lec10a-203-12-gravbest

lec10a-203-12-gravbest - F GMm R2 Satellite Motion GMm U(r...

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10a-0 2 GMm F R GMm U (r) - r 0 U (r )    f i E E how high does it go? Escape velocity Kepler’s 2nd Law ::= Areas Angular Mom. Conservation !!!! Satellite Motion

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Newton’s Universal Law of Gravity 1) F acts along the line connecting the centers of objects “Central Force” (for spherical objects) 2) F points toward M (attractive force) 3) Newton says: F = G=6.67 x 10 -11 [m 3 /Kg s 2 ] G M m r 2 for special case on the Earth’s surface, this acceleration is: g = 9.81 m/s 2 G is a very small number! r M m F= force of gravity on m (M) due to M (m) F F 10a-1
10a-1 10a-1a e Recall

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10a-1b
Properties of Gravity Gravitation from a Sphere Gravitational force between an object and a sphere is the same as if all the mass of the sphere was concentrated at its center. 10a-2

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2 2 (2 ) R a T 8 12 2 (10) 28.6 (10) m s 8 3.84(10) Rm 2 0.00286 Moon m a s 28 62 (2[3.14]) 3.84(10) [2.3(10) ] m s 10a-3 What is a moon in orbit ? Calculate a moon-in-orbit for later (circular orbit)
10a-4 2 e R Moon apple Moon dist aa R    e R 1 .0166 60.2 Moon dist R  2 2 1 9.8 60.2 Moon m a s 2 0.0027 Moon m a s 6 e 8 R 6.378(10) 3.84(10) Moon dist m Rm Newt. nailed it !!! dead right higher velocity - earth curves away under falling object cannon fired horizontally low velocity- ~parabolic path For special ”orbital” velocity the ball falls at the same rate that the earth curves away Same idea for moon in orbit- moon “falling” toward Earth 2 GMm F ma R 2 moon GM a R 2 2 2 2 moon e apple e GM aR R GM R apple ag 2 2 e moon apple R R 2 2 e moon R R moon earth Newton’s connection a falling-apple =a orbiting-apple =g !!!!!!

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lec10a-203-12-gravbest - F GMm R2 Satellite Motion GMm U(r...

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