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Gravitation

Gravitation. Chapter 7, section 3. Geocentric Models. Aristotle (384 – 322 BC) taught that the earth was surrounded by crystalline spheres on which the planets and stars were located

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Gravitation

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  1. Gravitation Chapter 7, section 3

  2. Geocentric Models • Aristotle (384 – 322 BC) taught that the earth was surrounded by crystalline spheres on which the planets and stars were located • Ptolemy (100 – 170) taught the planets and sun orbit the earth in the order Mercury, Venus, Sun, Mars, Jupiter, Saturn

  3. Heliocentric Model • Nicholaus Copernicus (1473 – 1543) proposed the sun was the center of the solar system explaining the motion of the planets • Tyco Brahe (1546 – 1601) made a long series of observations trying to resolve the debate between the two models. He hired Johannes Kepler to analyze the data

  4. Kepler’s Laws of Planetary Motion • Johannes Kepler (1571 – 1630) Used observations of Tyco Brahe to analyze planetary motion • 1st Law: planets follow elliptical paths with sun at one focus • 2nd Law: planets move so that imaginary line from planet to sun sweeps out equal areas in equal time intervals

  5. Kepler’s Laws • 3rd Law: The square of a planet’s orbital period is proportional to the cube of its mean distance from the sun • Newton was able to use his laws of motion and gravitational law to prove Kepler’s laws • Laws apply to all satellites

  6. Isaac Newton • Lived 1642 – 1727 • First formulated theory of gravity in 1666 • Published in Principia Mathematica in 1686

  7. Isaac Newton and Gravity • Newton realized an apple falls because of force of gravity • Analyzed motion of the moon--it follows a circular path, so a force is needed • Newton first to realize gravity causes both. • Newton extended gravitation theory to all objects, realized gravitational attraction is property of all mass

  8. Universal Law of Gravitation • First formulated by Newton, based on the work of Kepler and others • G = 6.67 x10-11 Nm2/kg2 , the constant of universal gravitation, first measured by Henry Cavendish in 1798 • r is the radial distance between the centers of mass of the two objects

  9. Gravitational Force • Mutual force of attraction between particles of matter • Attractive force is universal—all matter attracts all other matter • Very weak force, only noticeable when large quantities of matter are present • Attractive forces are equal and opposite between two objects

  10. An Inverse-Square Law • Gravitational force is inversely proportional to the square of the distance between objects. • Doubling the separation distance produces one-fourth the force • If the distance is reduced by one-half, force is four times as great

  11. Gravitational Fields • Gravitational force acts over a distance without contact • Caused by interaction with gravitational field • Field can be thought of as lines of force radiating from objects • Strength of field is force per unit mass exerted on object: g = F/m

  12. Gravity and the Earth • To find the gravitational force on earth, use the radius of the earth for the distance and the mass of the earth as one of the bodies. • Since the gravitational force is weight, • therefore, • g is strength of gravitational field

  13. Satellite Motion • Satellites are “falling” but tangential motion keeps them in orbit • Gravitational force acts a centripetal force changing direction of motion • so • In circular orbit, speed is constant, altitude depends on orbital speed

  14. Satellite Motion • Geosynchronous satellites have 24 hour orbital period and remain “motionless” in sky • If speed is greater or less than needed for circular orbit, elliptical orbit results • Speed is not constant in elliptical orbit but greatest when satellite is closest to earth (perigee) and least when farthest away (apogee) • Total energy is constant, transferring from kinetic to potential and back again

  15. Gravitational Effects • Tides—caused by the moon’s gravitational pull on the earth • Stars form when clouds of hydrogen gas coalesce because of gravitational attraction, compressing until nuclear fusion occurs • Black Holes—created when large stars exhaust their nuclear fuel and undergo gravitational collapse

  16. Gravity and the Universe • “Big Bang” theory says universe hurled outward from big explosion • Universe is expanding, only pull of gravitation can stop it. • Unknown whether enough matter exists to stop expansion and begin contraction leading to “Big Crunch” and another big bang-expansion-contraction cycle.

  17. General Relativity • Einstein explained the pull of gravity with his theory of general relativity • The attractive force is the result of the warping of the fabric of space-time by large amounts of mass • Like a heavy weight on a trampoline, smaller objects are pulled toward a large mass

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