lecture07spring2009 - Astronomy100Dr.Rhodes Lecture Chapter...

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Astronomy 100 - Dr. Rhodes Lecture # 7 - 1/28/2009
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Chapter 3: Gravity and the Rise of Modern Astronomy The Law of Universal Gravitation This law states that between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects. In equation form: F = -Gm 1 m 2 / d 2 where G is the Universal Constant of Gravitation, m 1 and m 2 are the masses, d is the distance between their centers, and the minus sign shows that the force is attractive.
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Chapter 3: Gravity and the Rise of Modern Astronomy The Law of Universal Gravitation For a person standing on the earth’s surface, the force of gravity on that person will be different for every different part of the earth since the distance to the man will be different for each part of the earth. If we assume that the earth is spherical, we can use calculus to show that the total of all of these different forces acting upon the person is the same as if all of the mass of the earth were concentrated into a point at its center.
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Individual Force Vectors from Each Part of Earth to the Man Effective Concentration of Earth’s Mass at its Center for the Man
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Chapter 3: Gravity and the Rise of Modern Astronomy The Law of Universal Gravitation Weight is the gravitational force between and object and the planetary body on which the object is located. According to Newton, gravity not only makes objects fall to Earth but keeps the Moon in orbit around the Earth and keeps the planets in orbit around the Sun. He could therefore explain the planets’ motions and why Kepler’s Laws worked.
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Chapter 3: Gravity and the Rise of Modern Astronomy The Law of Universal Gravitation Testing the Law of Universal Gravitation The statement that force is proportional to mass can be tested by showing that mass is proportional to weight here on Earth. To test the proportionality of force and distance, Newton compared accelerations of objects near the Earth’s surface and the Moon in orbit around the Earth.
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Chapter 3: Gravity and the Rise of Modern Astronomy The Law of Universal Gravitation Because the distance from the center of the
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