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**Gravitation Newton’s Law of Gravitation; Kepler’s Laws of Planetary Motion.**

Lecture 14 Monday: 1 March 2004

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**Physical Principles of Design Forces 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 encountered:frictional 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 earth’s 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 of the Earth**

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**Characteristics of the Gravitational Force**

The force is always attractive. There is a Newton’s 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 CIRCULAR ORBITS**

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