cornish's updated version of Lagrange's proof that orbits
at L4 and L5 are stable.
Respected Sir,
Gravity, electrostatic and magnetic fields exert forces spatially by
the same Inverse Squared Law.
Except for magnetism.
We can see lines of magnetic force using iron filings.
There are no lines of magnetic force. You are viewing an artifact.
Please correct this if and where in error: In a pure magnetic
dipole(elecromagnetics) and in a pair of opposite
charges(electrostatics) forces act on any point as per Inverse Squared
Law, with a constant angle between the forces, and so the lines of
force are circles through the poles/charges. Imaginary lines of Force
and Equipotential lines are given by the complex variable function
using bipolar co-ordinates z = i a coth[(zeta+ i eta)/2]..
If you think you have something, pursue it. Since the unification of
electromagnetism and gravitation have been seriously and voluminously
pursued (Kaluza-Klein treatments and others) *unsuccessfully* you had
better have a Flemish Giant rabbit ready to pull out of your hat.
28-lb rabbits are few and far between. Don't claim you have something
extraodinary until you demonstrably do - and present a pile of
refereed literature citations to back you up along every inch of the
new path until it forks.
I've never seen a real world magnetic field calculation that wasn't a
hellish nastiness. Neither have you. Point monopoles and clusters of
them have potentially clean mathematics re the inverse square law
locally and Green's function for clusters' far field. Clusters of
interacting finite extent dipoles have no clean mathematics near
field. Magnetic lattices are Hell to calculate (spin glasses, spin
frustration). If there are electric monopoles there are no magnetic
monopoles. Electrons, protons.
There are 40,000+ PhD members of the American Physical Society alone.
If there were any hint, the smallest hallucination, of the physics
about which you eructate, untenured faculty would be all over it in a
New York second. The obvious will not be overlooked by everybody
skilled in the art - not when there are 100,000 PhD level folks plus
untold numbers of grad students plus untold numbers of undergrads all
looking at it from a plethora of cultural biases worldwide. New
insight must either be frightfully clever (how did he ever think of
that!) or interdisciplinary (no physicist is expected to discover
something dependent upon the Woodward-Hoffmann rules in chemistry).
Physics contains no internal errors of mathematical self-consistency.
Physics is deeply empirically examined for falsification at every
possible level, scale, and magnitude. Physics works to spec in the
real world. Physics is hugely dripping with elegant theoretical
***** - M-theory, lattice quantum gravitation. Where would a new
surprise be hidden?
1) A new observation. The Pioneer anomaly is a pretty thing,
http://arxiv.org/abs/gr-qc/0205059
Pioneer anomaly
http://arXiv.org/abs/gr-qc/0307042
Rationalized Pioneer anomaly
http://arXiv.org/abs/gr-qc/9810085
Believable rationalized Pioneer anomaly
http://arXiv.org/abs/gr-qc/gr-qc/0310088
Believable Pioneer anomaly updated
so are the mechanisms of high temp ceramic superconductors and why
spiral galaxies persist over all visible time. You don't have a
volunteered new observation.
2) A falsified hypothesis. No axiomatic construct can defend its
postulates or they would be derived not postulated. General
Relativity postulates the Equivalence Principle (EP). The EP has only
been deeply tested for chemical composition, polarized spin bodies
(magnets), and physically spinning bodies. Uncle Al identified and
calculated another never-tested property of falling bodies,
http://www.mazepath.com/uncleal/qz.pdf
The first of three parity Eotvos experiments is currently in progress
in Huazhong University. We'll know by Summer 2005. There is no
reason why the experiments are going to give net output, or not give
net output. It's unexplored territory.
3) New theory consistent with prior observation and making new and
empirically falsifable predictions. If you insist you have something
new gravitionally despite examples posted to the contrary, use it to
calculate Mercury's perihelion precession, GPS correction,
<http://relativity.livingreviews.org/Articles/lrr-2003-1/>
http://www.eftaylor.com/pub/projecta.pdf
<http://www.public.asu.edu/~rjjacob/Lecture16.pdf>
falling light,
http://arXiv.org/abs/gr-qc/9909014
Phys. Rev. Lett. 92 (2004) 121101
etc. If you pull it off, you get the laurel wreath. Outrageous
claims require outrageous proofs. Go for it. Make a testable
prediction external to extant physics.
