4 Kepler’s Laws Why you can get there from here.

4 Goals Kepler: Astrologer turned Astronomer. Kepler’s Laws. Proof of Kepler’s Laws.

4 Astrology to Astronomy Kepler was an astrologer. Looked for Perfect Solids Wants did not match with Observations (tests). Followed the facts where they led. The result works.

4 Kepler’s Laws 1.Orbits are always ellipses. 2.Sweep out equal areas in equal times. 3.The period of orbit is related to average separation.

4 Gravity is the Force Newton’s Law of Gravity: So: Becomes: units

4 Concept Test Which of the following orbits is NOT allowed under Kepler’s First Law?

4 Concept Test Kepler’s Second Law says “a line joining a planet and the Sun sweeps out equal areas in equal amounts of time.” Which of the following statements means nearly the same thing? a.Planets move fastest when they are moving toward the Sun. b.Planets move equal distances throughout their orbit of the Sun. c.Planets move slowest when they are moving away from the Sun. d.Planets move farther in a given time when they are closer to the Sun. e.Planets move the same speed at all points during their orbit of the Sun.

4 Concept Test You want to launch a satellite into geostationary orbit (i.e., it takes 24 hours to orbit the Earth so it always stays over the same spot as the Earth turns), what is the only thing you need to know in order to determine how far from the Earth the satellite needs to orbit? a.The mass of the satellite. b.The period of the satellite’s orbit. c.The mass of the Earth. d.The mass of the Sun. e.The average distance to the Sun.

4 Concept Test You discover a new comet around our Sun: –Average distance from Sun = 4 AU. –What is the period? a.1 year b.4 years c.8 years d.64 years e.Don’t have all the necessary information.

4 Concept Test Saturn takes about 30 years to make one orbit around the Sun. About how far away from the Sun is it? a.1 AU b.5 AU c.10 AU d.30 AU e.900 AU

4 Concept Test Aliens attack our Sun and reduce it to a tiny cinder only 1/16 th its original mass. If the Earth stays at a distance of 1 AU from the Sun, how long will it now take to orbit the Sun? a.1 year b.4 years c.8 years d.16 years e.1/16 year

4 Orbital Mechanics Courtesy David Crisp and WFPC2 Science Team

4 Courtesy NASA/JPL/Cornell Mars: It Works

4 Cassini at Saturn

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4 Homework #3 Due Friday 20-Jan: Read B4 Do Chapter 4 Quick Quiz on Pearson website.