The 8th Doctrine of Kepler
- From: oriel36 <geraldkelleher@xxxxxxxxx>
- Date: Sun, 02 Sep 2007 11:50:57 -0700
Kepler explains his coming to the insight -
"...if you want the exact time, was conceived mentally on the 8th of
March in this year One Thousand Six Hundred and Eighteen but
unfelicitously submitted to calculation and rejected as false,
finally, summoned back on the 15th of May, with a fresh assault
undertaken, outfought the darkness of my mind by the great proof
afforded by my labor of seventeen years on Brahe's observations and
meditation upon it uniting in one concord, in such fashion that I
first believed I was dreaming and was presupposing the object of my
search among the principles. 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."
http://www.sacred-texts.com/astro/how/how04.htm
Any astronomer can admire how the orbital comparisons based on orbital
'periodic times was transfered to orbital distances from the Sun.They
can even see where it turns into a convoluted mess by Newton and his
followers,something they now call 'Kepler's third law' -
"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." Newton
It is an occasion for dynamicists to revist Keplerian orbital geometry
in a proper way without destroying Kepler's work or taking shortcuts
as Newton did.They can do this by actually looking down at the Earth
from space and extracting Keplerian orbital geometry directly by
gauging the relationship between axial and orbital orientations over a
given period.
.
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