Ch. 8 Universal Gravitation

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Ch. 8 Universal Gravitation

• Milbank High School

2
Sec. 8.1Motion in the Heavens and on Earth

• Objectives
• Relate Keplers laws of planetary motion to
  Newtons law of universal gravitation.
• Calculate the periods and speeds of orbiting
  objects.
• Describe the method Cavendish used to measure G
  and the results of knowing G.

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Kepler

• Johannes Kepler (1571-1630)
• Was convinced that geometry and mathematics could
  be used to explain the motion of the planets.

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Keplers laws

• 1. The orbits of the planets are ellipses, with
  the sun at one focus.
• (Law of Ellipses)
• The closer the planets
• are to one another,
• the more circular the
• orbit.

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Keplers Laws

• 2. An imaginary line drawn from the center of the
  sun to the center of the planet will sweep out
  equal areas in equal intervals of time.
• (Law of Equal Areas)
• Deals with speed
• faster when closer
• to the sun.

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Keplers Laws

• 3. The ratio of the squares of the periods of any
  two planets is equal to the ratio of the cubes of
  their average distances from the sun.
• (Law of Harmonies)
• (TA/TB)2 (rA/rB)3

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Universal Gravitation

• Isaac Newton
• 24yrs old
• Watching an apple fall to the ground made him
  wonder if gravity extended beyond Earth
• Came up with universal gravitation
• Attractive force between two objects
• The apple was also attracting the Earth
• Proposed Law of Universal Gravitation

8
Law of Universal Gravitation

• The force of attraction between any two masses is
  constant throughout the universe
• F G(mAmB/d2)
• G is a universal gravitational constant between
  two masses
• 6.67 x 10-11 Nm2/kg2

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Sec. 8.2Using the Law of Universal Gravitation

• Objectives
• Solve problems involving orbital speed and period
• Relate weightlessness to objects in free fall
• Distinguish between inertia mass and
  gravitational mass
• Contrast Newtons and Einsteins views about
  gravitation

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Satellite Motion

• If a projectile moves fast enough, it falls at
  the same rate that the Earth curves

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How fast are satellites moving?

• F ma or F mv2/r
• (ac v2/r)
• F G(mAmB/d2)
• Solve for velocity? Set them equal to each other
• G(mAmB/d2) mv2/r
• which gives you.

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Period of a Satellite Circling Earth

• T 2pvr3/GmE
• or if we know the velocity
• T 2pr/v

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Weightlessness

• What is gravity in outer space?
• Where space shuttle orbitsg 8.7m/s2
• How come astronauts
• are floating then?
• g F/m