Learning Objectives. one night? Over the course of several nights? How do true motion and retrograde motion differ?

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1 Kepler s Laws

2 Learning Objectives! Do the planets move east or west over the course of one night? Over the course of several nights? How do true motion and retrograde motion differ?! What are geocentric and heliocentric models? What are inferior and superior planets? What are opposition, and inferior and superior conjunction? What is an epicycle?! Can you sketch Ptolemy s and Copernicus models & how they explain retrograde motion & inferior planets?! What was Tycho Brahe s contribution to astronomy? Who was Kepler and what are each of Kepler s Laws?! Note the [xtra] beside lectures 1-7 on the schedule. These may be helpful to learn difficult concepts

3 The Planets! In ancient times, people noted five bright stars that moved through the constellations of the Zodiac over time! These stars were called planets, from Greek for wanderers Saturn Venus Jupiter Mercury

4 Planetary Motion! On a single night, the planets will rise and appear to move from east to west across our sky (due to the Earth s rotation)! just like the stars and the Sun! Over multiple nights, planets move west to east with respect to distant background stars (due to the Earth and the planets all orbiting the Sun counter-clockwise)! this is their true motion! Like the Sun, the planets appear to move through the Zodiac, close to the ecliptic

5 Explaining Planetary Motion! The Greek philosophers almost all believed that we lived in a geocentric (Earth-centered) system! The heavens move in perfect circles! The celestial domain (the sphere of the stars is pure and unchanging)! The geocentric system held sway for over 2000 years

6 Planetary Language! Inferior conjunction!when a planet passes in front of the Sun! Superior conjunction!when a planet passes behind the Sun! Opposition!When a planet is opposite the Sun in the sky (and is therefore visible in the middle of the night)

7 Inferior vs. Superior Planets! Venus, Mercury are always close to the Sun! Venus is always within 46º of the Sun! Mercury is always within 22º of the Sun! Referred to as the inferior planets! Show inferior and superior conjunctions but no oppositions! Mars, Jupiter, and Saturn are not tied to the Sun in the sky! Referred to as the superior planets! Show oppositions and superior conjunctions but no inferior conjunctions

8 ! A planet's west-to-east true motion with respect to the stars over multiple nights can stop and reverse to a slow east-to-west motion Retrograde Motion! This is called retrograde motion

9 Ptolemy (140 AD)! The basic geocentric model is quite simple! The Earth is in the center!! Ptolemy created a geocentric model with uniform circular motion to explain retrograde motion and inferior planets! The Ptolemaic system

10 Ptolemy Explains Retrograde Motion! Planets move on epicycles, which move along a larger circular orbit! Ptolemy s system could explain retrograde motion in an Earth-centered system!

11 ! Venus' and Mercury's orbits are locked to the Sun and they just move around their epicycles Ptolemy Explains the Inferior Planets! This still doesn t explain superior conjunctions of Mercury and Venus (which are very hard to see, so Ptolemy may not have known about them)! Ptolemy s model becomes very complex

12 Nicholas Copernicus (ca. 1540)! Resurrected the heliocentric model

13 !The inner planets move faster than the outer planets Copernicus Explains Retrograde Motion! Retrograde motion occurs when the Earth overtakes and passes (or is passed by) another planet

14 Copernicus Explains! Inferior planets have orbits closer to the Sun than the Earth s orbit is! They always appear close to the Sun as seen from Earth! This can explain the superior conjunctions of inferior planets Inferior Planets

15 Tycho Brahe (ca. 1580)! Observed a new star (a nova ) in 1572 and showed it was farther away than the planets! At the time the distant heavens (Ptolemy s sphere of the stars ) were considered unchangeable! Brahe compiled very careful observations over decades! Accurate to 1 arcminute (1/30 th the Moon s size)! And Tycho did all this without a telescope

16 Johannes Kepler (ca. 1600)! Inherited a set of very accurate observations of the planets when Brahe (his boss) died! Used the data to guide the creation of a new heliocentric theory! The data could not be fit by circular orbits! Considered an ellipse

17 Kepler's First Law The orbits of the planets are ellipses with the Sun at one focus The heavens do not move in perfect circles!

18 Kepler's Second Law The line that connects the planet to the Sun sweeps out equal areas in equal time! Planets move faster when closer to the Sun! Fastest at perihelion (closest to the Sun)! Slowest at aphelion (farthest from the Sun)

19 Kepler's Third Law A planet s orbital period (P) in years, squared, equals the semimajor axis of its orbit (a) in AUs, cubed P 2 = a 3 years AUs astronomical unit (1 x Earth-Sun distance)

20 Planetary Orbits! The farther away from the Sun, the longer it takes for the planet to orbit AND the slower its average orbital speed Planet P (yr) a (AU) P 2 a 3 Mercury Venus Earth Mars Jupiter Saturn

21 Kepler's 3 rd Law by Newton! Isaac Newton used his Law of Gravity to derive a general version of Kepler s 3rd Law! The extra M (mass) arises as Kepler only considered how the Sun s gravity affects the planets and ignored the fact that the planets also have a (tiny) gravitational effect on the Sun (P is in years, a is in AUs, M is in solar masses)! Kepler's Law works because the Sun s mass is much larger than any planet s mass (M 1 >> M 2 )

22 Next Time Our Home: The Earth

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