Kepler’s Laws

Kepler’s Laws

The “Wanderers”• Planets observed to move eastward across the

sky. This is called direct motion.• Retrograde motion is the occasional apparent

change in direction of planet movement.

Confusion!• Greeks couldn’t rectify this strange,

nonuniform movement of the planets.

• Aristarchus in 300 BC proposed we live in a heliocentric solar system.

Copernicus• 2000 years later in 1543 Copernicus published

his theory of a heliocentric solar system.• This solved the problem of the retrograde

motion of planets.

Horse and Pedestrian

• Different planets take different amounts of time to complete an orbit.

• When Earth overtakes Mars, it appears that Mars is moving backwards (retrograde motion)

• Retrograde motion is a result of our own motion.

Period…• … is the time to complete one orbit.• Sidereal Period: the true orbital period • Synodic Period: time between two successive

identical configurations in the sky.

Tycho Brahe 1546-1601• Attempted to prove the heliocentric model of

the solar system. But without a telescope he could not gather the data needed to prove this theory.

• Could not detect parallax.

Johannes Kepler• Proposed elliptical orbits for the planets.

• Ellipses have two foci. • Aphelion: point farthest from the sun, slowest• Perihelion: point nearest the sun, fastest.• Eccentricity is the shape of the ellipse.

0= circle 1= straight line

Kepler’s 1st Law• Planets orbit the sun in an ellipse with the sun

at one foci.

Kepler’s 2nd Law• Law of Equal Areas: the speed of a planet changes

in relation to it’s orbit.

• A to B = C to D and Area of C to D = Area A to B

Kepler’s 3rd Law

• Relates the size of a planet’s orbit with the period of time it takes the planet to orbit the sun.

• P2 = a3

• P= planet’s sidereal period• a= semimajor axis(1/2 longest diameter of ellipse)in AU

Galileo• Did not invent the telescope but was the first

to use the telescope to observe the sky.• Most important observation was the Venus

appears to have phases as viewed from Earth.