Kepler’s laws describe the motion of astronomical bodies and were discovered by Johannes Kepler. They paved the way for Isaac Newton’s theory of interaction of bodies. The laws state that planets follow elliptical paths, trace out equal areas in equal times, and the square of the period of the orbit is directly proportional to the cube of the semimajor axis.
Kepler’s laws are three equations that govern the motion of astronomical bodies. Kepler’s laws were first discovered by 17th-century astronomer Johannes Kepler while analyzing data collected by Tycho Brahe. Kepler’s laws are an extension of Copernicus’ earlier heliocentric theory and eventually paved the way for Isaac Newton’s comprehensive theory of the interaction of bodies. Newton’s equations of gravity and motion can be used to derive Kepler’s laws, if it is assumed that there are only two bodies, one of which is stationary and one of which is orbiting at less than escape velocity. Although Kepler’s laws were originally developed to explain planetary motions, they apply to any body that is in orbit around a much more massive body.
The first of Kepler’s laws states that a planet, or any other object orbiting the Sun, follows an elliptical path with the Sun at one focus. The shape of these ellipses depends on the mass of the Sun, the position of the planet, and the speed of the planet. A set of six numbers, called Keplerian elements, can be used to specify the exact path a planet takes.
The second of Kepler’s laws says that an orbiting planet traces out equal areas in equal times. If you draw a line from the planet to the Sun and add up the area that the line travels during a given time interval, it is always constant. This law is a consequence of the conservation of angular momentum; if the planet is moving faster, it must also be closer to the Sun. The increase in area covered by the greatest angular motion, and the decrease in area covered by the shortest distance, must exactly cancel each other out.
The third law states that the square of the period of the orbit must be directly proportional to the cube of the semimajor axis of the orbit. The semimajor axis is half the total distance between perihelion, or closest approach to the Sun, and aphelion, or furthest distance from the Sun. A planet that is very far from the Sun, such as Neptune, has a very wider; it also moves more slowly, taking longer to cover the same distance as a planet like Mercury. The exact relationship between orbital period, semimajor axis, mass and gravitational constant was later worked out by Isaac Newton.
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