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The spirals don't seem intuitive to me. Do most people really think the moon has a negative velocity during parts of its orbit about the sun?



Why wouldn't it? When it's going around the earth, it's going to be going in the opposite direction from the earth's orbit part of the time. The question is which motion is bigger.


That is the pattern the planets trace in the sky and for thousands of years people thought that was literally their path.

http://en.wikipedia.org/wiki/Apparent_retrograde_motion

In the ptolemeic system, the planets were thought to move with epicycles, or "wheels within wheels". This is why astrolabes had gears attached to gears.

http://en.wikipedia.org/wiki/Deferent_and_epicycle

Then copernicus came along and blew that all away with his heliocentric model, which was then given mathematical foundation by Johannes Kepler and his laws of planetary motion.


I would really like to meet these mathematicians who described it that way. I suspect he asked two and one of them was busy at that moment and not really paying much attention to his question.




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