Newton,while formattting his time,space and motions distinctions in
line with the Equation of Time method created an error by shifting to
the sidereal format.However convenient it may have been for his
gravitational agenda to make the shift,it creates an astronomical
picture of such a limited value it is almost worthless.Anyone who
calls himself an astronomer can judge correctly that Newton used
Flamsteed's isochronos value and changed to that perspective as it is
the only means to determine that geocentric coordinates are equivalent
to heliocentric coordinates.



"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 "

http://members.tripod.com/~gravitee/...tions.htm#time




"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


An astronomer of distinction would recognise why one picture is
incompatible with the other from those two excerpts taken from the
Principia.Fundamentally,the Equation of Time description of the first
excerpt refers to the isolating of the axial rotation of the Earth
from its variable orbital motion while the sidereal format treats the
motions of the Earth as a single homogenised movement and has no
astronomical justification whatsoever.

http://astrosun2.astro.cornell.edu/a...1/sidereal.htm


The Actual Main Component of the Equation of Time




There are two major consequences in recognising the changing
orientation of the daylight/darkness line as a property of the Earth's
orbital motion.

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


The daylight/darkness line is always tangential to the Sun/Earth line
as indicated by the arrows in the above graphic and represents the
distinction between the Earth's orbital shadow and the change in that
shadow in accordance with Kepler's second law against the distant
stars.

The changing reference of the daylight/darkness line to the distant
stars is useful for grafting in the axial rotation of the Earth
insofar as an observer axially rotates out of the orbital shadow
(Dawn),the direction of orbital motion can be gauged against the
daylight/darkness line.At the perihelion and aphelion,the orbital
direction of the Earth lies on the daylight/line (as seen in the
graphic)-

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

Depending on where the Earth in in its orbital motion,at other
times,it will exist closer to dawn darkness and at other time closer
to dawn daylight.


The changing orientation of the daylight/darkness line in accordance
with Kepler's second law and the constant axial rotation of the Earth
passing through that line and on to the alignment with the Sun/Earth
line is what generates the natural unequal day.

The Equation of Time, with its positive and negative minute and second
values which are added and subtracted to the noon determination to
facilitate the isolation of the axial rotation of the Earth to the 24
hour/360 degree equivalency over the course of an annual orbital
cycle exists as a product between constant axial rotation and the
shift in the daylight/darkness line.

There never was an axial tilt component in the Equation of Time and
for about 400 years the changing orientation of the daylight/darkness
line as a property of the Earth's orbital orientation to the Sun (the
line is 90 degrees perpendicular to the Sun Earth line) has been
ignored.

Anyone who discerns the general direction of the Earth's orbital
motion at dawn as the Earth axially rotates out of its orbital shadow
will experience something new ,the rediscovery of astronomy and the
works of Copernicus and especially Kepler.

http://www.serve.com/wizjd/pics/hale05_m.jpg

If there is a problem recognising the changing orientation of the
daylight/darkness line in accordance with Kepler's second law,this
simplified graphic may help along with the main graphic demonstrating
how the line changes over an annual orbit.

http://www.museum.vic.gov.au/scidisc...00779_w150.gif

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