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parsa418
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How did Kepler exactly prove that the period squared is proportional to the radius cubed? If he didn't prove it. Then how is it proven?
parsa418 said:How did Kepler exactly prove that the period squared is proportional to the radius cubed? If he didn't prove it. Then how is it proven?
Mapes said:
Kepler discovered the relationship between T^2 and r^3 while studying the orbit of Mars. He noticed that the ratio of a planet's orbital period (T) to its average distance from the sun (r) cubed was constant for all planets in our solar system.
This relationship means that as the distance of a planet from the sun increases, its orbital period will also increase, but not at a linear rate. Instead, the orbital period will increase exponentially as the distance increases.
To prove this relationship, Kepler used data from Tycho Brahe's observations of the planets' positions and calculated their orbital periods and distances from the sun. He then plotted a graph of T^2 against r^3 and found that it formed a straight line, providing evidence for the relationship.
Kepler's discovery of the relationship between T^2 and r^3 was crucial in the development of modern astronomy. It helped to disprove the widely accepted belief that planets moved in circular orbits, and instead, provided evidence for elliptical orbits. It also laid the foundation for Newton's law of universal gravitation.
Kepler's discovery is still used in modern science to calculate the orbital periods and distances of planets, moons, and other celestial bodies. It also plays a crucial role in the search for exoplanets, as scientists can use this relationship to estimate the size and distance of planets orbiting other stars.