Re: rotation of the earth

George Murphy (
Sat, 13 Dec 1997 13:45:49 -0500

Glenn Morton wrote:

> I may get rapped over this again. Sometimes I don't learn so quickly. :-)
> Let me suggest that the damage to the Ptolemaic system by Magellan's voyage
> lay in the relative motion of two of Ptolemy's spheres AND the theological
> position that there was a prime mover outside of the siderial sphere who
> gave motion to the heavens. This motion was then translated downward into
> the inner spheres like a clockwork.
> There are four different angular velocities that need to be considered,
> 'wd' is the angular velocity of the stellar sphere (which moves westward);
> 'ws' is the angular velocity of the given sphere (which moves eastward in
> relation to the stellar sphere); 'we' is the angular velocity of the
> epicycle; and 'wdef' is the angular velocity of the earth around the center
> of the deferent.............................................
> I stand ready for the corrections from my betters in physics. Does this
> work? I would like to either figure out my error and not get my knuckles
> rapped again, or put this to rest. My knuckles are extended for a sound
> thrashing..............................
> > So I am curious as to what the evidence from the voyage of
> >Magellan's surviving crew did convince the church authorities. On what
> >issue and how did they change their minds?

First, I think we need something from the historians of science
about whether or not this aspect of Magellan's voyage _was_ seen as a
challenge to the Ptolemaic model in the early 16th century. In my own
rather eclectic reading relative to geocentric-heliocentric debates I've
never seen anything about this. That itself proves nothing, but some
reference would be helpful.
It seems to me you've made things more complicated than
necessary by introducing 4 motions. The essence of the problem can be
seen just with the rotation of the "fixed stars" and the motion of the
sun around the earth in an approximately circular orbit. The epicycles
& deferent are unneeded refinements for this purpose.
Then IMHO Don is correct. Moving (generally) west, the ship
sees a smaller angular speed of the sun & a solar day longer by a factor
ws/(ws-wm). The ship returns to the island after sidereal time T (which
both agree on, since they see the sun in the same position relative to
the stars) & N days have passed for the islanders. Thus Tws = 2Np where
p = pi = 3.14... & N is the # of solar days which have passed on the
island. The number of solar days passed for the ship is N'
(ws-wm)/Nws = [(ws-wm)/ws][Tws/2p] = N - Twm/2p. But Twm = 2p (since
the ship has just gone around the earth once) so N' = N - 1. One gets
the same result with a heliocentric model.
People in the early 16th century may have been puzzled by
"losing a day" but I can't see why a thoughtful geocentrist would have
any basic problem with it. &, as I said, it would be helpful to have
some refernce to any who did have such a problem.

George L. Murphy