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Universal Gravitation - Isaac Newton

Universal Gravitation - Isaac Newton Combine Kepler’s Laws with Newton’s three laws of motion to get:

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Universal Gravitation - Isaac Newton

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  1. Universal Gravitation - Isaac Newton Combine Kepler’s Laws with Newton’s three laws of motion to get: “Between any two objects there exist an attractive force acting along the lien joining their centers that varies in direct proportion to the product of their masses and inversely with the square of the separation distance”.

  2. Kepler’s 2nd law plus Newton’s laws of motion concludes: Force is either attractive or repulsive and acts along live joining centers. • Kepler’s 1st law plus Newton’s laws of motion concludes: Force is attractive and varies inversely as square of separation distance. • Kepler’s 3rd law plus Newton’s laws of motion concludes: Force varies in direct proportion to product of two masses.

  3. Henry Cavendish (1731 - 1810) • Introvert ; Cavendish Lab est.1869 • Used torsion balance to measure “G” (the constant needed in universal gravitation). • So: if given radius of the earth = 6.37 x 106 m (known fairly accurately by ancients) and acceleration due to gravity = 9.80 m/s2, find the mass of the earth = 5.98 x 1024 kg.

  4. Acceleration of Earth Given: drop board eraser (mass = 100g = 0.1kg) MEARTH = 5.98 x 1024 Kg : REARTH = 6.38 x 106 m G = 6.67 x 10-11 n*m2/Kg2 GMBME MEAE = AE = 1.64 X 10-25 m/s2 RE2 GMBME MBAB = AB = ? RE2

  5. Inverse Square Law: Force varies as 1/R2 So if: F = 720 N at Re Then: F = 180 N (1/4 the attraction) @ 2 Re F = ? (?) @ 3 Re F = ? (?) @ 6 Re

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