Kepler's LawsJohannes Kepler, working with data painstakingly collected by Tycho Brahe without the aid of a telescope, developed three laws which described the motion of the planets across the sky. 1. The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus. 2. The Law of Areas: A line that connects a planet to the sun sweeps out equal areas in equal times. 3. The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit. Kepler's laws were derived for orbits around the sun, but they apply to satellite orbits as well. 
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The Law of OrbitsAll planets move in elliptical orbits, with the sun at one focus.This is one of Kepler's laws. The elliptical shape of the orbit is a result of the inverse square force of gravity. The eccentricity of the ellipse is greatly exaggerated here.

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Examples of Ellipse Eccentricity

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The Law of AreasA line that connects a planet to the sun sweeps out equal areas in equal times.

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The Law of PeriodsThe square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.
Kepler's Law of Periods in the above form is an approximation that serves well for the orbits of the planets because the Sun's mass is so dominant. But more precisely the law should be written In this more rigorous form it is useful for calculation of the orbital period of moons or other binary orbits like those of binary stars.

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Data: Law of PeriodsData confirming Kepler's Law of Periods comes from measurements of the motion of the planets.
The quantity T^{2}/a^{3} depends upon the sum of the masses of the Sun and the planet, but since the mass of the Sun is so great, adding the mass of the planet makes very little difference. Data from Halliday, Resnick, Walker, Fundamentals of Physics 4th Ed Extended. Table 153 
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