the solar system planetary orbits. johannes kepler december 27, 1571 – november 15, 1630 german...

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The Solar System The Solar System Planetary Orbits Planetary Orbits

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The Solar SystemThe Solar SystemPlanetary OrbitsPlanetary Orbits

Johannes KeplerJohannes KeplerDecember 27, 1571 – November 15, 1630December 27, 1571 – November 15, 1630

German mathematician, astronomer and astrologer

Kepler’s 3 Laws of Planetary Motion

Law #1Law #1#1 -The orbit of every planet is an ellipse with the

Sun at one of the two foci Explanation:Explanation:

Planets revolve in an Planets revolve in an ellipseellipse around the sun. around the sun. An ellipse has An ellipse has two fixed points called foci that are on either side that are on either side

of the center of the axisof the center of the axis The sun lies at The sun lies at one focus and is not the center of Earth’s orbit and is not the center of Earth’s orbit

Planet

Law #2Law #2#2 - A line joining a planet and the Sun sweeps out

equal areas during equal intervals of time

Planet moves faster

Planet moves slower

Perihelion Aphelion

Covers equal areas in

Equal amount of time

Closer to Sun = faster in orbit because of gravitational pull of Sun on planet

Law #3Law #3

Law #3 - Mathematical formula to prove Law 1 + 2

Eccentricity = Eccentricity = distance between the focidistance between the foci

length of the major axislength of the major axis

e = d/Le = d/L

In ESRT

Length of Major Axis

Foci

All measurements

are in cm

E= 2.2 cm

In ESRT

4.1 cm

2.2 cm

Eccentricity = Eccentricity = distance between the focidistance between the foci length of the major axislength of the major axis

4.1 cm

E= 0.53658

E= 0.537

•Eccentricity is always 3 numbers past the decimal point…to the

nearest 1000ths place.

•NEVER more than 1

•NEVER less than 0

•Eccentricity has no label!

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

eccentricitye = 1

e=0

e=0.150

e=0.305

E= 0E= 0E= 0.015 E= 0.356

E= 0.569 E= 0.897

Eccentricity of an Orbit LabEccentricity of an Orbit LabThis lab is on the Regents ExamThis lab is on the Regents Exam

Video

December December 20122012