Newtons Universal Gravitation

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• Newtons Universal Gravitation
• Gravity is More Than a Name

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• How and by whom was gravity discovered? What is
  the cause of this force which we refer to with
  the name of gravity? What variables affect the
  actual value of the force of gravity? Why does
  the force of gravity acting upon an object depend
  upon the location of the object relative to the
  Earth? How does gravity affect objects which are
  far beyond the surface of the Earth? How
  far-reaching is gravity's influence? And is the
  force of gravity which attracts my body to the
  Earth related to the force of gravity between the
  planets and the Sun?

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• In the early 1600's, German mathematician and
  astronomer Johannes Kepler mathematically
  analyzed known astronomical data in order to
  develop three laws to describe the motion of
  planets about the sun.

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• The path of the planets around the sun are
  elliptical in shape, with the center of the sun
  being located at one focus. (The Law of Ellipses)
  
• 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. (The Law of
  Harmonies)

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• 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. (The Law
  of Equal Areas)

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• 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. (The Law of
  Harmonies)

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• Kepler could only suggest that there was some
  sort of interaction between the sun and the
  planets which provided the driving force for the
  planet's motion. To Kepler, the planets were
  somehow "magnetically" driven by the sun to orbit
  in their elliptical trajectories. There was
  however no interaction between the planets
  themselves.

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• Newton was troubled by the lack of explanation
  for the planet's orbits. To Newton, there must be
  some cause for such elliptical motion. Even more
  troubling was the circular motion of the moon
  about the earth. Newton knew that there must be
  some sort of force which governed the heavens

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• The fact is certain that it was Newton's ability
  to relate the cause for heavenly motion (the
  orbit of the moon about the earth) to the cause
  for Earthly motion (the fall of an apple to the
  Earth) which led him to his notion of universal
  gravitation.

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What is it about the force of gravity which
causes the more distant moon to accelerate at a
rate of acceleration which is approximately
1/3600-th the acceleration of the apple?
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The force of gravity between the earth and any
object is inversely proportional to the square of
the distance which separates that object from the
earth's center.
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• The force of gravity follows an inverse square law

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• 1 . Suppose that two objects attract each other
  with a force of 16 units. If the distance between
  the two objects is doubled, what is the new force
  of attraction between the two objects?

2. Suppose that two objects attract each other
with a force of 16 units. If the distance between
the two objects is tripled, then what is the new
force of attraction between the two objects ?
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Newton's law of universal gravitation is about
the universality of gravity.
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The precise value of G was determined
experimentally by Henry Cavendish in the century
after Newton's death.
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• Sample Problem 1
• Determine the force of gravitational attraction
  between the earth (m 5.98 x 1024 kg) and a
  70-kg physics student if the student is standing
  at sea level, a distance of 6.37 x 106 m from
  earth's center.

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• 2. Suppose that two objects attract each other
  with a force of 16 units. If the distance between
  the two objects is doubled, what is the new force
  of attraction between the two objects?

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• 3. Suppose that two objects attract each other
  with a force of 16 units. If the mass of both
  objects was doubled, and if the distance between
  the objects remained the same, then what would be
  the new force of attraction between the two
  objects?

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• 4. If our sun shrank in size to a black hole,
  would the Earth's orbit be affected? Explain.

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• 5. What would happen to your weight if the mass
  of the Earth somehow increased by 10?