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PiRsq
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How did Kepler come about to conclude that his third law is
Radius3/Period2? How did he derive this equation?
Radius3/Period2? How did he derive this equation?
Originally posted by PiRsq
So does R3 have any relationship with the fact that the planets are orbiting in 3 dimension?
Kepler's Third Law, also known as the Law of Harmonies, states that the square of a planet's orbital period is directly proportional to the cube of its semi-major axis. In other words, the further a planet is from its star, the longer it takes to complete one orbit.
By using Kepler's Third Law and the fact that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them, one can derive the relationship between a planet's radius and its orbital period. This relationship is known as the Radius3/Period2 formula.
The Radius3/Period2 formula represents the relationship between a planet's radius and its orbital period. It states that the cube of a planet's semi-major axis (which is proportional to its radius) is equal to the square of its orbital period multiplied by a constant, known as the gravitational constant.
Kepler's Third Law is important in the study of planetary motion because it allows scientists to calculate the orbital period and distance of a planet from its star using only the mass of the star and the semi-major axis of the planet's orbit. This information is crucial in understanding the dynamics of our solar system and other planetary systems.
Johannes Kepler derived his Third Law by analyzing the observational data of his predecessor, Tycho Brahe. He noticed a pattern in the orbital periods and distances of the planets and used this data to formulate his Third Law, which became one of the three laws of planetary motion.