Re: rotation of the earth

Glenn Morton (
Sat, 13 Dec 1997 11:14:31 -0600

Hi Don,

At 10:20 AM 12/12/97 -0700, Don Page wrote:
> Glenn, I noticed what appears to be a minor error in something you
>wrote several months ago, though it raises some historical questions that I
>am curious about.

If I recall, I got rapped on the knuckles pretty hard about that particular
post. And now it is time for another rapping. Here are my knuckles, but I
hope you have misplaced your ruler. :-)
Your question has caused me to spend about 6 hours studying the issue again
however. I put this out with great fear and trepidation.

> Glenn, the same observation would have been made if the earth were
>not rotating but the sun were going around the earth, since in that case the
>ship would have gone around the earth in the same direction as the sun and
>thus seen one fewer sunrise than the islanders who stayed fixed. Given
>enough people considering this question, and enough time (which I realize
>that you would not have had on this particular issue, since you write so
>prolifically), I'm sure that those in the 16th century (particularly those
>who really believed that the sun went around the earth) would have realized
>that this datum was consistent both with rotation of the earth and a fixed
>sun, and with a fixed earth and rotation of the sun around the earth.

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. God was the initiator of the daily
rotation of the entire universe. Because God was immutable the ratios of the
various motions of the heavens initiated by God must also be immutable.
Magellan's crew found a flaw in that immutability. It was a jarring
introduction to relativity. The unit of time by which they measured things,
the sidereal day, was not constant.

The epicycle speed should not have been affected by the voyage around the earth.

This can be drawn as follows:

... A ***** *****
... ..** **
. ** . **
. ** . **
P *e . **
. ** . **
..** ... **
* ... C *
B** **
** **
** E **
** **
** **
** **
***** *****

Where E is the earth which is offcenter from the Deferent (the big circle of
*'s) The epicycle is the small circle (made of .'s), A and B are the most
advanced and most retarded position of the epicycle. C is the center of the
eccentric (deferent) and the earth revolves around it; e is the center of
the epicycle and P is the planet. Here is what I think is the problem with
Magellan's voyage and Ptolemy.

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.

The line CE rotates daily with an angular velocity of wd-ws. The epicycle
rotates with an angular velocity of 'we'. The islanders AND Magellan's crew
experienced the same time T. For the islanders, they measure the ratio of
epicycle velocity to daily velocity is


Magellan's crew in traveling around the world moved at an average angular
velocity of wd-wm, where 'wm' is the averaged angular velocity of the boat.
Now, when they get back to the island Magellan's crew sees the same point in
the epicycle's orbit as the islanders. But they measure the ratio as:


One can say that what the boaters saw was

wd'=wd-wm (the crew went west seeing a slower velocity with the stellar sphere)
ws'=ws+wm (the crew went west seeing a faster velocity with the planet spheres)

While we and wdef remained constant, their speed was based upon a presumed
causality in that 'we' was driven by 'ws' as was 'wdef'.

At the end of the 3 years when everyone was back together, the angular
positions were


Since wmT=360, wd'T=wdT and ws'T=wsT. But there is a significant difference
physically between the two end points. You have lost one day, but gained
one revolution of the planetary sphere! And since 'wd' is supposed to drive
'ws' how could this occur? This difference is a contradiction and Ptolemy
must be wrong. Of course the easiest out was what happened, everybody
thought the mariners had lost count.

The islanders would never have observed the variable angular velocities or
the separation in the rotations of the two spheres. To the medieval mind
this must have appeared as perplexing to them as does the fact that I can
decide how light behaved billions of years ago does to moderns. If I set up
a telescope to count photons being bent around a galaxy 10 billion
lightyears ago, I see the photons going on one or the other side of the
galaxy. If I chose to observe light as a wave phenomenon rather than a
particle, I see the light waves going on both sides of the galaxy. My
decision today as to how to view the light, appears to have determined how
light behaved 10 billion years ago when it actually went around the galaxy.
To the medievals they must have not felt that their actions (sailing around
the world) could possibly affect how God moved the universe.

