To Brian

If you are good enough to see that Newton transfered Flamsteed's axial
rotational/stellar circumpolar equivalency at 23 hours 56 min to a
geocentric /heliocentric orbital equivalency to get his mean Sun/Earth
distances,an unethical maneuver,you will be doing well.

I refer you to page 86 of the following work which provides the
geocentric coordinates of the motion of Mars transfered to the
heliocentric orbital motion of Mars against the orbital motion of the
Earth.You have to drop the reference to the background stars to
appreciate what Kepler is doing and how he isolates the orbit of the
Earth from that of Mars.

http://mitpress.mit.edu/journals/pdf/POSC_13_1_74_0.pdf

You can get the stretching and shortening of orbital distances from the
Sun alright but it is impossible to fit it into a Keplerian elliptical
framework.Astronomers such as Kepler worked from mean motions through
the center of a planet's orbit just as the primary Copernican insight
is made through the annual orbital motion of the Earth but it all
depends on the translation from the motion observed against the
background stars to motions against the Earth's orbital motion.

An examination of the diagram on page 86 demonstrates that retrogrades
are drawn nearest to the Earth's orbital distance to Mars thereby it is
possible to compare the actual Keplerian statement with Newton's
mangled version -

"PH=C6NOMENON 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.


http://members.tripod.com/~gravitee/phaenomena.htm


"The proportion existing between the periodic times of any two planets
is exactly the sesquiplicate proportion of the mean distances of the
orbits, or as generally given,the squares of the periodic times are
proportional to the cubes of the mean distances." Kepler


It is clear that none of you ever heard of Kepler's Panis
Quadragesimalis before and what it represents.The more a person becomes
familiar with it the more they will look up at Mars rather than retreat
to string and paper.