Solution_Set_09 - 6 km = 0.073 AU 5b. sin θ = D / d =...

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SOLUTION SET 9 Physics 2022 – Spring 2008 1. m = +14.3 L * / L sun = 88 M sun = +5.0 M sun – M * = 2.5 log ( L * / L sun ) = 2.5 log ( 88 ) = 4.86 M * = 5.0 4.86 = 0.14 mag m M = 5 log ( d / 10 ) = 14.3 0.14 = 14.16 D = [ dex ( 14.16 / 5 ) ] ( 10 ) 6800 pc 2. E = h c / λ = (6.63 x 10 -34 Js) (3 x 10 8 m/s) / (0.21 m) = 9.5 x 10 -25 J 3a. P = 2 π d / v = 2 π (20,000 pc) (3.086 x 10 13 km) / [(400 km/s) (60 x 60 x 24 x 365.25)] P = 3.08 x 10 8 year = 308 million years 3b. M = d 3 / P 2 = [ (20,000 pc) (206265 AU/pc) ] 3 / [ 3.08 x 10 8 yr] 2 M = 7.4 x 10 11 solar masses 4a. P = 2 π d / v = 2 π (16,000 pc) (3.086 x 10 13 km) / [(270 km/s) (60 x 60 x 24 x 365.25)] P = 3.64 x 10 8 yr 4b. M = d 3 / P 2 = [ (16,000 pc) (206265 AU/pc) ] 3 / (3.64 x 10 8 yr) 2 M = 2.7 x 10 11 solar masses
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5a. R sch = 2 G M / c 2 R sch = 2(6.67 x 10 -11 N m 2 /kg 2 ) (3.7 x 10 6 ) (1.989 x 10 30 kg) / (3 x 10 8 m/s) 2 R sch = 10.9 x 10 9 m = 10.9 x 10
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Unformatted text preview: 6 km = 0.073 AU 5b. sin θ = D / d = (0.073 AU) / [ (8,000 pc) (206265 AU/pc) ] = 4.42 x 10-11 θ = 2.53 x 10-9 degree = 9.12 x 10-6 arcsec half-angle full-angle = 2 θ = 1.8 x 10-5 arcsec 5c. sin θ = D / d = (0.073 AU) / [ 120 AU ] = 6.08 x 10-4 θ = 3.49 x 10-2 degree = 125 arcsec half-angle full-angle = 2 θ = 250 arcsec Can be seen by naked eye 6a. C = 2 π r = 2 π (530 AU) (1.5 x 10 8 km/AU) = 5.0 x 10 11 km P = C / v = (5.0 x 10 11 ) / 2500 km/s = 2.0 x 10 8 seconds = 6.3 years 6b. ( M 1 + M 2 ) = a 3 / P 2 = (530 AU) 3 / (6.3 yr) 2 = 3.8 x 10 6 solar masses 7. d = v / H o = (16,000 km/s) / (70 km/s/Mpc) d = 229 Mpc = 229 x 10 6 pc ( x 3.26 ly/pc) = 745 x 10 6 ly Problems 2, 5a, 6a, and 7 are worth 1 point each. Problems 3 and 4 are worth 2 points each....
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This note was uploaded on 04/30/2008 for the course PHYSICS 2022 taught by Professor Sowell during the Spring '08 term at Georgia Tech.

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Solution_Set_09 - 6 km = 0.073 AU 5b. sin θ = D / d =...

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