To forestall (some) objections: My notation in the following is
inconsistnt with what Glenn was using. Here ws is the net angular speed
of the sun with respect to a stationary observer on the (stationary &
nonrotating) earth in the Ptolemaic model.
> 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
> gmurphy@imperium.net
> http://www.imperium.net/~gmurphy
-- George L. Murphygmurphy@imperium.nethttp://www.imperium.net/~gmurphy