(Axel Harvey) wrote in message . com...
Is the "heliocentric" idea this: we choose a coordinate system in
which angular momentum is minimized?

It is far more complicated than that but I have'nt seen you shy away
from these things before and perhaps you may see where errors built on
Newton's view snowballed in later centuries.

Newton's gravitational laws compliment Kepler's planetary laws however
Newton treats the Earth's variable orbital motion alone and dispenses
with the Earth's constant axial rotation within the variation in
orbital motion.He can then say -



"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

Later scientists took this too far and shifted planetary longitudes
based on the 24 hour/360 degree equivalency to the sidereal value of
23 hours 56 min 04 sec to geocentric longitudes to suit the purpose of
justifying Newton's treatment of orbital motion and nothing could be
worse.

http://www.absolutebeginnersastronomy.com/sidereal.gif

The problem with the sidereal picture is that there is no equable
motion corresponding to 24 hours wrt to the Sun which is why the
Equation of Time was applied daily by astronomers.Newton could
correctly say that there is no observed equable motion corresponding
to the 24 hour/360 degree equivalency for the axial rotation of the
Earth.

"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 "

Axel,there is a disaster in the making in there and especially the
decision to jettison the EoT bridge between the constant 24 hour day
and the natural unequal day or what amounts to the same
thing,jettisoning the relationship between absolute time and relative
time as Newton phrased it.With the Sun based Equation of Time format
which is a direct consequence of Kepler's second law,constant axial
rotation and variable orbital motion are combined in the natural
unequal day but the Equation of Time correction isolates axial
rotation by equalising the orbital variation,the following graphic of
Kepler's second law may be of use -

http://ircamera.as.arizona.edu/NatSc...res/kepler.htm

What is absent from the graphic is constant axial rotation within the
comparison or orbital motion,it makes all the difference because the
sidereal value imposes a clockwork picture on the Earth's orbital
motion where naturally the combined axial and orbital motion generates
a far more complex picture,one in which you cannot say the motion of
Earth around the Sun is the same as the Sun around the Earth.The
addition and subtraction of minutes and seconds which facilitates the
seamless transition from one 24 hour day to the next via the Equation
of Time determines that there is no equable combined motions of the
Earth around the Sun and subsequently it is a terrible error to
imagine that the combined motions of the Earth can be treated as a
single sidereal motion.

Newton ,while being aware of the Equation of Time and its components
never fully understood it,when he goes to tackle Flamsteed's data
based on the isochronos value he cannot make head nor tails of the
data and with good reason.