The original attempt to explain the Equation of Time within
heliocentricity was made by Kepler who assigned a variable speed to
axial rotation over the course of an annual orbit to account for the
unequal length of a day.Of course axial rotation is constant.

The next attempt was the 17th century analemmatists who attributed a
variable axial tilt component to the astronomical correction but that
mixes daylight/darkess asymmetry with the Equation of Time when the
correction is based strictly on the total length of the natural day.

The actual solution is at once more simple yet rapidly becomes complex.

Apart from a tiny component,the Equation of Time reflects the rate of
change of orbital orientation as axial rotation passes back to a line
at 90 degrees to the Sun/Earth line.

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

The arrows represent the change in rate of orbital orientation in
accordance with Keplerian geometry and orbital motion.The reason this
change has not been noted up to now may be due to the fact that axial
rotationtends to diminish the orbital effect as axial longitudes run
almost paralell to orbital orientation and only hemispherical weather
patterns and variations in daylight/darkness asymmetry indicate the
changing relationship.

The extreme local variation between axial longitudes and changing
orbital orientation are best understood through the axial orientation
of Uranus and the Earth's relationship is in accordance with this
though far less pronounced -

http://physics.uoregon.edu/~jimbrau/...13/FG13_06.jpg

An accurate relationship between axial and orbital motions/orientations
is crucial for recognising global climate norms which can be reduced
further to hemispherical weather patterns (seasons) and from there to
climate balances and imbalances.