Physics 20 Motion in the Heavens

Kepler’s Laws Before 1600 – Danish Astronomer Tycho Brahe and the world believed the the Earth was the center of the universe and all the planets and the sun orbited us. His assistant, Johannes Kepler, used Brahe’s data to prove that our solar system was actually helicentric – sun centered Kepler also discovered the elliptical, not circular nature of the orbits – although they are nearly circular

Kepler’s First Law – Law of Elliptical Orbits Each planet moves in an elliptical orbit, with the sun as one of the focal points The planets get closer and further from the sun in different points in the orbit–radius of orbit changes. The radius we see is often an avg. value-semi maj. Axis The ellipse for most planets is nearly a perfect circle

Kepler’s Second Law – Law of equal Areas During equal time intervals, a straight line drawn from the sun to the planet will sweep out equal areas in equal times. One consequence of this is that the planets must change speeds for this to work The planet is faster when it is closer to the sun The planet is slower when further form the sun

Kepler’s Third Law – Law of Periods The period of revolution is related to its radius of revolution (distance to the sun) in the following rate K = T2 r3 T= Period of revolution (time for one rotation r = radius of revolution (distance from the sun) K = Kepler’s constant

Example Knowing that the earth’s orbital radius is 1.49x1011 m and its period of revolution is 1.00 year, calculate the period of revolution of Jupiter, whose orbital radius is 7.78 x 1011 m

Assignment Reading Questions Pearson Physics pgs 269-271 SNAP 275 #’s 1-4 Pearson Physics Pg 286 #’s 2-4