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Lecture 18

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This lecture explores the principles of circular orbits according to Newton's Law of Gravity. We discuss the gravitational force directed towards the Earth's center and analyze the implications for objects in orbit, such as satellites and the moon. The concepts of mass, gravitational force, and the interactions between objects, such as two bowling balls or a person and Earth, are examined. We also delve into Kepler’s laws and determine the altitude required for a geostationary satellite orbiting over the equator.

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Lecture 18

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  1. Lecture 18 Circular Orbits Newton’s Law of Gravity

  2. The force of gravity is directed towards the center of the earth • Circular orbit

  3. Orbit just above the surface of the earth

  4. Move out to the moon • Rem=3.84 x 108 m • What is wrong here? • What did we assume that is incorrect?

  5. Newton’s Law of Gravity

  6. Determine the mass of the earth • M1 is your mass = ____________ • Rearth = 6.37 x 106 m • G=6.67 x 1011 N•m2/kg2 • g=9.80 m/s2 • M2 = Mass of the earth =

  7. Example A typical bowling ball is spherical, weighs 16 pounds, and has a diameter of 8.5 in. Suppose two bowling balls are right next to each other in the rack. What is the gravitational force between the two—magnitude and direction? What is the magnitude and direction of the force of gravity on a 60 kg person? Slide 6-32

  8. A coin sits on a rotating turntable. • At the time shown in the figure, which arrow gives the direction of the coin’s velocity? Slide 6-38

  9. A coin sits on a rotating turntable. • At the time shown in the figure, which arrow gives the direction of the frictional force on the coin? Slide 6-40

  10. A coin sits on a rotating turntable. • At the instant shown, suppose the frictional force disappeared. In what direction would the coin move? Slide 6-42

  11. 6.7 Gravity and Circular Orbits • M = mass of parent, m=mass of satellite • Kepler’s law

  12. Geostationary Satellite • At the equator, how far above the earth’s surface should a satellite orbit so it stays overhead? • Rearth = 6.37 x 106 m • G=6.67 x 1011 N•m2/kg2 Mearth = 5.98 x 1024 kg

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