406_Physics ProblemsTechnical Physics

406_Physics ProblemsTechnical Physics - 408 *P13.67...

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408 Universal Gravitation *P13.67 Let m represent the mass of the meteoroid and v i its speed when far away. No torque acts on the meteoroid, so its angular momentum is conserved as it moves between the distant point and the point where it grazes the Earth, moving perpendicular to the radius: FIG. P13.67 LL if = : mm ii f f rv r v ×= × mRv m Rv vv Ei E f fi 3 3 bg = = Now energy of the meteoroid-Earth system is also conserved: KU g i g f += + ej : 1 2 0 1 2 22 mv mv GM m R E E 1 2 1 2 9 GM R E E =− GM R v E E i = 4 2 : v GM R i E E = 4 *P13.68 From Kepler’s third law, minimum period means minimum orbit size. The “treetop satellite” in Figure P13.35 has minimum period. The radius of the satellite’s circular orbit is essentially equal to the radius R of the planet. Fm a = : GMm R mv R m R R T 2 2 2 2 == F H G I K J π GV
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .

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