Universal Gravitation

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Universal Gravitation

• Sir Isaac Newton The Universal Law of
  Gravitation

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The Falling Apple

• Newton reasoned the moon is falling for the same
  reason the apple falls they are both pulled by
  the Earths gravity.

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Newtons Excellent Idea

• Now came Newton's truly brilliant insight if the
  force of gravity reaches to the top of the
  highest tree, might it not reach even further in
  particular, might it not reach all the way to the
  orbit of the Moon! Then, the orbit of the Moon
  about the Earth could be a consequence of the
  gravitational force, because the acceleration due
  to gravity could change the velocity of the Moon
  in just such a way that it followed an orbit
  around the earth.

Source http//csep10.phys.utk.edu/astr161/lect/hi
story/newtongrav.html
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The Falling Moon

• Newtons First law
• An object (the moon) will remain in motion in a
  straight line unless acted on by an outside
  unbalanced force (gravitational attraction)
• The force that pulls an apple to the ground also
  keeps the moon in orbit.

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The Falling Earth

• Newtons theory of gravitation confirmed the
  Copernican theory of the solar system.
• A planets tangential speed allows the planets to
  orbit the sun without being pulled into it.

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Newtons law of Universal Gravitation
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The Gravitational Constant Henry Cavendish 1798

• He used a device with two objects on a rod that
  was hung on a wire. These masses were attracted
  to two larger objects, twisting the rod slightly.
  The measurement of the masses, distance between
  them and the torque on the wire allowed G to be
  determined.

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The Universal Gravitational Constant A G-thing

• G is a constant of proportionality.
• The magnitude is the force exerted by two 1-kg
  masses 1 meter apart.
• G 6.67 x 10-11 Nm2/kg2

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Weight and Mass
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Gravity and Distance The Inverse Square Law

• A quantity varies as the inverse square of its
  distance from its source
• A localized source spreads evenly throughout the
  surrounding space.

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The Weight of an Apple?
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Gravity and Orbits

• Centripetal acceleration
• ac v2/r
• Centripetal Force
• Fc mac
• The force in circular motion is directed towards
  the center - centripetal

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Why is the Earth round?

• Because of gravitation earth attracted itself
  together.
• The deviation of a planet from its normal orbit
  is called a perturbation. It is caused by other
  planets.

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Reviewing

• Objects orbiting around the Earth are actually
  falling toward Earth but have great enough
  tangential velocity to avoid hitting the earth.
• Everything pulls on everything else with a force
  that depends on the mass of the objects and
  distances between them.
• Gravitation decreases according to the inverse
  square law.

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Geosynchronous Orbits
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GPS