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**The Solar System Planetary Orbits**

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**Johannes Kepler December 27, 1571 – November 15, 1630**

German mathematician, astronomer and astrologer Kepler’s 3 Laws of Planetary Motion

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Law #1 #1 -The orbit of every planet is an ellipse with the Sun at one of the two foci Explanation: Planets revolve in an ellipse around the sun. An ellipse has two fixed points called foci that are on either side of the center of the axis The sun lies at one focus and is not the center of Earth’s orbit Planet

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Law #2 #2 - A line joining a planet and the Sun sweeps out equal areas during equal intervals of time Closer to Sun = faster in orbit because of gravitational pull of Sun on planet Perihelion Aphelion Planet moves faster Planet moves slower Covers equal areas in Equal amount of time

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**All measurements are in cm**

Law #3 Law #3 - Mathematical formula to prove Law 1 + 2 Eccentricity = distance between the foci length of the major axis e = d/L In ESRT Foci All measurements are in cm Length of Major Axis

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**Eccentricity = distance between the foci length of the major axis**

In ESRT E= 2.2 cm E= 4.1 cm E= 0.537 Eccentricity is always numbers past the decimal point…to the nearest 1000ths place. NEVER more than 1 NEVER less than 0 Eccentricity has no label! 2.2 cm 4.1 cm

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If the two foci are located near the ends of the axis, an ellipse is long and narrow… highly elliptical Many comets have this type of path If the foci move closer together, the shape of the ellipse becomes more circular A circle has NO eccentricity e = 0 A straight line is the maximum eccentricity e = 1 e=0 e=0.150 e=0.305

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E= 0.356 E= 0.015 E= 0 E= 0 E= 0.569 E= 0.897

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**Eccentricity of an Orbit Lab This lab is on the Regents Exam**

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December 2012

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