the solar system planetary orbits. johannes kepler december 27, 1571 – november 15, 1630 german...
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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
Eccentricity of an Orbit LabEccentricity of an Orbit LabThis lab is on the Regents ExamThis lab is on the Regents Exam
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