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In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler in 1609 (except the third law, and was fully published in 1619), describe the orbits of planets around the Sun. These laws replaced circular orbits and epicycles in the heliocentric theory of Nicolaus Copernicus with elliptical orbits and explained how planetary ...
English: Diagram illustrating Kepler's laws: 1. Two elliptical orbits with major half axes a 1 and a 2 and focal points F 1, F 2 for planet 1 and F 1, F 3 for planet 2; the sun in F 1. 2. The two sectors A 1, A 2 of equal area are swept in equal time. 3. The ratio of orbital periods t 2 /t 1 is (a 2 /a 1) 3/2.
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Kepler's laws apply only in the limited case of the two-body problem. Voltaire and Émilie du Châtelet were the first to call them "Kepler's laws". Nearly a century later, Isaac Newton had formulated his three laws of motion. In particular, Newton's second law states that a force F applied to a mass m produces an acceleration a given by the ...
The two-body problem is interesting in astronomy because pairs of astronomical objects are often moving rapidly in arbitrary directions (so their motions become interesting), widely separated from one another (so they will not collide) and even more widely separated from other objects (so outside influences will be small enough to be ignored safely).
Geometric diagram for Newton's proof of Kepler's second law. 1602-1608 – Galileo Galilei experiments with pendulum motion and inclined planes; deduces his law of free fall; and discovers that projectiles travel along parabolic trajectories. [3] 1609 – Johannes Kepler announces his first two laws of planetary motion. [4]
Mathematically, the second epicycle and the equant produce nearly the same results, and many Copernican astronomers before Kepler continued using the equant, as the mathematical calculations were easier. Copernicus' epicycles were also much smaller than Ptolemy's, and were required because the planets in his model moved in perfect circles.
Kepler's 2nd law: equal areas are swept out in equal times (area bounded by two radial distances and the orbital circumference): = | | where L is the orbital angular momentum of the particle (i.e. planet) of mass m about the focus of orbit,