How did Kepler arrive at his equation without calculus?

  • Thread starter alemsalem
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  • #1
alemsalem
174
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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.
 

Answers and Replies

  • #2
stevenb
700
6
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
alemsalem
174
5
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
Michel_vdg
107
1
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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