To derive Keplerian orbital motion/geometry

The relationship between axial and orbital motion using the Sun's light
as a reference has been known for centuries as especially the asymmetry
between one noon to the next as a location rotates to face the Sun
directly.

If divided into equal periods,from one natural noon to the next,would
result in an unequal pace peculiar to that day.The pre-Copernican
astronomers created an equalisation of the natural unequal periods to
an equality based on equal divisions of either 24 hours,1440 min or 86
400 sec.The mechanism for transfering the natural inequality to the
equable pace is a astronomical noon correction called the Equation of
Time.This exquisite correction facilitates the seamless transition from
one 24 hour day to the next and every single person here will use the
principle today and as long as they will live.

The early heliocentrists adapted the Equation of Time principle to the
newly discovered Copernican principle of constant axial rotation at 15
degrees per hour and 24 hours/360 degrees in total.This is how clocks
will always keep pace with the axial rotation of the Earth however the
difference between natural noon and clock noon wil also exhibit the
behavior of orbital motion as an isolated and indepedent motion.

The principle of constant axial rotation over the course of an annual
orbit was not immediately tied to the noon correction however that it
transpired that the 24 hour day,terrestial longitudes and axial
rotation were adapted as intermeshing principles permits the attentive
man from using the natural discrepancy between clock noon and natural
noon in terms of Keplerian variations in orbital geometry.

The Equation of Time reflects not just the change in orbital
orientation against fixed axial orientation but also the Keplerian
rate of changes in orbital orientation in what is commonly refered to
as the second law.

http://www.mhhe.com/physsci/astronom...ages/04f15.jpg

The arrows reflect only orbital orientation without any reference to
axial orientation or motion.

As orbital orientation is changing in accordance with Kepler's second
law and subsequently as constant axial rotation is occuring within it,a
some times of the year,the rotating Earth takes longer to get from one
noon to the next and at other times will take a shorter period.

The variation in the total length of the natural day has Nothing to do
with the Sun's orientation against the Equator/axis even though this
analemmatic fudge is proposed since the era of Flamsteed and as a
factor in the Equation of Time.

http://www.analemma.com/Graphics/sum...lemmaCurve.GIF

The discrete corrections seen in minutes and seconds and which comprise
the Equation of Time correction reflect the change in orbital
orientation to the Sun as an indepedent orbital motion.It also reflects
Keplerian motion and geometry of our planet using the Sun's light as a
reference.