www.byzcath.org Forums General Discussions Town Hall Copernicus

That is true, but then the geocentric theory had problems accounting for the recession of planets (i.e., apparent retrograde motion in the sky). All told, the Copernican theory was much simpler and more accurate, in spite of its error in assuming circular orbits. Once Kepler deduced elliptical orbits, the heliocentric theory accounted for all observed motions.

Pastor Thomas--I hope it's typo on the website, but Copernicus was born in 1473!

Even with circular orbits, heliocentrism would produce better navigational results than geocentrism . . .

Anyway, I'm recalling high school Physics, taught wonderfully by Fr. Capitulo, S.J., and our assiggment in which we plotted eliptical orbits.

One student ended up with one of the spikes *way* to short. He solved this by, yes, drawing an epicycle of retrograde motion . . . .

hawk

My impression is that geo/helio-centrism in their original forms entailed more than just what the names imply; they comprised various assumptions, approximations and idealizations that either appealed to a prior philosophical viewpoint and/or made calculations possible. For example, orbits must be circular because the circle is a "perfect" geometrical form.

Even today scientific insights are aided by idealizations and limiting cases that are easier to conceptualize and calculate. Even fairly recently, ca. 1940, detailed calculations (especially digital) were not the norm. There are those of us who used slide-rules for some time, not hand-held calculators.

So, the sun "immovable" (a very good limit but still an approximation) at the "center" (actually one of the two foci of the ellipse in the Kepler model) of elliptically orbiting planets is a model that works well and simplifies our view and understanding of what is happening without abandoning accuracy. However, as a general rule, the "laws of physics" do not change as a result of changing coordinate systems. The calculations may become more difficult as a result of a choice (earth at the center) of origin for the coordinates, but the results are the same as a choice (sun at the center)that allows a straightforward simple mathematical description (elliptical orbits) of the phenomenon. (Or, calculate in the more straightforward heliocentric coordinates and then transform the results to geocentric.)

Consequently, geo/helio-centrism in their generic meaning are just two different views giving the same results. With today's personal computers one can easily perform the calculations with either model with the same results. And for all the talk about geo/helio-centrism that misinforms about what it really means in today's terms (not all the idealizations and assumptions of the past) it is ultimately a geocentric viewpoint (in fact topocentric: "as seen from the observer's place on the Earth's surface" [Astronomical Algorithms, J. Meeus, p. 279]) that is invoked because, after all, that is our viewpoint as the observer.

Thank you, John K.! I read 1673, and thought, "Wow!? So Copernicus did his work in the early 1700s?! That's a lot later than I remember learning in school! I gotta go back and read up on this stuff!

Under all of the other layers, I'm a mathematician--even as to how I understand physics, statistics, and economics. This drove the faculty at the ISU Statistics Lab mad a couple of times, but that's another issue.

Anyway, get mathematicians involved, and the estimates and get, uhh, interesting. Agricultural problems? "Assume a perfectly spherical cow of radius 1 . . ." Yeah, that's silly. Cubical cows of side length 1 also have a volume of 1. More importantly, they stack *so* much better than spheres . . .





Yes, which is why I'd expect the calculations (without cheap heavy computation) to come out better from heliocentric--one less approximation/rounding. Helio would give a measurement from the sun, and another from the earth, while geo would give an earth/sun estimate to multipy/whatever the sun estimate, adding one more level of confusion.

Then again, if we're only talking errors in the third digit, that's relative small and probably good enough to have the right port in sight . . .

And since I don't remember enough general relativity to argue it, I'll refrain from typing, "twin paradox." oops !

hawk

Just to be clear, I had in mind the so-called "hard" (real?) sciences. Something like the ideal gas equation of state for instance, PV=nRT, is still taught and used effectively within (and even outside at times) its proper range of applicability. In the given form it is predicated on all particles/species being indistinguishable, that they exhibit no attractive or repulsive forces, and that they occupy no space -- hefty idealized conditions for a concept that has considerable scientific utility and respectability.

Hey, *I* didn't say that, but now that the door is open . . .



I have a Ph.D. Economics, and I still don't know what a "social science" is . . . I most often see it used when claiming exemption from the Scientific Method . . .

putting the "doc" back into dochawk . . .

Social science is to science as social disease is to disease.

Bingo!

A prime impetus of this Seeker's quest was the adoption of a "Social Teaching Statement on Human Sexuality" by the Evangelical Lutheran Church in America which places the "new learnings from the social sciences" on a plane at least equal to (if not superior) to the Scriptures.