I thought that what we learnt in school with a bar magnet and oriented
iron filings was in principle just this, a visualization of lines of
magnetic force.
Does an equipotential surface exist as a physical entity? (If you do
auto racing, do not chrome plate your roll axis - it will become
brittle.) What would it look like if you used cubic 10-nanometer edge
iron dust to decorate it? What is the intrinsic spacing of magnetic
"lines of force?" Do Saturn's rings show gravitational lines of
force?
The lines of force may be seen fictitious or real, but a force causing
the push along the fictitious (man invented) lines is real...
Accelerations,velocities and and so the integrand displacements are
all real in this sense, like paths taken by planets around the sun.
What path does the Earth take about the sun? Consider geocenter vs.
Earth-moon barycenter origin for the big swirls, and the composite
orbit including the Milky Way center of mass. Add the measurable
relativistic perihelion precession even at Earth orbit. The moon's
orbit is increasing its radius by a few cm/year from tidal dissipation
- more so if Enviro-whiners cause tidal electrical generators to be
built. The solar system is not stable, it is chaotic. Digital
orreries show a general breakdown of predictablity over long
timespans. It isn't that simple - not if you care about the decimal
places.
If you think you have something, pursue it. Since the unification of
electromagnetism and gravitation have been seriously and voluminously
pursued (Kaluza-Klein treatments and others) *unsuccessfully* you had
better have a Flemish Giant rabbit ready to pull out of your hat.
28-lb rabbits are few and far between. Don't claim you have something
extraodinary until you demonstrably do - and you had better have a
pile of refereed literature citations to back you up every inch of the
way.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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| User: "Robert Israel" |
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| Title: Re: Lagrange Points |
25 Oct 2004 10:30:29 PM |
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In article <676dc11a.0410250822.2f36e432@posting.google.com>,
Narasimham G.L. <mathma18@hotmail.com> wrote:
Gravity, electrostatic and magnetic fields exert forces spatially by
the same Inverse Squared Law. We can see lines of magnetic force using
iron filings. Are there similar demonstrative physics experiments of
moving poles or charges that simulate gravity, convincingly showing
relative locations of stable points L4 and L5 among motions of the
three bodies? It may perhaps be more instructive than fictitious
computer games and animations.
As Uncle Al said, magnetic fields aren't inverse square (well they
would be if you had magnetic monopoles, but those are in short supply
right now). In principle you could set up an electrostatic simulation
of two-body motion under gravity (although I think it would be very
difficult to do this on earth if you don't want friction and external
forces to affect it significantly), but _not_ three-body motion.
The simple reason is that it's opposite charges that attract: if the
first two bodies are attracted to each other, the third will be attracted
by one but repelled by the other.
Robert Israel
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
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| User: "ZZBunker" |
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| Title: Re: Lagrange Points |
27 Oct 2004 10:40:43 PM |
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(Robert Israel) wrote in message news:<clkgcl$32l$1@nntp.itservices.ubc.ca>...
In article <676dc11a.0410250822.2f36e432@posting.google.com>,
Narasimham G.L. <mathma18@hotmail.com> wrote:
Gravity, electrostatic and magnetic fields exert forces spatially by
the same Inverse Squared Law. We can see lines of magnetic force using
iron filings. Are there similar demonstrative physics experiments of
moving poles or charges that simulate gravity, convincingly showing
relative locations of stable points L4 and L5 among motions of the
three bodies? It may perhaps be more instructive than fictitious
computer games and animations.
As Uncle Al said, magnetic fields aren't inverse square (well they
would be if you had magnetic monopoles, but those are in short supply
right now). In principle you could set up an electrostatic simulation
of two-body motion under gravity (although I think it would be very
difficult to do this on earth if you don't want friction and external
forces to affect it significantly), but _not_ three-body motion.
The simple reason is that it's opposite charges that attract: if the
first two bodies are attracted to each other, the third will be attracted
by one but repelled by the other.
But as Uncle Al says, and idiot mathematicians
say, is because the strong force is also not
inverse square, that means the strong is not a FORCE.
