Kepler's Second Law: Equal Area in Equal Time

In summary, Kepler's second law, also known as the Law of Equal Areas, was derived from the conservation of angular momentum while following an elliptical path. This explanation may be considered a modern overview, since Kepler likely formulated his laws based on observational evidence rather than a knowledge of orbital angular momentum. It was later proven by Newton to be directly derivable from his mechanics and law of gravitation.
  • #1
harp AP 2010
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How did Kepler figure out his second law: Equal area in equal time?
 
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  • #2
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
 
  • #3
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.
 

1. What is Kepler's Second Law?

Kepler's Second Law, also known as the Law of Equal Areas, states that a planet will sweep out equal areas in equal times as it orbits around the sun. This means that a planet will move faster when it is closer to the sun and slower when it is farther away.

2. How did Kepler come up with this law?

Johannes Kepler, a German astronomer, developed his three laws of planetary motion in the early 17th century after studying the observations of his mentor, Tycho Brahe. He observed that the planets move in elliptical orbits around the sun and noticed that they sweep out equal areas in equal times.

3. What is the significance of Kepler's Second Law?

Kepler's Second Law helped to further our understanding of how planets move in their orbits and provided evidence for the heliocentric model of the solar system. It also paved the way for Newton's law of universal gravitation, which explains the force that keeps planets in their orbits.

4. Does Kepler's Second Law apply to all planets?

Yes, Kepler's Second Law applies to all planets in our solar system, as well as other celestial bodies that orbit around a central object. However, it may not apply to objects with highly eccentric orbits or those that are affected by external forces, such as comets.

5. How is Kepler's Second Law related to the conservation of angular momentum?

Kepler's Second Law is a consequence of the conservation of angular momentum, which states that the total angular momentum of a system remains constant unless acted upon by an external torque. As a planet moves closer to the sun, its speed increases to maintain the same amount of angular momentum.

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