The Universal Law of Gravitation

The Universal Law of Gravitation - This force has some...

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The Universal Law of Gravitation Newton's Law Qualitatively Newton's Law of gravitation states that: Every massive particle attracts every other massive particle with a force directly proportional to the product of their masses and inversely proportional to the square of distance between them In vector notation, if is the position vector of mass m 1 and is the position vector of mass m 2 , then the force on m 1 due to m 2 is given by: = = The difference of the two vectors in the numerator gives the direction of the force. The appearance of a cube, instead of a square, in the denominator is in order to cancel this direction- giving factor of | - | in the numerator. Figure %: Direction of force is the difference of the position vectors.
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Unformatted text preview: This force has some remarkable properties. First, we note that it acts at a distance , meaning that irrespective of any intervening matter, every particle in the universe exerts a gravitational force on every other particle. Furthermore, gravity obeys a principle of superposition. This means that to find the gravitational force on any particle it is necessary only to find the vector sum of all the forces from all the particles in the system. For example, the force of the earth on the moon is found by vector summing all the forces between all the particles in the moon and earth. This sounds like an immense task, but actually simplifies calculation....
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