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