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Unformatted text preview: Homework # 9 Solutions 1. Do problem 5.8 in the text. Using V 2 = G M ( &lt; r ) /r , and using ( r ) = (3 a 2 M / 4 )( a 2 + r 2 ) 5 / 2 we find M ( &lt; r ) = M r 3 ( a 2 + r 2 ) 3 / 2 and V ( r ) = G M r ( a 2 + r 2 ) 3 / 4 . The maximum occurs when 3 r 2 / 2 = r 2 + a 2 or r = 2 a . The spider diagram is shown in the figure. To get the proper perspective on the sky, one has to foreshorten the figure appropriately so that the outline is elliptical rather than circular. 2. Do problem 5.13 in the text. Determine the ratio of the two areas of the zones in the disk where 2 and 4 armed spirals are stable. Does this depend on the value of p ? The epicyclic frequency is determined from 2 = parenleftbigg R d 2 dR + 4 2 parenrightbigg R For uniform rotation, R 1 , so 2 = 2 2 and ( R ) = 2 V /R 36 km/s if we use V 220 km/s and R 8 kpc....
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This note was uploaded on 01/25/2012 for the course AST 346 taught by Professor Lattimer during the Spring '11 term at SUNY Stony Brook.
- Spring '11