Depending upon the accuracy of the measurements, there would also be some
effects observable from the fact that the earth was not at the geometric
center of the universe (see George Abell, Exploration of the Universe, Holt
Rinehart and Winston, 1969, p. 28-29)

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

> Of course, it seems that this datum would have hard to reconcile
>with a theory of a flat earth, so those who supported that view would no
>doubt have felt threatened. But I was under the impression that the
>intellectuals of the day were quite convinced by even the Greek arguments
>and evidence for a round earth, and I thought that one of the objections to
>granting money for Columbus to try to sail to India was that it was known
>that the earth was so large that he would not likely be able to get there on
>a reasonable budget.

Not all Christians were convinced of the roundness of the earth. Magellan's
voyage destroyed other theological concepts. Because Paul had written that
the Gospell had been preached throughout the world, and everybody knew that
none of the apostles had traveled to the geometrical opposite side of the
earth, the antipodes, everybody concluded that no people lived at the
antipodes. Some people didn't beleive that you could go to heaven if you
believed in life at the antipodes. Magellan brought back people and reports
of people from the antipodes. Magellan's voyage also destroyed a widely
popular cosmology at the time.

"During the Dark Ages literal interpretation of the Bible
had led the Church to endorse the absurd geographical dicta of
Topographia Christiana, a treatise by the sixth-century monk
Cosmas. Cosmas, who had traveled to India and should have known
better, held that the world was a flat, rectangular plane,
surmounted by the sky, above which was heaven. Jerusalem was at
the center of the rectangle, and nearby lay the Garden of Eden,
irrigated by the four Rivers of Paradise. The sun, much smaller
than the earth, revolved around a conical mountain to the north.
The monk's arguments were fragile, and not everyone accepted them
- the Venerable Bede, among others insisted that the earth was
round - but Cosmas scorned them. Rome agreeing with him,
rejected their protests as an affront to common sense.
"This patristic dismissal of so elementary a fact was a sign
of how deeply the wisdom of the ancient world had been buried.
More than three hundred years before the birth of Christ,
Aristotle had determined that the planet must be a sphere; after
an eclipse he pointed out that only an orb could throw a circular
shadow on the moon. The existence of India and Spain was known
in Athens. However, few other geographical or scientific facts
were available to Aristotle, and this led him into error.
Holding that land was heavier than water, and that the masses of
each must balance. he inferred that the distance between the
Iberian Peninsula and the Indian subcontinent could not be great,
and that, consequently, there was no land between them - that is,
no North or South America. Therein lay the origin of Columbus's
error, which others would challenge and which Magellan,
ultimately, would discredit."~William Manchester, A World Lit
Only By Fire: The Medieval Mind and the Renaissance: Portrait of
an Age, (Boston: Little, Brown & Co., 1992), p. 230

I also agree with what Paul Arveson wrote about the theology of the issue.

> 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?

I read this question differently than Paul did. I would answer that
Magellan's data didn't convince the Church authorities. In fact there was a
catholic priest in the 1800's who believed at least part of Cosmas's theory
and advocated that the sun was only 6 feet in diameter. Hugh Miller writes:

"The old theologian could scarce have held, with a living
ecclesiastic of the Romish Church in Ireland, Father Cullen, that the
sun is possibly only a fathom in diameter; or have asserted with a
most Protestant lecturer who addressed an audience in Edinburgh
little more than three years ago, that, though God created all the
wild animals, it was the devil who made the flesh-eaters among them
fierce and carnivorous; and, of course, shortened their bowels,
lenghthened their teeth, and stuck formidable claws into the points
of their digits."~Hugh Miller, Testimony of the Rocks,(New York:
Hurst and Company, 1857) p. 394-395

Even if I turn out wrong on this, I want to thank you for making me re-think
the entire issue.


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