Kepler ,Newton and orbital geometry

The Wikipedia article is being quite honest but the chain of reasoning
Newton applied to Keplerian orbits are technically present and can be
dealt with easily,at least for people who are familiar with
astronomical methods -

"Newton's actual historical chain of reasoning is not known with
certainty, because in his writing he tended to erase any traces of how
he had reached his conclusions." Kepler's third law

http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion

'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."

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

Rather than go through the details,and they are intricate,perhaps it
is best to demonstrate why it is neccessary to revisit the explanation
for Keplerian orbital geometries and how the late 17th century
shortcuts creates multiple problems elsewhere such as the pressing
need to modify the cause for the seasons by concentrating on the
orbital motion of the Earth and Keplerian orbital geometry.

.

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