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Solution_Set_05

# Solution_Set_05 - SOLUTION SET 5 Physics 2022 1 2 The two...

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SOLUTION SET 5 Physics 2022 1. The two curves cross at about 20,000 K, which is about at the B3-B4 spectral type. 2. L rigel = 1.6 T sun L rigel = 64,000 L sun L rigel / L sun = (R rigel / R sun ) 2 (T rigel / T sun ) 4 (64,000) = (R rigel / R sun ) 2 (1.6) 4 R rigel = 98.8 R sun 3. R P = 2R Q T P = 4000 K T Q = 8000 K L P / L Q = (R P 2 / R Q 2 ) (T P 4 / T Q 4 ) = (2) 2 (4000/8000) 4 = 4 (1/2) 4 = ¼ L Q = 4 L P 4. L X = 12 L Y T X = 3500 K T Y = 7800 K L X / L Y = (R X 2 / R Y 2 ) (T X 4 / T Y 4 ) (R X 2 / R Y 2 ) = (7800/3500) 4 (12) = (2.2) 4 (12) = 296 R X = 17 R Y 5. L star = 130 L sun B8 therefore T star 15,000 K L star / L sun = (R star / R sun ) 2 (T star / T sun ) 4 (130) = (R star / R sun ) 2 (15000 / 5800) 4 R star = 1.7 R sun

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6a. d = 1 / p = 1 / 0.2 = 5 pc 6b. D = d tan = (5 pc) tan[(4.5 arcsec)/(3600 arcsec/deg] = (5 pc) (206,265 AU/pc) (2.18 x 10 -5 ) = 22.5 AU 6c. ( M 1 + M 2 ) P 2 = a 3 ( M 1 + M 2 ) = (22.5) 3 / (87.7) 2 = 1.5 solar masses 7a. ( M 1 + M 2 ) P 2 = a 3 ( M 1 + M 2 ) = (10) 3 / (5) 2 = 40 solar masses 7b. M 1 / M 2 = 4.0 solar masses M 1 = 4.0 M 2 4.0 M 2 + M 2 = 5.0 M 2 = 40 solar masses M 2 = 8 solar masses M 1 = 32 solar masses 8. ( M 1 + M 2 ) P 2 = a 3 (2 + 2) P 2 = (5) 3 P 2 = 125 / 4 = 31.25 P = 5.59 yr 9. ( M 1 + M 2 ) P 2 = a 3 (1.96 + 0.3) P 2 = (12,000) 3 P 2 = ( 1.728 x 10 12 ) / 2.26 = 7.646 x 10
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