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Unformatted text preview: Lecture 28 Newton’s Law of Gravity Newton and the Moon 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 × 10 8 m R Earth = 6.35 × 10 6 m (see Appendix) r moon-Earth R Earth 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 ω = = = 2 pointing toward the Earth This inspired him to suggest that F gravity ∝ 1/ r 2 Yes!! = 0.000278 c a g ω = = = ×-6-1 1 rotation ... 2.66 10 s 27.3day = 2 E constant g R = 2 constant a r Newton’s Law of Gravitation 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 The value of G was unknown to Newton and was first measured in 1798 by Cavendish with a torsion balance. m 2 m 1 m 1 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 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 ....
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