(28)Newton's Laws of Gravity

(28)Newton's Laws of Gravity - Lecture 28 Newton's Law of...

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Lecture 28 Newton’s Law of Gravity
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Newton and the Moon What is the centripetal acceleration of the Moon for its rotation around the Earth? We know (Newton also knew): T = 27.3 days = 2.36 × 10 6 s r moon-Earth = 3.84 × 8 m R Earth = 6.35 × 6 (see Appendix) r R
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Newton noticed that 2 2 0.000273 E R r = Angular frequency of the moon: 2 0.00272 m/ s 0.000278 c a r g ϖ = = = 2 pointing toward the Earth This inspired him to suggest that F gravity 1/r 2 Yes!! = c a g ϖ= = = -6 -1 1 r ot at ion ... 2.66 10 s 27.3 day
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= 2 E const ant g R = 2 a r
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Newton’s Law of Gravitation = 1 2 2 mm F G r Two point-like bodies of mass m 1 and m 2 that are separated by a distance r attract each other with a force with magnitude - = 2 11 2 Nm 6.67 10 kg G and direction along the line between both bodies. Gravitational constant m 1 r F F m 2
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The value of G was unknown to Newton and was first measured in 1798 by Cavendish with a torsion balance. m 2 m 2 F g F g m 1 (movable) attracted to m 2 (fixed) Rotation of rod twists supporting shaft and moves mirror Laser beam to mirror Mirror Deflected angle is proportional to magnitude of the force
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Spherical shell theorem An important result that we will not prove until the lecture on Gauss’s law… The gravitational force exerted by a spherically symmetric object of radius R and mass M is the same as the force exerted by a particle of mass M located at the center of the sphere, for distances r R. m 1 r m 1 r Same force in both cases
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Weight Force by the Earth on an object of mass m at distance h from the ground = + E 2 E ( ) g M F m G R h ?
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(28)Newton's Laws of Gravity - Lecture 28 Newton's Law of...

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