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Unformatted text preview: Ph-507. Homework 3 (due: Monday, February 14).PROBLEM 3-1 (3 pts)Four point particles of the same massesm, are placed at the corners of a square of sizedd. They are releasedwith no initial speed at timet= 0. After what time will the particles collide?PROBLEM 3-2 (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 3-3 (3 pts)Consider a confned motion of a particle in gravitationalfeld with1/r2correction:U(r) =GMr+r2m,Because of the correction, the principle axes of the elliptical orbit rotate with certain angular velocity(calledprecession rate). Find.PROBLEM 3-4 (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 non-zeroD.PROBLEM 3-5 (3 pts)Episode I (phantom menace):Long time ago, in a galaxy far, far away...In a six-dimentional space, wherethe gravitational potential energy of massesmandMis given byU(r) =Mmr4,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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