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Unformatted text preview: Assignment #9 PHYSICS 8.284 Due 11:04am Wednesday 26th April 2006 Reading: Binney and Tremaine: Chapter 1 and 3.1. Note: This set requires numerical integration of differential equations and probably cannot be finished if started the night before its due! (1) The potential for the Mestel disk is given by r ( r, ) = v c 2 ln + ln 1 + | cos | . r 2 a) Using Gauss law, verify that the axisymmetric thin disk giving rise to the Mes- tel potential, has a surface density which varies as 1/r. b) What is the surface density in terms of v c and r ? What would the surface den- sity (in M / pc 2 ) be at the Suns position in the Milky Way, where v c = 220 km/s and R = 8 kpc, if the Milky Way had a Mestel disk potential? (2) A parabolic telescope mirror, the primary, has diameter D and focal length L , giv- ing it an f-ratio of L/D . Suppose that a hyperbolic secondary is installed a distance L/ 3 from the prime focus bringing on-axis light to a perfect focus at the center of primary...
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- Spring '06