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1 Gravity and Motion II Heliocentric Astronomy

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2 Topics l Recap l Heliocentric Astronomy l Copernicus l Brahe l Kepler l Galileo l Newton l Summary

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3 Recap l 4000 BC ~ 500 BC astronomy astrology l The science of astronomy grew from the superstition of astrology. l 600 BC ~ 100 BC l Abandonment of superstition l Embrace of reason l Dogma of circular motion – “perfect” motion l 100 BC ~ 200 AD l Establishment of Ptolemaic system l 642 l Fall of Alexandria

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4 Copernicus to Newton

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5 The Great Awakening l 1000 l Islamic empire reaches Spain l 1452 l Birth of Leonardo da Vinci l 1473 l Birth of Copernicus l 1492 l Discovery of the Americas by Columbus l 1519 l Death of Leonardo da Vinci l 1543 l Death of Copernicus l 1546 l Birth of Tycho Brahe l 1564 l Birth of Galileo l 1571 l Birth of Kepler

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6 Age of Reason and Unreason l 1600 l Giordano Bruno burned to death by Holy Office l 1601 l Death of Tycho Brahe l 1616 l Galileo censured by the Holy Office l 1618 The Harmony of the World l Kepler publishes The Harmony of the World l The Counter-Reformation begins. l 1619 l Enslavement of Africans, by Europeans, begins in the Americas l 1632 Dialogues l Galileo publishes Dialogues l 1665-1667 l Synthesis of laws of motion by Newton l 1687 Principia l Newton publishes the Principia.

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7 99 Years of Astronomy

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8 Nicolaus Copernicus (1473-1543) l Simplicity and Beauty l 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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9 Copernicus – II l The Copernican Model l Copernicus wanted a simpler model. l Less concerned about finding an accurate one. l Indeed, the Copernican model was less accurate in its prediction of planetary motion than the Ptolemaic model. circular l This was largely because of Copernicus' insistence on circular orbits. l But Copernicus preferred his model because it explained retrograde motion in a very simple way.

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11 Retrograde Motion

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13 Tycho Brahe (1546 – 1601) l Tycho’s Observatory l Established an observatory on island near Denmark under the auspices of Frederick II. l 1576 to 1597 l Tycho collected a vast amount of precise astronomical data.

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14 Johannes Kepler (1571-1630) l 1599 – Kepler hired by Tycho Brahe l Work on the orbit of Mars l 1609 – Kepler’s 1 st and 2 nd Laws ellipsesfocus l Planets move on ellipses with the Sun at one focus radius vector l The radius vector sweeps out equal areas in equal times l 1618 – Kepler’s 3 rd Law squareorbital period P cubesemi-major axis R l The square of a planet’s orbital period P is proportional to the cube of its semi-major axis R.

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15 Kepler’s First Law R = Semi-major axis focus Radius vector Eccentricity= Distance between foci / Length of major axis = 0.017 for Earth = 0.224 for Pluto

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16 Kepler’s Second Law Faster Slower Equal areas law

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17 Kepler’s Third Law l Kepler’s 3rd law l Divide 3 rd law for planet by 3 rd law for the Earth P R l If P is measured in Earth years and R is measured in Astronomical Units (AU) then can write

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18 Examples l R = 1.5 AU l P = 1.837 Earth years l R = 5.2 AU l P = 11.86 Earth years l P = 4 Earth Years l R = 2.52 AU

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19 AST0305.swf

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20 But Why ? l Kepler’s Laws l Do an excellent job of describing the motion of the planets, but they do not explain why the planets move as they do howwhy l Science tries to learn both how as well as why l Two great scientists helped answer these questions l Galileo Galilei (1564-1642) l Isaac Newton (1642-1727)

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21 Galileo Galilei (1564-1642) l 1610 l Discovered the four largest moons of Jupiter l Laws of Motion inertiaforces l Introduced the notion of inertia and forces. same acceleration l Discovered that objects fall with the same acceleration. l 1632 Dialogues l Published Dialogues

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22 Fig. 5-24, p.89

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23 Gravity ~ 1642 All objects fall at the same rate How can this be?

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24 Isaac Newton (1642 – 1727) l 1642 l Born Christmas Day l 1661 l Admitted to Trinity College, Cambridge l 1665 – 1667 l Synthesized laws of motion l 1687 l Philosophiae Naturalis Principia Mathematica l Philosophiae Naturalis Principia Mathematica.

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25 Newton’s Laws of Motion l 1 st Law unbalanced force l A body at rest, or in uniform motion, will remain so unless acted upon by an unbalanced force. l 2 nd Law acceleration l The change in motion (acceleration) is proportional to the unbalanced force l 3 rd Law action reaction l For every action there is an equal and opposite reaction

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26 Gravity l Gravity is the force that l holds us to the Earth l causes a rock to fall towards the ground l causes the Earth to go around the Sun l causes the Sun to be pulled towards the center of the Milky Way galaxy l Gravity acts between any two objects even if they are far apart. action at a distance l “action at a distance”

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27 Newton’s Law of Gravity l F= Gravitational force l G= Gravitational constant l m 1 = Mass of particle 1 l m 2 = Mass of particle 2 l Newton’s version of Kepler’s Law d m2m2 m1m1

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28 Summary l Kepler’s and Galileo’s Laws provided Newton with important clues that helped him formulate his laws of motion l Newton arrived at 3 laws that govern the motion of objects l The law of inertia l The law of force l The law of action and reaction l Newton also arrived at a law of gravity l But it seemed to require action at a distance!

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