How did Kepler arrive at his equation without calculus?

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Discussion Overview

The discussion centers on how Johannes Kepler derived his equation relating mean anomaly and eccentric anomaly without the use of calculus, focusing on the methods he employed based on his laws of planetary motion. Participants also explore how he formulated his second law regarding areal velocity without differentiation, highlighting the challenges of his time, including the absence of computational tools.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants note the Kepler equation: M = E - e Sin(E), questioning how Kepler derived it without calculus.
  • Others emphasize that Kepler's insights were achieved without modern computational tools, relying solely on his intellectual capabilities.
  • A participant mentions an analogy involving a rowboat to illustrate Kepler's basic idea about motion and speed in relation to his laws.

Areas of Agreement / Disagreement

Participants express admiration for Kepler's achievements, but there is no consensus on the specific methods he used or how he conceptualized his laws without calculus.

Contextual Notes

The discussion reflects on historical limitations, such as the lack of calculus and computational tools during Kepler's time, which may influence interpretations of his methods.

alemsalem
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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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alemsalem said:
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:
 
stevenb said:
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 want to be a genius! :-p
 
alemsalem said:
Cool, I want to be a genius! :-p
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
 
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