How did Kepler arrive at his equation without calculus?

  • Thread starter alemsalem
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  • #1
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The Kepler equation is: M = E - e Sin(E); where M is the mean anomaly and E the eccentric anomaly and e is the eccentricity.

we get it from integrating dr/r' and changing variables to E, how did Kepler get it without calculus and using only his laws.

Another thing how did he see his second law (areal velocity) without differentiation.
 

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  • #2
699
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The Kepler equation is: M = E - e Sin(E); where M is the mean anomaly and E the eccentric anomaly and e is the eccentricity.

we get it from integrating dr/r' and changing variables to E, how did Kepler get it without calculus and using only his laws.

Another thing how did he see his second law (areal velocity) without differentiation.

Even more amazingly, he did it without computers to manipulate, calculate and visualize the data he was working with.

Bottom line, he did it all with brains and sweat. That's how geniuses always do the amazing things they do. :smile:
 
  • #3
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Even more amazingly, he did it without computers to manipulate, calculate and visualize the data he was working with.

Bottom line, he did it all with brains and sweat. That's how geniuses always do the amazing things they do. :smile:

Cool, I wanna be a genius! :tongue2:
 
  • #4
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Cool, I wanna be a genius! :tongue2:
99% hard work and 1 good idea ... I once read that the basic idea he had, was that of a row boat, and how the boat goes the fasted where the oar is in the water, more or less :smile:

[PLAIN]http://img593.imageshack.us/img593/5549/rowboat.jpg [Broken]
 
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