set8 - particle as long as screening is relatively weak,...

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Department of Physics Prof. R. Bundschuh The Ohio State University Eighth Problem Set for Physics 664 (Theoretical Mechanics) Spring quarter 2004 Important dates: May 31 no class, Jun 9 9:30am-11:18am Fnal exam Due date: Thursday, May 27 20. Satellite 10 points An earth satellite has a perigee of 300 km and an apogee of 3 , 500 km above Earth’s surface. a) Calculate the typical radius α and the eccentricity ² of the satellite. b) How far above the Earth’s surface is the satellite after it has rotated 90 o from the perigee? c) How far above the Earth’s surface is the satellite when it has traveled half the distance from perigee to apogee? 21. Yukawa potential 8 points If two particles interact via electrostatic attraction and this interaction is screened by other charge carriers, the electrostatic potential V ( r ) = - k/r has to be replaced by the Yukawa potential V ( r ) = - k r e - r/a where a is the screening length. We want to study how this screening a±ects the orbits of a
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Unformatted text preview: particle as long as screening is relatively weak, i.e., for r < a . a) Expand the Yukawa potential to Frst order in r/a . b) Calculate the orbits r ( ) of this approximated potential. [Hint: You do not have to redo calculations that we already did in class.] c) Describe qualitatively how the orbit changes compared to the unscreened case (i.e., a = ). 22. Double stars 8 points In this problem we want to look at the motion of double stars. We assume that each double star system rotates in a circular orbit around its respective center of mass. We know the distance between the double stars and their masses. Calculate their period of revolution in years if a) both stars have the same mass as the sun and their distance is 4 light years. b) one star has the same mass as the sun while the other is three times as massive and their separation is 6 light years. 1...
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This note was uploaded on 07/17/2008 for the course PHYS 664 taught by Professor Bundschuh during the Fall '04 term at Ohio State.

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