Since most transformers don't even have dipoles,
but they have a force that would sap any moron
Maxwellian into the next Euclid sphere of
French Frog non-existience, it is still a force.
Robert Israel
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
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| User: "John M. Gamble" |
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| Title: Re: Lagrange Points |
27 Oct 2004 05:49:15 PM |
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In article <clkgcl$32l$1@nntp.itservices.ubc.ca>,
Robert Israel <israel@math.ubc.ca> wrote:
As Uncle Al said, magnetic fields aren't inverse square (well they
would be if you had magnetic monopoles, but those are in short supply
right now). In principle you could set up an electrostatic simulation
Are magnetic monopoles no longer considered possible? It has been
years since i've read anything about a search for them, or read
an article about their hypothetical existence.
--
-john
February 28 1997: Last day libraries could order catalogue cards
from the Library of Congress.
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| User: "Chan-Ho Suh" |
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| Title: Re: Lagrange Points |
24 Oct 2004 07:43:15 PM |
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In article <clhg2p$n4p$1@glue.ucr.edu>, John Baez <baez@galaxy.ucr.edu>
wrote:
http://math.ucr.edu/home/baez/langrange.html
To those who would just click on this (like I did), should note that
"langrange" should be replaced by "lagrange".
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| User: "Robert Israel" |
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| Title: Re: Lagrange Points |
24 Oct 2004 07:41:40 PM |
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In article <clhg2p$n4p$1@glue.ucr.edu>, John Baez <baez@galaxy.ucr.edu> wrote:
If you like physics and astronomy, check out my new improved
webpage on "Lagrange points" - those orbits where a small third
body can stay in equilibrium rotating along with two more massive
ones:
http://math.ucr.edu/home/baez/langrange.html
^^^^^^^^^
That should be lagrange, of course.
Nice site.
Robert Israel
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
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| User: "Uncle Al" |
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| Title: Re: Lagrange Points |
24 Oct 2004 08:14:51 PM |
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John Baez wrote:
If you like physics and astronomy, check out my new improved
webpage on "Lagrange points" - those orbits where a small third
body can stay in equilibrium rotating along with two more massive
ones:
http://math.ucr.edu/home/baez/langrange.html
Watch a movie of Trojan asteroids, read about the rare Mars
Trojans and the one known Neptune Trojan, see a movie of the
crazy horseshoe-shaped orbit of the asteroid 3753 Cruithne,
read about the search for alien spacecraft at the earth-moon
Lagrange points, and learn what was *found* at these Lagrange
points! Read about the mysterious missing extra moons of the
Earth: Lilith and Kleinchen! There's some nice math here, too:
Neil Cornish's updated version of Lagrange's proof that orbits
at L4 and L5 are stable.
The ohnosecond is that exquisitely small time interval between
clicking "send" and seeing the dreadful error.
http://math.ucr.edu/home/baez/lagrange.html
Hang in there, John. It isn't serious until you spend two hours in
Starbucks, walk out, see another Starbucks across the street, and
decide that a cup of joe is just what you need.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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| User: "Eric Gisse" |
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| Title: Re: Lagrange Points |
25 Oct 2004 07:17:12 PM |
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Uncle Al <UncleAl0@hate.spam.net> wrote in message news:<417C538B.75A222CC@hate.spam.net>...
John Baez wrote:
If you like physics and astronomy, check out my new improved
webpage on "Lagrange points" - those orbits where a small third
body can stay in equilibrium rotating along with two more massive
ones:
http://math.ucr.edu/home/baez/langrange.html
Watch a movie of Trojan asteroids, read about the rare Mars
Trojans and the one known Neptune Trojan, see a movie of the
crazy horseshoe-shaped orbit of the asteroid 3753 Cruithne,
read about the search for alien spacecraft at the earth-moon
Lagrange points, and learn what was *found* at these Lagrange
points! Read about the mysterious missing extra moons of the
Earth: Lilith and Kleinchen! There's some nice math here, too:
Neil Cornish's updated version of Lagrange's proof that orbits
at L4 and L5 are stable.
The ohnosecond is that exquisitely small time interval between
clicking "send" and seeing the dreadful error.
http://math.ucr.edu/home/baez/lagrange.html
Hang in there, John. It isn't serious until you spend two hours in
Starbucks, walk out, see another Starbucks across the street, and
decide that a cup of joe is just what you need.
