Gravitation Newton

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GravitationNewtons Law of GravitationKeplers
Laws of Planetary Motion.

• Lecture 14
• Monday 1 March 2004

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Physical Principles of DesignForces and Motion

• Learning to analyze and predict the motion of
  objects moving with constant accelerations.-
  Topics of kinematics, projectile motion .
• Coming to understand the causes of motions and
  changes in motion-topics of (linear and
  rotational) forces, momentum, energy
• Forces we have encounteredfrictional force,
  normal force, applied forces of pushes/pulls,
  tension in strings, and the GRAVITATIONAL FORCE

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How Many Different Forces are There?

• All of the forces we have worked with or will
  work with are specific examples of following
  general types of forces
• The Fundamental Forces of Nature
• Gravitational Force
• Electromagnetic Force
• Strong Force (Nuclear)
• Weak Force (Nuclear)

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A General Expression for the Gravitational Force
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Revisiting Gravitational Force
More Specifically,
Where , is the acceleration due to the
earths gravitational attraction. It is not
only the earth that attracts other objects. Any
object with mass will attract any other object
with mass.
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At the surface ofthe Earth
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Characteristics of the Gravitational Force

• The force is always attractive.
• There is a Newtons third law force pair
  involved.
• It acts along a line connecting the centers of
  the two objects (called a Central Force)
• It is inversely proportional to r2 (called a one
  over r squared force)
• Experimental measurement show us that it is a
  conservative force (the gravitational force on
  earth is conservative-remember? This is a general
  expression of that same force)

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Defining the Potential Energy Associated with
this Force
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POTENTIAL ENERGY

• Choose U 0 at r

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Gravitational Potential Energy Near Earth
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KEPLER'S LAWS

• 1. The Law of Orbits All planets move in
  elliptical orbits having the Sun at one focus.
• 2. The Law of Areas A line joining any planet to
  the Sun sweeps out equal areas in equal times.

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The Law of Areas
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KEPLER'S LAWS

• 3. The Law of Periods The square of the period
  of any planet about the Sun is proportional to
  the cube of the semimajor axis of its orbit.

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The Law of Periods
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ENERGY IN CIRCULARORBITS
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