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The Law of Universal Gravitation

The Law of Universal Gravitation. A little background ….

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The Law of Universal Gravitation

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  1. The Law of Universal Gravitation

  2. A little background… Legend has it that Sir Isaac Newton was struck on the head by a falling apple while napping under a tree. This prompted Newton to imagine that all bodies in the universe are attracted to each other in the same way that the apple was attracted to the Earth. Newton analyzed astronomical data on the motion of the Moon around the Earth and stated that the law of force governing the motion of the planets has the same mathematical form as the force law that attracts the falling apple to the Earth.

  3. Newton’s Law of Universal Gravitation • every particle in the universe attracts every other particle with a force • The force is directly proportional to the product of their masses • The force is inverselyproportional to the square of the distance between them. • So, if the particles have masses m1 and m2 and are separated by a distance d, the magnitude of the gravitational force is:

  4. A closer look… G is the universal gravitational constant, which has been measured experimentally as: The distance, d, between m1 and m2 is measured from the center of m1 to the center of m2.

  5. Remember Third Law? • Newton’s third law says that the magnitude of the force exerted by m1 on m2 is equal to the force exerted by m2 on m1, but opposite in direction – an action-reaction pair.

  6. Properties of the Gravitational Force • A long range force – it exists between two particles, regardless of the medium that separates them. • It varies as the inverse squareof the distance between the particles. • Gravitational force decreases rapidly with increasing distance between the particles. • The force is directly proportional to the mass of each particle. • A larger mass will yield a larger gravitational force

  7. Weight and Gravitational Force Remember... Fg = m·g, where g is the magnitude of the acceleration due to gravity. So, The m’s cancel out, giving us “g” (gravity).

  8. Formula Summary • ME = 5.97 x 1024 kg • rE = 6.37 x 106 m • G = 6.67 x 10-11 Nm2/kg2

  9. Scientific Notation Practice 6.67 x 10-11 x 2000 = 6.67 x 10-11 x 52 = 6.67 x 10-11 x 5.98 x 1024 =

  10. Example 1) Two masses, 25000 kg and 80000 kg, are separated by 200 meters. What is the force of attraction between them?

  11. Example 2) What is the force of attraction between a 2000 g mass and a 4000 g mass if their centers are 15 cm apart?

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