Someone is a fan of Lewis Black...
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| User: "Uncle Al" |
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| Title: Re: Lagrange Points |
25 Oct 2004 08:01:26 PM |
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Eric Gisse wrote:
Uncle Al <UncleAl0@hate.spam.net> wrote in message news:<417C538B.75A222CC@hate.spam.net>...
John Baez wrote:
If you like physics and astronomy, check out my new improved
webpage on "Lagrange points" - those orbits where a small third
body can stay in equilibrium rotating along with two more massive
ones:
http://math.ucr.edu/home/baez/langrange.html
Watch a movie of Trojan asteroids, read about the rare Mars
Trojans and the one known Neptune Trojan, see a movie of the
crazy horseshoe-shaped orbit of the asteroid 3753 Cruithne,
read about the search for alien spacecraft at the earth-moon
Lagrange points, and learn what was *found* at these Lagrange
points! Read about the mysterious missing extra moons of the
Earth: Lilith and Kleinchen! There's some nice math here, too:
Neil Cornish's updated version of Lagrange's proof that orbits
at L4 and L5 are stable.
The ohnosecond is that exquisitely small time interval between
clicking "send" and seeing the dreadful error.
http://math.ucr.edu/home/baez/lagrange.html
Hang in there, John. It isn't serious until you spend two hours in
Starbucks, walk out, see another Starbucks across the street, and
decide that a cup of joe is just what you need.
Someone is a fan of Lewis Black...
Baez and Black, artisans both.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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| User: "John Baez" |
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| Title: Re: Lagrange Points |
26 Oct 2004 02:14:47 AM |
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In article <417DA1E6.C6540DA2@hate.spam.net>,
Uncle Al <UncleAl0@hate.spam.net> wrote:
John Baez wrote:
http://math.ucr.edu/home/baez/lagrange.html
The ohnosecond is that exquisitely small time interval between
clicking "send" and seeing the dreadful error.
http://math.ucr.edu/home/baez/lagrange.html
Whoops. And you don't mean Yoko.
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| User: "Ken S. Tucker" |
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| Title: Re: Lagrange Points |
26 Oct 2004 05:03:01 PM |
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(John Baez) wrote in message news:<clkth7$l33$1@glue.ucr.edu>...
In article <417DA1E6.C6540DA2@hate.spam.net>,
Uncle Al <UncleAl0@hate.spam.net> wrote:
John Baez wrote:
http://math.ucr.edu/home/baez/lagrange.html
The ohnosecond is that exquisitely small time interval between
clicking "send" and seeing the dreadful error.
http://math.ucr.edu/home/baez/lagrange.html
Whoops. And you don't mean Yoko.
The yokosecond is that interval when you think everything
is fine as the ENTER decision is made, just before the
ohnosecond. When the ohnosecond occurs, time reverses
and you realize you were using yoko-time.
1) I have been told the Lagrange itself contains
no more *physical* content than 1+1=2 does, and
that it's a math theorem - as addition etc is -
that can be applied physically.
Opinions invited.
2) Looking at the Lagrange point *contours*,
in the sun-earth-moon system together with
J. Baez's dust accumulation notions, at his
site made me think of a *probability field*.
Suppose we had a even distribution of dust
in a volume (I'm also thinking about iron
fillings before a magnet is employed),
((J. Baez usually uses coffee grains)).
Now we place into our dust the sun-earth-moon
in a stable dynamic relation, and find the
distribution of the dust acquires a variation
in a problistic manner, consistent with the
Lagrange "field".
Is that reasonable?
TIA
Ken S. Tucker
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| User: "George Dishman" |
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| Title: Re: Lagrange Points |
27 Oct 2004 02:11:33 PM |
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"Ken S. Tucker" <dynamics@vianet.on.ca> wrote in message
news:2202379a.0410261403.44d1ae2@posting.google.com...
1) I have been told the Lagrange itself contains
no more *physical* content than 1+1=2 does, and
that it's a math theorem - as addition etc is -
that can be applied physically.
Opinions invited.
Maths is a tool that we can use to model
the world around us. There is a physical
meaning to lagrange points otherwise
objects would not gather there.
