For what it's worth, Marlelar, Tycho Brahe, the renowned astronomer, after having died and his materials taken by Keppler (who would subsequently save Copernicus' doctrine) stated:
“There really are not any spheres in the heavens… Those of which have been devised by the experts to save the appearances exist only in the imagination, for the purpose of enabling the mind to conceive the motion which the heavenly bodies trace in their course and, by the aid of geometry, to determine the motion numerically through the use of arithmetic.”
-Tycho Brahe, On the Most Recent Phenomena of the Aetherial World, 1588
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There are two n's in Kepler's name but not two p's:
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You appear to be conflating Brahe's use of the word "spheres" with the shapes of heavenly bodies. That is false.
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When he referred to "spheres" he was talking about the invisible structures the ancients imagined held the planets in place like as it were layers of an onion.
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They were concentric zones of force or influence that kept planets moving about in their own region and not crashing into each other or drifting away from the sun.
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They also imagined what they called
"epicycles" which were like little circles hung on the perimeter of these "spheres" and which kept the planets moving in an orderly way in their orbits, and which accounted for the manifest retrograde motions of the planets as seen from earth. Incidentally, later mechanical development would name the innovation of a set of gears keyed to each other, "planetary gears," as a consequence of the concept of epicycles, because planetary gears move in fact like the epicycles were thought to move hundreds of years prior.
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As further study and mapping improved it eventually became clear that retrograde planetary motion was not in need of any "epicycles" to explain why they moved in precisely the way they did.
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Those "spheres" which had been devised by the "experts" in that age to explain the appearances of planetary retrograde motion existed only in their imaginations for the purpose of enabling their minds to conceive the retrograde motions which the heavenly bodies trace in their courses and orbits; and by the aid of geometry, those imaginary spheres would determine the motion numerically through the use of arithmetic. Or so they hoped! Only problem was, no geometry or arithmetic ever got complex enough to account ACCURATELY for all the retrograde gyrations that the planets made!
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And even today, when geometry, arithmetic and higher mathematics have been pushed beyond the limits (pun) of Brahe's wildest imagination, there is still none that can account for retrograde motion by way of "spheres."
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If you want to really stretch the meaning of the word, though, you
could say that
gravitational attraction directly proportional to the relative masses of the concerned bodies and inversely proportional to the square of the distance between them has taken the place of Brahe's "geometry and arithmetic."
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Typical answer to proof beyond your ability to respond.
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Whenever you'd like to "proof beyond your ability to respond" you're more than welcome to give it a shot.
But do try to be careful and avoid misspellings like that.
Or, will your "book" be full of such gibberish?
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Topic: Are other planets flat? (Read 2515 times)