Universal Gravitation

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Universal Gravitation

• Motion in the Heavens on Earth
• Using the Law of Universal Gravitation

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Gravity

• Greeks
• Fall/rise according to their nature
• Hot air, smoke, rocks
• Levity gravity
• Galileo
• we do not really understand the principle or
  what force it is that moves stones downward
• Einstein
• Detailed different description of gravitational
  attraction

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Observed Motion

• Tycho Brahe
• Danish Astronomer
• Spent years observing recording exact location
  of planets stars
• Johannes Kepler
• German
• Believed that sun was center of universe
• Would better (mathematically/geometrically)
• Three mathematical laws

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Keplers laws of planetary motion

• The paths of the planets are ellipses, with the
  sun at one focus

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Keplers laws of planetary motion

• 2. An imaginary line from the sun to a planet
  sweeps out equal areas in equal time intervals.
• Planets move faster when they are closer to the
  sun slower when they are further away from the
  sun

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Keplers laws of planetary motion

• 3. The square of the ratio of the periods of any
  two planets revolving about the sun is equal to
  the cube of the ratio of their average distances
  from the sun
• If TA TB are the planets periods, and rA rB
  are the average distances from the sun
• (TA / TB)2 (rA / rB)3

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Problem

• The moon has a period of 27.3 days has a mean
  distance of 3.9 x 105 km from the Earth. Find the
  period of an artificial satellite that is in
  orbit 6.7 x 103 km from the center of Earth.
• (Ts / Tm)2 (rs / rm)3
• Ts2 (rA / rB)3 TB2
• Ts 6.15 x 10-2 days 88.6 min

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Universal Gravitation

• Gravitational force
• Attractive force that exists between all objects
• Law of Universal Gravitation
• Gravitational force between any two objects is
  directly proportional to the product of their
  masses inversely proportional to the square of
  the distance between their centers

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Law of Universal Gravitation

• F G (mAmB/d2)
• d distance between the centers of the masses
• G universal constant
• 6.7 x 10-11 Nm2/kg2

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Law of Universal Gravitation

• Period of Planetary Motion
• T2 (4p2 / Gms)r3
• Keplers 3rd Law of planetary motion

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Using Law of Universal Gravitation

• Satellite that orbits the earth at the same
  height move with circular motion
• ac v2/r
• F m v2/r
• Speed of an Object in Circular Motion
• v v(GmE / r)
• Period for Satellite Circling Earth
• T 2p v(r3 / GmE)

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