Kepler’s Laws of Planetary Kepler’s Laws of Planetary MotionMotion

Mr. FinnNovember, 2008

BackgroundBackground

• Greek astronomy• Ptolemy• Copernicus• Tycho Brahe• Johannes Kepler

Mars

Greek AstronomyGreek Astronomy

• Planets– “little wanderers” hard to explain

• Mars– red planet = “fiery one”– retrograde motion hardest to explain

• Aristarchus– heliocentric system– explains retrograde motion

Retrograde Motion of MarsRetrograde Motion of Mars

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Ptolemaic SystemPtolemaic System

• The Algamest– geocentric system– orbits = system of epicycles– explains retrograde motion– infinitely malleable

• adjusts to new data• extremely accurate predictions

Copernican SystemCopernican System

• Heliocentric system– planet orbits = circles– not centered on Sun, but points nearby– explains retrograde motion– simple but inaccurate

• not fully consistent with existing data• retains some epicycles

Tycho BraheTycho Brahe

• Observational astronomer– best observatory in Europe at Hven (1576-1596)

– naked-eye observation• telescope by Galileo in 1609

– 20 years of data on planets• Compromise system

– Earth at center– other planets orbit sun

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Johannes KeplerJohannes Kepler

• Mathematician– worked for Brahe 1600-1601

• inherited Brahe’s astronomical data

• Copernican system– Kepler strong believer

• Trials & Tribulations– repeatedly fled wars, religious persecution– mother on trial for witchcraft

Experimental DataExperimental DataKepler’s “War on Mars”Kepler’s “War on Mars”

• Brahe data on Mars– position relative to distant stars for 20yrs from Earth

• Data relative to moving Earth– find positions 1 Martian year apart– Mars at same point in orbit around Sun– seen from different perspectives on Earth

• Earth in different position in its orbit– where lines intersect = position of Mars

• Find orbit without any preconceptions– traces out ellipse!

Theory - Kepler’s LawsTheory - Kepler’s Laws

1. Orbits of planets are ellipses with sun at one foci

2. Planets sweep out equal areas in equal times

3. Relationship between size of orbit & its period

– P a3/2

– P2/a3 = constant

Harmonies in the Heavens

Kepler’s 1st LawKepler’s 1st Law

Sun at one foci

2a

a = semi-major axisperihelion

aphelion

Kepler’s 2nd LawKepler’s 2nd Law

Equal Areas:

A

Equal Times: 1 23 4

planets move faster when closer to the sun

Planet

Sun

Kepler's Third Law

0

50

100

150

200

250

300

0 5 10 15 20 25 30 35 40 45

Semi-Major Axis (AU)

Period (yr)

Kepler’s 3rd LawKepler’s 3rd Law

P a3/2

Unknown to Kepler

Newtonian SynthesisNewtonian Synthesis

• Newton’s Universal Law of Gravity

• Newton’s Laws of Motion– same laws explain heavenly and earthly motion– Aristotle believed two separate laws

€

r F g = −G mM

d2ˆ r d

Grand Synthesis #1Grand Synthesis #1

Celestial MechanicsCelestial Mechanics

• Pierre-Simon Laplace– Treatise on Celestial Mechanics (1799)

• Napoleon - Why is God missing?Why is God missing? – Laplace: “I have no need of that hypothesis.”

• “Je n’ai pas besoin de cette hypothèse.”

• Rise of the “Mechanical UniverseMechanical Universe”

PredictionsPredictions

• Edmund Halley predicts return of comet• Discovery of new planets

– Neptune, Pluto• Effect of planets on each other

– precession of orbits– Mercury partially unexplained