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Solution_Set_07 - π 3(6378 x 10 5 cm 3 = 1.84 x 10 6 g/cm...

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SOLUTION SET 7 Physics 2022 1. L * = 1000 L sun T * = 100,000 K T sun = 5800 K L * / L sun = (R * / R sun ) 2 (T * / T sun ) 4 1000 = (R * / R sun ) 2 (100,000 / 5800) 4 (R * / R sun ) 2 = 1.13 x 10 -2 R * = 0.11 R sun 2. v = 20 km/s d = 2,700 LY θ = 1.2 arcmin = 72 arcsec d = 2,700 LY ( 1pc / 3.26 LY ) = 828 pc R = d tan θ = (828 pc) (206,265 AU/pc)( 1.5 x 10 8 km/AU) tan [(72 / 2) / 3600] = 4.5 x 10 12 km Radius because half of the angle was used. t = D / v = (4.5 x 10 12 km) / (20 km/s) = 2.2 x 10 11 sec = 6970 yr 3a. λ max = 0.0029 / T = 0.0029 / 30,000 = 9.67 x 10 -8 m = 96.7 nm 3b. Because of Wien’s Law, much more light is being emitted in the X-ray because the temperature of the White Dwarf is 30,000 K but temperature of its companion is about 10,000 K. 4. M = 1.0 M sun = 2 x 10 30 kg R * = R earth = 6378 km ρ = M / V = (2 x 10 33 g) / (4
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Unformatted text preview: π / 3) (6378 x 10 5 cm) 3 = 1.84 x 10 6 g/cm 3 5. Radius = 0.1 m Density = 10 6 g/cm 3 Volume = 4/3 π R 3 = 4/3 π (10 cm) 3 = 4.2 x 10 3 cm 3 Mass = Volume x Density = (4.2 x 10 3 cm 3 ) x (10 6 g/cm 3 ) = 4.2 x 10 9 g = 4.2 x 10 6 kg = 4,200 metric tons 6. Δ m = 20 m = 2.5 log ( l 1 / l 2 ) l 1 / l 2 = 10 8 7. d = 425 LY ( / 3.26 LY/pc) = 120 pc m - M = 5 log ( d / 10 ) m = 5 log ( 120 / 10 ) + (-17) = -11.6 mag 8. Because the spectrum showed Si lines, it is a Type Ia supernova. Therefore, the peak absolute magnitude is M = -19 mag. m - M = 5 log ( d / 10 ) 16.5 - (-19) = 35.5 = 5 log ( d / 10 ) 7.1 = log( d / 10 ) d = 1.3 x 10 8 pc = 130 Mpc Problems 1, 3a, 4, 5, 6, and 7 are worth 1 point each....
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