kepelar law

For a more historical approach, see in particular the articles Astronomia nova and Epitome Astronomiae Copernicanae.

In astronomy, Kepler's laws of planetary motion are three scientific laws describing the motion of planets around theSun.

Figure 1: Illustration of Kepler's three laws with two planetary orbits.
(1) The orbits are ellipses, with focal points ƒ₁ and ƒ₂for the first planet and ƒ₁ and ƒ₃ for the second planet. The Sun is placed in focal point ƒ₁.

(2) The two shaded sectors A₁ and A₂ have the same surface area and the time for planet 1 to cover segment A₁ is equal to the time to cover segment A₂.

(3) The total orbit times for planet 1 and planet 2 have a ratio a₁^3/2 : a₂^3/2.

Astrodynamics
Orbital mechanics
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1. The orbit of a planet is an ellipse with the Sun at one of the twofoci.
2. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.^[1]
3. The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

Most planetary orbits are almost circles, so it is not apparent that they are actually ellipses. Calculations of the orbit of the planet Mars first indicated to Kepler its elliptical shape, and he inferred that other heavenly bodies, including those farther away from the Sun, have elliptical orbits also.

Kepler's work improved the heliocentric theory of Nicolaus Copernicus, explaining how the planets' speeds varied, and using elliptical orbits rather than circular orbits with epicycles.^[2]

Isaac Newton showed in 1687 that relationships like Kepler's would apply in the solar system to a good approximation, as consequences of his own laws of motion and law of universal gravitation.

So Kepler's laws are part of the foundation of modern astronomy andphysics.^[3]