Kepler's Second Law: Equal Area in Equal Time

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SUMMARY

Kepler's Second Law, known as the Law of Equal Areas, is derived from the conservation of angular momentum while following an elliptical orbit. Although the modern interpretation connects this law to Newtonian mechanics, Kepler formulated his laws based solely on meticulous observational evidence prior to Newton's work. The relationship between Kepler's laws and Newton's gravitational theory illustrates the evolution of astronomical understanding from empirical observation to theoretical physics.

PREREQUISITES
  • Understanding of Kepler's Laws of Planetary Motion
  • Familiarity with the concept of angular momentum
  • Basic knowledge of elliptical orbits
  • Introduction to Newtonian mechanics
NEXT STEPS
  • Study the derivation of Kepler's laws from observational data
  • Explore the principles of angular momentum in celestial mechanics
  • Investigate the historical context of Kepler's work compared to Newton's theories
  • Learn about the mathematical formulation of elliptical orbits
USEFUL FOR

Astronomy students, physics enthusiasts, historians of science, and anyone interested in the foundational principles of celestial mechanics.

harp AP 2010
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How did Kepler figure out his second law: Equal area in equal time?
 
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harp AP 2010 said:
How did Kepler figure out his second law: Equal area in equal time?

Wikipedia has the derivation. It comes from conservation of angular momentum while following the elliptical path.

http://en.wikipedia.org/wiki/Kepler's_laws
 
zhermes said:
Wikipedia has the derivation. It comes from conservation of angular momentum while following the elliptical path.

http://en.wikipedia.org/wiki/Kepler's_laws

This may be the "modern" overview (modern = after Newton), but since Kepler was around before Newton, I highly doubt he knew anything about how to manipulate orbital angular momentum.

I think Kepler formulated his laws based purely on observational evidence. He noticed from the observations that these 3 "laws" seem to hold. Later Newton proved that these laws are directly derivable from his mechanics and law of gravitation.
 

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