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Gravity and Motion II

Gravity and Motion II. Heliocentric Astronomy. Topics. Recap Heliocentric Astronomy Copernicus Brahe Kepler Galileo Newton Summary. Recap. 4000 BC ~ 500 BC The science of astronomy grew from the superstition of astrology . 600 BC ~ 100 BC Abandonment of superstition

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Gravity and Motion II

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  1. Gravity and MotionII Heliocentric Astronomy

  2. Topics • Recap • Heliocentric Astronomy • Copernicus • Brahe • Kepler • Galileo • Newton • Summary

  3. Recap • 4000 BC ~ 500 BC • The science of astronomy grew from the superstition of astrology. • 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

  4. Copernicus to Newton

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

  6. 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 Harmony of the World The Counter-Reformation begins. 1619 Enslavement of Africans, by Europeans, begins in the Americas 1632 Galileo publishes Dialogues 1665-1667 Synthesis of laws of motion by Newton 1687 Newton publishes the Principia. Age of Reason and Unreason

  7. 99 Years of Astronomy

  8. Nicolaus Copernicus(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”

  9. Copernicus – 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 circular orbits. • But Copernicus preferred his model because it explained retrograde motion in a very simple way.

  10. Retrograde Motion

  11. Tycho Brahe(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.

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

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

  14. Kepler’s Second Law Equal areas law Slower Faster

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

  16. Examples • 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

  17. AST0305.swf

  18. 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 how as well as why • Two great scientists helped answer these questions • Galileo Galilei (1564-1642) • Isaac Newton (1642-1727)

  19. Galileo Galilei (1564-1642) • 1610 • Discovered the  four largest moons of Jupiter • Laws of Motion • Introduced the notion of inertia and forces. • Discovered that objects fall with the sameacceleration. • 1632 • Published Dialogues

  20. Fig. 5-24, p.89

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

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

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

  24. Gravity • 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 distance”

  25. m1 d m2 Newton’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

  26. Summary • 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!

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