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Solution_Set_08

# Solution_Set_08 - SOLUTION SET 8 Physics 2022 1 Convert...

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SOLUTION SET 8 Physics 2022 1. Convert parsecs to light years d = 2000 pc x 3.26 ly/pc = 6520 ly The supernova was observed in AD 1054. The light began its journey 6520 years before, so the explosion happened in AD 1054 6520 = 5466 BC 2. time = 2010 1054 = 956 years ( x 60 x 60 x 24 x 365.25 ) = 3.0 x 10 10 s radius = velocity x time = 1450 km/s x (3.0 x 10 10 s) = 4.35 x 10 13 km = 2.90 x 10 5 AU = 1.4 pc = 4.6 ly diameter = 9.2 ly 3. For a neutron ρ = M / (4/3 π R 3 ) = 1.7 x 10 -27 kg / (4/3 π (10 -15 m) 3 ) = 4.1 x 10 17 kg/m 3 For a neutron star ( M = 1.4 solar masses; R = 9.7 km ) ρ = M / (4/3 π R 3 ) = 1.4 x 2.0 x 10 30 kg / (4/3 π (9,700 m) 3 ) = 7.3 x 10 17 kg/m 3 4a. λ max = 0.0029 / T = 0.0029 / ( 3 x 10 7 ) = 9.7 x 10 -11 m = 9.7 x 10 -2 nm (X ray) 4b. L * = 4 π R * 2 σ T * 4 = 4 π (10 4 m) 2 (5.669 x 10 -8 ) (3 x 10 7 ) 4 = 5.8 x 10 31 W = 5.8 x 10 31 (/ 3.9 x 10 26 W) = 1.5 x 10 5 L sun

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5. P = 7.75 hr = 8.84 x 10 -4 yr a = 2.8 solar radii x (6.96 x 10 5 km) / (1.5 x 10 8 km/AU) = 1.30 x 10 -2 AU ( M 1 + M 2 ) = a 3 / P 2 = (1.30 x 10 -2 ) 3 / (8.84 x 10 -4 yr) 2 = 2.8 solar masses 6. R sch = 2 G M / c 2 = [ 2 (6.67 x 10 -11 ) / (3 x 10 8 m/s) 2 ] M = (1.48 x 10
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