Johannes Kepler

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Johannes Kepler
Three basic laws of Planetary Motion
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1. Elliptical orbits orbital shape
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Circles have one focus
Ellipses have two foci
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sun
Planet
Aphelion
Perihelion
Because the sun is at a fixed focus, a planets
distance from the sun will change throughout its
orbit.
The distance that a planet is from the sun is
determined by averaging its aphelion and
perihelion
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The extension of the ellipse is referred to as
its eccentricity
A circles eccentricity is 0
Earth has an eccentricity of of 0.0167
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2. Equal Areas Laws - orbital speeds change
through out the orbit
Since the sun is at one focus, the planets speed
around the sun is NOT constant.
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January 15
June 15
July 15
December 15
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Sweeps to show equal areas
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3. Harmonic Law - the period of a planet
(squared) is equal to its distance (cubed)
P2 D3
Period time it takes a planet to travel around
the sun once
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According to Kepler, the further a planet is from
the sun, the longer its period of revolutions
The average speed of Earth is 30 km/sec
The average speed of Mercury is 49 km/sec