Kepler’s Laws of Planetary Motion

Debate on Planet Motions Geocentric or Heliocentric Universe

Claudius Ptolemy Ptolemy developed a geocentric model of the solar system that was so successful in predicting the positions of the planets that it endured for more than 1300 years.

Geocentric Model - Earth Centered Universe everything revolves around the Earth

Retrograde Motion If you watch the planets carefully, you will see that they move through the sky from night to night. However, a given planet will appear to stop, move backward for a while, stop again, and then continue its forward motion.

Ptolomey’s Epicycles

Heliocentric Model -Sun centered Universe everything revolves around the sun

Heliocentric Theory Nicolaus Copernicus ( ) argued that the motion of the Sun and planets could be equally described by a Sun centered (heliocentric) system. Galileo ( ) was the first scientitst to use a telescope to observe the sky. He observed the phases of Venus and the moons of Jupiter. Both observations supported the heliocentric model.

Retrograde Motion

Phases of Venus

Kepler’s Laws of Planetary Motion –Law 1 - Law of Ellipses –Law 2 - Law of Equal Areas –Law 3 - Harmonic Law (P 2 =ka 3 ) Kepler’s laws provide a concise and simple description of the motions of the planets. Discovered in 1609.

Kepler’s First Law

Kepler’s First Law: Each planet moves about the Sun in an orbit that is an ellipse, with the Sun at one focus of the ellipse.

Kepler’s First Law The major axis is the widest diameter of the ellipse. The semimajor axis is ½ this distance. –This is the average distance of the planet from the Sun. The eccentricity is a measure of the roundness of the ellipse: –An eccentricity of 0 is a perfect circle. –An eccentricity near 1 is a very elongated ellipse.

Lunar Orbit of Explorer 35 Moon

Major Axis Minor Axis Focus Points Center 90° Semi-major Axis = ½ Major Axis e=0 perfect circle e=1 flat line The Ellipse

Kepler’s Second Law

Kepler’s Second Law: The straight line joining a planet and the Sun sweeps out equal areas in space in equal intervals of time.

Kepler’s Third Law: The sqaures of the planets’ periods of revolution are in direct proportion to the cubes of the semimajor axes of their orbits.

Kepler’s Third Law Kepler’s Third Law can be expressed as: (distance) 3 =(period) 2 D 3 = P 2 if distance is measured in AU and the period in years. –Examples: The semimajor axis of the Earth’s orbit is 1 AU and its period is 1 year. Therefore, we can easily see that: 1 3 =1 2.

Kepler’s Third Law Halley’s Comet takes 76 years to orbit the Sun. What is its average distance from the Sun?

Kepler’s Third Law Kepler’s Third Law allows you to determine the semimajor axis of the orbit if you know the period, or the period if you know the semimajor axis.