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Unformatted text preview: Physics 7A Final Review (by Pavan Hosur) 1 Problems 1. Problem summary: A planet of mass m revolves around a star of mass M ( m ) in a circular orbit of radius R. A comet of mass m C ( m ) moving with a speed v C straight towards the star lands on the planet. Find the function r ( t ) (the radius as a function of time) that describes the new orbit. You may treat all objects as point masses. See if you can come up with a strategy to solve this. If not, read ahead. (a) First consider a more general situation: i. Show the following for a general orbit of any shape : E = 1 2 m r 2 + L 2 2 mr 2- GMm r where E is the total energy of the planet-star system and L is the angular momentum of the planet about the star. ii. What quantities are conserved in this motion? What is dE/dt ? Evaluate r in terms of r and the other constants. (Notation: x = dx/dt, x = d 2 x/dt 2 etc.) (b) Now return to the problem described above....
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