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Gravity and MotionGravity and MotionIIII

Heliocentric Astronomy

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TopicsTopics

Recap Heliocentric Astronomy

Copernicus Brahe Kepler Galileo Newton

Summary

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RecapRecap

4000 BC ~ 500 BC The science of astronomyastronomy grew from the superstition

of astrologyastrology. 600 BC ~ 100 BC

Abandonment of superstition Embrace of reason Dogma of circular motion – “perfect” motion

100 BC ~ 200 AD Establishment of Ptolemaic system

642 Fall of Alexandria

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Copernicus to NewtonCopernicus to Newton

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The Great AwakeningThe Great Awakening

1000 Islamic empire

reaches Spain 1452

Birth of Leonardo da Vinci

1473 Birth of CopernicusBirth of Copernicus

1492 Discovery of the

Americas by Columbus

1519 Death of Leonardo da

Vinci 1543

Death of Copernicus 1546

Birth of Tycho BraheBirth of Tycho Brahe 1564

Birth of GalileoBirth of Galileo 1571

Birth of KeplerBirth of Kepler

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Age of Reason and UnreasonAge of Reason and Unreason

1600 Giordano Bruno burned to

death by Holy Office 1601

Death of Tycho Brahe 1616

Galileo censured by the Holy Office

1618 Kepler publishes The The

Harmony of the WorldHarmony of the World The Counter-Reformation

begins.

1619 Enslavement of Africans,

by Europeans, begins in the Americas

1632 Galileo publishes

DialoguesDialogues 1665-1667

Synthesis of laws of motion by Newton

1687 Newton publishes the

PrincipiaPrincipia.

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99 Years of Astronomy99 Years of Astronomy

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Nicolaus CopernicusNicolaus Copernicus (1473-1543) (1473-1543)

Simplicity and Beauty Sentiment expressed

by William of Ockham (14th century):

“it is vain to do with more what can be done with fewer”

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Copernicus – IICopernicus – II

The Copernican Model Copernicus wanted a simpler model. Less concerned about finding an accurate one. Indeed, the Copernican model was less accurate in its

prediction of planetary motion than the Ptolemaic model.

This was largely because of Copernicus' insistence on circularcircular orbits.

But Copernicus preferred his model because it explained retrograde motion in a very simple way.

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Retrograde MotionRetrograde Motion

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Tycho BraheTycho Brahe (1546 – 1601)(1546 – 1601)

Tycho’s Observatory Established an

observatory on island near Denmark under the auspices of Frederick II.

1576 to 1597 Tycho collected a vast

amount of precise astronomical data.

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Johannes KeplerJohannes Kepler (1571-1630)(1571-1630)

1599 – Kepler hired by Tycho Brahe Work on the orbit of Mars

1609 – Kepler’s 1st and 2nd Laws Planets move on ellipsesellipses with the Sun at one focusfocus The radius vectorradius vector sweeps out equal areas in equal

times

1618 – Kepler’s 3rd Law The squaresquare of a planet’s orbital period Porbital period P is

proportional to the cubecube of its semi-major axis Rsemi-major axis R.

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Kepler’s First LawKepler’s First Law

R = Semi-major axis

focus focus

Rad

ius

vect

or

Eccentricity = Distance between foci / Length of major axis= 0.017 for Earth= 0.224 for Pluto

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Kepler’s Second LawKepler’s Second Law

Faster Slower

Equal areas law

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Kepler’s Third LawKepler’s Third Law

Kepler’s 3rd law

Divide 3rd law for planet by 3rd law for the Earth

If PP is measured in Earth years and RR is measured in Astronomical Units (AU) then can write

32 RkP

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Earth

Planet

Earth

Planet

R

R

P

P

32 RP

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ExamplesExamples

R = 1.5 AU P = 1.837 Earth years

R = 5.2 AU P = 11.86 Earth years

P = 4 Earth Years R = 2.52 AU

32 RP

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AST0305.swfAST0305.swf

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But Why ?But Why ?

Kepler’s Laws Do an excellent job of describing the motion of

the planets, but they do not explain why the planets move as they do

Science tries to learn both howhow as well as whywhy

Two great scientists helped answer these questions Galileo Galilei (1564-1642) Isaac Newton (1642-1727)

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Galileo Galilei Galileo Galilei (1564-1642) (1564-1642)

1610 Discovered the  four

largest moons of Jupiter

Laws of Motion Introduced the notion

of inertiainertia and forcesforces. Discovered that

objects fall with the samesame accelerationacceleration.

1632 Published Dialogues Dialogues

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Fig. 5-24, p.89

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Gravity ~ 1642Gravity ~ 1642

All objects fall at the same rate

How can this be?

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Isaac NewtonIsaac Newton(1642 – 1727)(1642 – 1727)

1642 Born Christmas Day

1661 Admitted to Trinity

College, Cambridge 1665 – 1667

Synthesized laws of motion

1687 Philosophiae Naturalis Philosophiae Naturalis

Principia MathematicaPrincipia Mathematica.

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Newton’s Laws of MotionNewton’s Laws of Motion

1st Law A body at rest, or in uniform motion, will

remain so unless acted upon by an unbalanced forceunbalanced force.

2nd Law The change in motion (accelerationacceleration) is

proportional to the unbalanced force 3rd Law

For every actionaction there is an equal and opposite reactionreaction

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GravityGravity

Gravity is the force that holds us to the Earth causes a rock to fall towards the ground causes the Earth to go around the Sun causes the Sun to be pulled towards the

center of the Milky Way galaxy

Gravity acts between any two objects even if they are far apart. “action at a distanceaction at a distance”

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Newton’s Law of GravityNewton’s Law of Gravity

F = Gravitational force G = Gravitational

constant m1 = Mass of particle 1

m2 = Mass of particle 2

Newton’s version of Kepler’s Law

221

d

mmGF

d

m2

m1

3

21

22

)(

4R

mmGP

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SummarySummary

Kepler’s and Galileo’s Laws provided Newton with important clues that helped him formulate his laws of motion

Newton arrived at 3 laws that govern the motion of objects The law of inertia The law of force The law of action and reaction

Newton also arrived at a law of gravity But it seemed to require action at a distance!