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Lecture 3 - Universal Gravity and Orbits Ch 12:4-5 Review...

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April 8, 2008 Physics 40B Lecture 3 1 Universal Gravity and Orbits Ch. 12:4-5 Review of Gravity Universal Force of Gravity Superposition of Forces Vector Addition Gravitational Potential Energy Gravitational Potential Energy for three masses U ( r ) = " G m 1 m 2 r m 1 m 3 m 2 U = " G m 1 m 2 r 12 + m 1 m 3 r 13 + m 2 m 3 r 23 # $ % & (
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April 8, 2008 Physics 40B Lecture 3 2 Review Continued Acceleration of Gravity at Earth’s Surface Gravitation force outside an uniform spherical shell is due to mass of shell concentrated at center of shell. Inside shell, force is zero. Gravitation force outside spherically symmetric sphere is due to mass of sphere concentrated at center. Inside sphere, force is due only to mass within distance to center. Total Energy and Escape Velocity g = F m = 1 m G mM E R E 2 " # $ % & = G M E R E 2 W = "# U K = 1 2 mv 2 E = K + U E = 1 2 mv 2 " GM E m r Escape Velocity (speed needed for mass m to just escape gravity of earth) Let E f = E i = 0 at r = $ ( v f = 0) E i = 1 2 mv i 2 " GM E m R E % v i = 2 GM E R E = 1.12 x 10 4 m
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