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Newton’s Law of Universal Gravitation

Newton’s Law of Universal Gravitation. Review: Kepler’s Laws. Newton’s Law of Universal Gravitation.

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Newton’s Law of Universal Gravitation

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  1. Newton’s Law of Universal Gravitation

  2. Review: Kepler’s Laws

  3. Newton’s Law of Universal Gravitation In 1666, some 45 years after Kepler did his work, 24-year-old Isaac Newton used mathematics to show that if the path of a planet were an ellipse, which was in agreement with Kepler’s first law of planetary motion, then the magnitude of the force, F, on the planet must vary inversely with the square of the distance between the center of the planet and the center of the sun.

  4. The Apple and the Moon? • Legend has it that Newton was struck by this idea while sitting under an apple tree, and he wondered whether the force that brought the apple to the Earth when it falls was the same as the force that held the moon in its orbit. • The amazing thing about Newton’s law is that he asserted, back in 1666, that it applied to ALL objects, EVERYWHERE in the universe. So far as we know, he was right!! (well, almost right…)

  5. Newton’s Law of Universal Gravitation The symbol a means is proportional to, and r is the distance between the centers of the two bodies.

  6. Newton’s Law of Universal Gravitation Every body in the universe attracts every other body with a force that is directly proportional to the product of the masses of the bodies and inversely proportional to the square of the distance between the bodies. (INVERSE SQUARE LAW)

  7. Universal Gravitational Constant

  8. Universal Gravitational Constant The proportionality constant, G is called the universal gravitational constant. Its value in the SI system of units is,G = 6.67  10-11N.m2/kg2. The law of gravitation is UNIVERSAL and FUNDAMENTAL. It can be used to understand the motions of planets and moons, determine the surface gravity of planets, and the orbital motion of artificial satellites around any central body.

  9. Cavendish experiment • The constant G was measured by Henry Cavendish in about 1797. • Amazingly accurate, yet simple, apparatus • Physics involved: Torque, simple harmonic motion, Hooke’s law, gravitation • http://en.wikipedia.org/wiki/Cavendish_experiment • He thought he was “weighing the world”, really he was also determining a fundamental constant of the universe. • Video: the Cavendish experiment

  10. Weight Weight = Mass x Gravity The weight of an object is the gravitational force that the planet exerts on the object. The weight always acts downward, toward the center of the planet. SI Unit of Weight: : newton (N)

  11. Acceleration Due to Gravity Calculate g for planet Earth at sea level.

  12. The Hubble Space Telescope

  13. Practice problem The mass of the Hubble Space Telescope is 11 600 kg. Determine the weight of the telescope (a) when it was resting on the earth and (b) as it is in its orbit 598 km above the earth's surface.

  14. Deriving Kepler’s Third Law from Newton’s Universal Law • In orbit, the centripetal force on a planet is provided by the gravity of its sun. Mechanical Universe video: The Apple and the Moon The Elegant Universe videos: Newton’s Secret, General Theory of Relativity

  15. Homework questions • P. 138 Question 7 • P. 141 Problems 25, 27, 29, 31, 35, 59b

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