2) Looking at the Lagrange point *contours*,
in the sun-earth-moon system together with
J. Baez's dust accumulation notions, at his
site made me think of a *probability field*.
Suppose we had a even distribution of dust
in a volume (I'm also thinking about iron
fillings before a magnet is employed),
((J. Baez usually uses coffee grains)).
Now we place into our dust the sun-earth-moon
in a stable dynamic relation, and find the
distribution of the dust acquires a variation
in a problistic manner, consistent with the
Lagrange "field".
Is that reasonable?
It seems reasonable to look at an aggregate
such dust in a statistical manner. When
considering a single object, it is perhaps
more informative to think in terms of the
specific forces that affect it. However you
look at it, Trojans don't carry calculators
so it is more than just maths.
George
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| User: "Dirk Van de moortel" |
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| Title: Re: Lagrange Points |
27 Oct 2004 02:15:36 PM |
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"George Dishman" <george@briar.demon.co.uk> wrote in message news:1098904315.27567.0@nnrp-t71-02.news.clara.net...
"Ken S. Tucker" <dynamics@vianet.on.ca> wrote in message
news:2202379a.0410261403.44d1ae2@posting.google.com...
1) I have been told the Lagrange itself contains
no more *physical* content than 1+1=2 does, and
that it's a math theorem - as addition etc is -
that can be applied physically.
Opinions invited.
Maths is a tool that we can use to model
the world around us. There is a physical
meaning to lagrange points otherwise
objects would not gather there.
2) Looking at the Lagrange point *contours*,
in the sun-earth-moon system together with
J. Baez's dust accumulation notions, at his
site made me think of a *probability field*.
Suppose we had a even distribution of dust
in a volume (I'm also thinking about iron
fillings before a magnet is employed),
((J. Baez usually uses coffee grains)).
Now we place into our dust the sun-earth-moon
in a stable dynamic relation, and find the
distribution of the dust acquires a variation
in a problistic manner, consistent with the
Lagrange "field".
Is that reasonable?
It seems reasonable to look at an aggregate
such dust in a statistical manner. When
considering a single object, it is perhaps
more informative to think in terms of the
specific forces that affect it. However you
look at it, Trojans don't carry calculators
so it is more than just maths.
George, I love that comment.
Very nice :-)
Dirk Vdm
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| User: "Sam Wormley" |
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| Title: Re: Lagrange Points |
24 Oct 2004 07:53:19 PM |
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John Baez wrote:
If you like physics and astronomy, check out my new improved
webpage on "Lagrange points" - those orbits where a small third
body can stay in equilibrium rotating along with two more massive
ones:
http://math.ucr.edu/home/baez/langrange.html
CORRECTION
http://math.ucr.edu/home/baez/lagrange.html
Watch a movie of Trojan asteroids, read about the rare Mars
Trojans and the one known Neptune Trojan, see a movie of the
crazy horseshoe-shaped orbit of the asteroid 3753 Cruithne,
read about the search for alien spacecraft at the earth-moon
Lagrange points, and learn what was *found* at these Lagrange
points! Read about the mysterious missing extra moons of the
Earth: Lilith and Kleinchen! There's some nice math here, too:
Neil Cornish's updated version of Lagrange's proof that orbits
at L4 and L5 are stable.
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| User: "JEMebius" |
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| Title: Re: Lagrange Points - URL not found |
24 Oct 2004 08:25:02 PM |
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URL not found - Looking forward to meet the Trojans in semi-real life! Johan
John Baez wrote:
If you like physics and astronomy, check out my new improved
webpage on "Lagrange points" - those orbits where a small third
body can stay in equilibrium rotating along with two more massive
ones:
http://math.ucr.edu/home/baez/langrange.html
Watch a movie of Trojan asteroids, read about the rare Mars
Trojans and the one known Neptune Trojan, see a movie of the
crazy horseshoe-shaped orbit of the asteroid 3753 Cruithne,
read about the search for alien spacecraft at the earth-moon
Lagrange points, and learn what was *found* at these Lagrange
points! Read about the mysterious missing extra moons of the
Earth: Lilith and Kleinchen! There's some nice math here, too:
Neil Cornish's updated version of Lagrange's proof that orbits
at L4 and L5 are stable.
.
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