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Re: Sig Figures and tides



At 4:18 AM -0800 2/3/00, David Bowman wrote:
Regarding Herb's comment:
...
In space everything is in relative motion. Although it is much simpler to
describe the sun and the moon as celestial objects that are relatively still
with respect to the earths motions, there is nothing wrong by believing
that the earth is motionless and everything else in space is in motion.

Gottlieb from New York City
(Where the sun rises in the East and sets in the West )

There might not be anything practically wrong with such a perspective for
a practical prescientific description, and there is nothing morally wrong
with this description either. But there *is* something scientifically
wrong with it if it is to be used to describe the motions of objects
farther than about 27.48 AU from the earth's spin axis. The rotating
coordinate system in which the earth's surface is at rest has a
cylinderical coordinate singularity at this distance from the rotation
axis, and it cannot be used for distances greater than that. (Objects
greater that this distance travel at speeds greater than c in this
coordinate system.) Such a situation *is* a real problem for a proper
scientific (i.e. relativisitic) description of the motions of distant
heavenly bodies. Even Neptune and Pluto are in this forbidden region--
let alone all the Kuiper belt objects, all the stars (other than the sun)
and interstellar gas and dust clouds, all the galaxies, all the galactic
clusters, all the superclusters, all the quasars, all the inhomogeneities
in the cosmic microwave background, etc.

It's even simpler than that. The rotation of the Earth can
readily be detected by "prescientific" techniques (e.g. the
various terrestrial Coriolis effects) as can the revolution
of the Earth about the Sun (stellar aberration).

I was afraid Herb was making what I call "Tycho's mistake"
when he made his contentious statement. Tycho Brahe observed
that the universe as it was then known could be described by
allowing the Sun and Moon to revolve about the Earth and the
other planets to revolve about the Sun, with appropriate
epicycles and equants, of course. It is merely a
transformation of coordinates from a heliocentric Copernican
universe to a geocentric Tychonic universe. At that time
Tycho was the best astrometer in the world, and he could not
see differences between the two systems in his observations.
With the size of the universe as small as he believed it to
be Tycho's universe was a better fit to observations than
Copernicus's. This situation ended soon after Newton's death
with the discovery of stellar aberration by James Bradley.

That's why I asked Herb the question in the first place.

Leigh