"cgbusch" wrote in message om...
Because of Earth's elliptical orbit, the planet varies its distance from the Sun.

(From http://science.msfc.nasa.gov/headlin...ast04jan_1.htm)
"perihelion both hemispheres were 147.5 million km from the Sun."
"152.6 million km in July, which astronomers call aphelion"
A difference of 5.1 million km.

the speed of light = 299 792 458 m / s

(5100000000 m)/(299792458 m/s)=17.01 seconds

How much variance would this introduce in the EoT? Would this
difference add up to an appreciable amount?

I make it +/- 23 milliseconds.

Paul Schlyter already answered this but maybe you missed it.
I don't know if you are familiar with stellar aberration, my
apologies if you already know this. If you point a telescope
at a star at some time of the year and again six months later,
you find you need to change the angle slightly. In the
heliocentric frame, the Earth is moving so you have to tilt
the telescope slightly to avoid the light hitting the sides
as in this diagram

http://physwww.mcmaster.ca/~kingb/2C...aberration.jpg

from these notes

http://physwww.mcmaster.ca/~kingb/2C...Lecture_3.html

It should be clear that the angle only depends on the speed
of the telescope relative to the star. For the same reason
it affects the angle of the shadow cast by the gnomon by the
same amount.

If you think of it from a geocentric perspective, the light we
see was emitted from the Sun roughly 500s earlier and the Sun
will have moved in that time. The error in position obviously
depends on the time taken and that depends on the distance,
but the angle by which the apparent location of the Sun is
displaced is independent of the distance since it depends on
the ratio of the error to the distance.

The speed of the Earth in orbit varies from 29.29km/s to
30.29km/s so by my calculations the aberration angle varies
from 20.15 to 20.84 arcseconds. The mean is 20.50 but remember
the EoT tells you the difference between true noon when the Sun
actually appears due south and noon based on mean time. If the
orbit of the Earth were circular, the constant 20.5 arcsec
offset would be incorporated in mean time so there would be no
contribution to the EoT. It is therefore only the variation we
need to consider. That is just +/-0.34 arc seconds and the Earth
rotates that much in 23 milliseconds.

If you compare the variation of 0.34 with the angular diameter
of the Sun of about 1900 arcsec, it means the error is 5000
times less than the width of the Sun's shadow from a fine wire
gnomon.

The rotation of the Earth subtracts 0.464km/s * cos(latitude)
from the orbital motion but again that is constant for any given
location so obviously doesn't affect the EoT.

The mean aberration angle means that the Sun appears to be due
south about 1.366 seconds before that alignment actually occurs,
reduced to 1.353s at my latitude of 51N by the Earth's rotation.
Compare that wit the 2 minutes plus it takes the Sun to cross
the meridian.

HTH
George