Kepler’s Laws �of Planetary Motion

Unit 2: History of Astronomy

After Brahe’s death, Kepler (pictured here with Tycho in the background) used Tycho’s observations to deduce the three laws of planetary motion.

LAW #1. The orbit of a planet around the Sun is an ellipse with the Sun at one focus.

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**good to know**

Eccentricity

• Orbital Eccentricity: the amount of elongation in a planet’s orbit
• An eccentricity of 0 is a perfect circle while an eccentricity close to 1 is nearly a straight line

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In an elliptical orbit, the distance from a planet to the Sun varies

• The point closest to the Sun is called perihelion
• The point farthest from the Sun is called aphelion

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LAW #2: A line from the sun to the planet sweeps out equal areas in equal time.

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Closer to the sun = faster velocity because of the gravitational pull

Faster �Velocity

greater gravitational pull

Slower�Velocity

LAW #3: The square of a planet’s orbital period around the sun is directly proportional to the cube of its average distance from the sun.

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Kepler’s 3^rd Law Practice

Jupiter has a revolutionary period of 11.86 years. What is the average distance between Jupiter and the Sun?

If we measure the orbital periods (P) in years and distances (a) in astronomical units, then the law mathematically can be written as P² = a³.

WHAT IT MEANS: the farther a planet is from the sun, the longer one orbital period will take

CHECKING IN

• What is the shape of the Earth’s orbit around the Sun?
• Elliptical
• Do the planets orbit the Sun at constant speeds?
• The closer a planet is to the Sun in its orbit, the faster it is moving. It moves fastest at perihelion and slowest at aphelion.
• Do all the planets orbit the Sun in the same amount of time?
• No. A the further a planet is from the sun, the longer it will take to complete one revolution.

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