UNIQUE 3 BODY PROBLEM

Thought you might be interested in this exotic solution of the 3 body problem in gravity - where the three bodies follow each other around a figure of eight route http://faculty.ifmo.ru/butikov/Proje...llection3.html

The Overview page...

http://faculty.ifmo.ru/butikov/Projects/Collection.html

.... shows other solutions, from different perspectives.

"palsing" wrote in message ...
Thought you might be interested in this exotic solution of the 3 body problem in gravity - where the three bodies follow each other around a figure of eight route http://faculty.ifmo.ru/butikov/Proje...llection3.html

The Overview page...

http://faculty.ifmo.ru/butikov/Projects/Collection.html

.... shows other solutions, from different perspectives.

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Canals on Mars all over again:
http://www.straitstimes.com/breaking...-suns-20121016

Astronomers see whatever they want to see

On Oct 18, 4:54*pm, palsing wrote:
Thought you might be interested in this exotic solution of the 3 body problem in gravity - where the three bodies follow each other around a figure of eight routehttp://faculty.ifmo.ru/butikov/Projects/Collection3.html

The Overview page...

http://faculty.ifmo.ru/butikov/Projects/Collection.html

... shows other solutions, from different perspectives.

Let me see -

"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 " Newton

The sun and planets around the Earth indeed !, the actual statement by
Kepler is -

"The proportion existing between the periodic times of any two planets
is exactly the sesquiplicate proportion of the mean distances of the
orbits, or as generally given,the squares of the periodic times are
proportional to the cubes of the mean distances." Kepler

What Isaac was trying to do was make celestial sphere geometry (fixed
stars) a common denominator for his absolute/relative space and motion
spiel and what I wouldn't give to find a genuine empiricist who could
walk through the process as a man rather than hide behind contemporary
voodoo.For everyone else,Kepler's proposal,although flawed, is easy
enough to accept despite the initial unfamiliarity as it requires the
usual spacial awareness when dealing with the relationship of
individual orbits to each other and to the central Sun.

"But it is absolutely certain and exact that the ratio which exists
between the periodic times of any two planets is precisely the ratio
of the 3/2th power of the mean distances, i.e., of the spheres
themselves; provided, however, that the arithmetic mean between both
diameters of the elliptic orbit be slightly less than the longer
diameter. And so if any one take the period, say, of the Earth, which
is one year, and the period of Saturn, which is thirty years, and
extract the cube roots of this ratio and then square the ensuing ratio
by squaring the cube roots, he will have as his numerical products the
most just ratio of the distances of the Earth and Saturn from the sun.
1 For the cube root of 1 is 1, and the square of it is 1; and the cube
root of 30 is greater than 3, and therefore the square of it is
greater than 9. And Saturn, at its mean distance from the sun, is
slightly higher than nine times the mean distance of the Earth from
the sun." Kepler

Do empiricists not wish to investigate geomagnetism,fluid
dynamics,plate tectonics and all those other topics which require the
amazing details supplied by contemporary data or do you still wish to
live back in the late 17th century praising mathematicians who made a
mess of things in exploiting astronomical intricacies inherent in
genuine astronomy ?.

The astronomical narrative is so unstable what with the next scam of
exoplanet attributes while our own planet suffers from people who
insist that it does not rotate 1461 times to the nearest rotation in
proportion to 4 orbital circuits of the Sun.