Newton

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Newtons Law of Universal Gravitation
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Who Found It?
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Universal Law of Gravitation
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Universal Law of Gravitation
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Universal Law of Gravitation
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Universal Law of Gravitation
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Universal Law of Gravitation
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Universal Law of Gravitation
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Universal Law of Gravitation
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Universal Law of Gravitation
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Cavendish
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The Statement of the Law

• Magnitude Every particle in the universe
  attracts every other particle with a force that
  is proportional to the product of their masses
  and inversely proportional to the square of the
  distance between them.
• Direction This force acts along the line joining
  the two particles.

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Gravity Near the Earths Surface
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Moon Special Satellite

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Earth the Satellite of the sun
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Keplers Laws
Johannes Kepler discovered 3 laws from the motion
of the planets as mapped by Tycho Brahe

• Planetary orbits are elliptical not circular
• Orbits sweep out equal areas in equal times
• T2 /r3 k where k constant

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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 2nd Law
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 2nd Law
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Keplers 3rd Law

• 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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Satellite Motion

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

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Satellites

• What keeps a satellite up?
• Its high speed
• How they move?

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How fast are satellites moving?
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Weightlessness
What is gravity in outer space? Where space
shuttle orbitsg 8.7m/s How come astronauts are
floating then?
g F/m