JOHANNES KEPLER 1571 1630 JOHANNES KEPLER Mathematically strong

JOHANNES KEPLER (1571 – 1630)

JOHANNES KEPLER • Mathematically strong • Assistant to Tycho Brahe – used observatory and other instruments to measure more precisely than ever before (especially about Mars) • Discovered 3 laws of planetary motion

1. THE PATH OF EACH PLANET IS AN ELLIPSE • “The Law of Ellipses” • The sun is located at one focus • Nothing at the other focus of the ellipse • All of the planets orbit the sun in this pattern/shape

2. EACH PLANET REVOLVES EQUAL AREAS IN TIME • “Law of Equal Areas” • An imaginary line connecting the Sun to a planet will sweep over equal areas in equal time intervals • Planet’s speed is constantly changing! • Moves fastest when closest to Sun, slowest when farthest from Sun

3. LENGTH OF TIME AND DISTANCE ARE PROPORTIONAL • “Law of Harmonies” • The length of time it takes a planet to orbit the Sun and its distance from the Sun are proportional • Comparison between motion characteristics of planets o Orbital Period (T) o Radius of Orbit/Distance from Sun (R) o T 2/R 3 ratio is the same for all planets • T 2 = R 3

Planet Period (s) Average Distance (m) T 2/R 3 (s 2/m 3) Earth 3. 156 x 107 s 1. 4957 x 1011 2. 977 x 10 -19 Mars 5. 93 x 107 s 2. 278 x 1011 2. 975 x 10 -19 Planet Period (yr) Average Distance (au) T 2/R 3 (yr 2/au 3) Mercury 0. 241 0. 39 0. 98 Venus . 615 0. 72 1. 01 Earth 1. 00 Mars 1. 88 1. 52 1. 01 Jupiter 11. 8 5. 20 0. 99 Saturn 29. 54 1. 00 Uranus 84. 0 19. 18 1. 00 Neptune 165 30. 06 1. 00 Pluto 248 39. 44 1. 00

• http: //unctv. pbslearningmedia. org/resource/npls 12. sci. ess. eiu. keplerorbits/solar-systemdynamics-orbits-and-keplers-laws-nasa-planetary-sciences/