Newton

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Newtons Law of Universal Gravitation
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• Any two objects exert a gravitational force of
  attraction on each other. The magnitude of the
  force is proportional to the product of the
  gravitational masses of the objects, and
  inversely proportional to the square of the
  distance between them.

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G6.67X10-11 N m2/kg2
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BASIC PROBLEM

• Find the gravitational force between a baseball
  (m0.3kg) and a billiard ball (m0.4kg) if the
  distance between their centers is 0.3m.

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A STELLAR PROBLEM

• We can consider the sun to be a satellite of our
  galaxy, the Milky Way. The sun, mass 2.0X1030kg,
  revolves around the center of thee galaxy with a
  radius of 2.2X1020 m. The period of one rotation
  is 2.6X108 years.
• a. Find the approximate mass of the galaxy.
• Assume the average star in the galaxy has the
  mass of the sun, find the number of stars in the
  galaxy.

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Keplers laws
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Keplers 1st law
The paths of the planets around the sun are
ellipses with the sun at one focus point
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Keplers 2nd law

• An imaginary line drawn from a planet to the sun
  sweeps out equal areas in equal amounts of time
  as the planet travels along its elliptical path.

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Keplers 2nd law

• An imaginary line drawn from a planet to the sun
  sweeps out equal areas in equal amounts of time
  as the planet travels along its elliptical path.

A1
A2
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Keplers 2nd law

• If A1 A2, then t1 t2

t1
A1
A2
t2
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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
  the planets average distances from the sun.

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Satellite problem

• Uranus requires 84 years to circle the sun. Find
  the distance from the sun to Uranus.

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Problem- A Geosynchronous satellite

• What is the orbital radius of a geosynchronous
  satellite? (______________________)
• How far up from the surface of the earth is this
  satellite?