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Unformatted text preview: Ph507. Homework 3 (due: Monday, February 14).PROBLEM 31 (3 pts)Four point particles of the same massesm, are placed at the corners of a square of sized×d. They are releasedwith no initial speed at timet= 0. After what time will the particles collide?PROBLEM 32 (3 pts)Att= 0, the distance between two objects of massesmand3m, is minimal and equal tormin. Find out how thisdistance changes with time, if the relative velocity of the particles approachesv, whenr→ ∞.PROBLEM 33 (3 pts)Consider a confned motion of a particle in gravitationalfeld with1/r2correction:U(r) =μ−GMr+αr2¶m,Because of the correction, the principle axes of the elliptical orbit rotate with certain angular velocityΩ(calledprecession rate). FindΩ.PROBLEM 34 (3 pts)Find the equation of the trajectory, and period of radial motion of a particle of massmin the following centralpotential:U(r) =kr2+Dr2,Show that the orbits are closed curves whenD= 0, and determine the rate of their precession for nonzeroD.PROBLEM 35 (3 pts)Episode I (phantom menace):Long time ago, in a galaxy far, far away...In a sixdimentional space, wherethe gravitational potential energy of massesmandMis given byU(r) =−ΓMmr4,a lonely planet was orbiting a lonely star. Eventually, the planet has left its circular orbit of radiusa lonely planet was orbiting a lonely star....
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 Spring '04
 ANON
 mechanics, Mass, Work, General Relativity, rmin, radial motion

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