Kepler’s Laws September 21, 2009

Taking Care of Business (TCB) Read textbook Unit 12 Read textbook Unit 12 Take Moon observations Take Moon observations 6 Observations due September 28 6 Observations due September 28 Test #1 – September 18 to September 21 Test #1 – September 18 to September 21 Sept 16 class – last day of test material Sept 16 class – last day of test material Reserve your test date/time ASAP Reserve your test date/time ASAP InQsit instructions on Blackboard InQsit instructions on Blackboard

Discussion Review How were Tycho Brahe’s observations critical to the development of astronomy? How were Tycho Brahe’s observations critical to the development of astronomy? He brought up the idea of the planets positions again, and tried to improve them He brought up the idea of the planets positions again, and tried to improve them Made a new model Made a new model

Kepler’s First Law The orbit of each planet about the Sun is an ellipse with the Sun at one focus The orbit of each planet about the Sun is an ellipse with the Sun at one focus

Kepler’s Second Law As a planet moves around its orbit, it sweeps out equal areas in equal times As a planet moves around its orbit, it sweeps out equal areas in equal times To do this, a planet must move slower at aphelion than it does at perihelion To do this, a planet must move slower at aphelion than it does at perihelion

Kepler’s Third Law More distant planets orbit the Sun at slower average speeds, obeying the mathematical relationship of p 2 =a 3 (p 2 =ka 3 ) where p is the planet’s orbital period in years and a is the average distance from the Sun in AU More distant planets orbit the Sun at slower average speeds, obeying the mathematical relationship of p 2 =a 3 (p 2 =ka 3 ) where p is the planet’s orbital period in years and a is the average distance from the Sun in AU

Example   What about comets? Assume a comet has a high eccentricity of 0.95(e) with a semi-major axis of 40(a)AU. How long will it take this comet to orbit the Sun? Where at in its orbit will it spend most of its time? Near the Sun at perihelion? Far from the Sun at aphelion? Or maybe somewhere in between? p 2 = ka 3 P=253 years, at the aphelion when it is furthest away If p is measured in years and a is measured in AU, then k = 1. If p is measured in years and a is measured in AU, then k = 1.

Post Tutorial Question If a small weather satellite and the large International Space Station are orbiting Earth at the same altitude above Earth’s surface, which object takes longer to orbit once around Earth? If a small weather satellite and the large International Space Station are orbiting Earth at the same altitude above Earth’s surface, which object takes longer to orbit once around Earth? a) the large space station a) the large space station b) the small weather satellite b) the small weather satellite c) They would take the same amount of time. c) They would take the same amount of time.

Post Tutorial Question Consider a planet orbiting the Sun. If the mass of the planet doubled but the planet stayed at the same orbital distance, then the planet would take Consider a planet orbiting the Sun. If the mass of the planet doubled but the planet stayed at the same orbital distance, then the planet would take a) more than twice as long to orbit the Sun. a) more than twice as long to orbit the Sun. b) exactly twice as long to orbit the Sun. b) exactly twice as long to orbit the Sun. c) the same amount of time to orbit the Sun. c) the same amount of time to orbit the Sun. d) exactly half as long to orbit the Sun. d) exactly half as long to orbit the Sun. e) less than half as long to orbit the Sun. e) less than half as long to orbit the Sun.