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Solution_Set_10

# Solution_Set_10 - H o = 1(20 x 10 9 yr(3600 x 24 x...

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SOLUTION SET 10 Physics 2022 1. m – M = 5 log (d / 10) = +10 – (-19.9) = 29.9 d = 9.5 x 10 6 pc = 9.5 Mpc 2a. d = v / H o = (10,800 km/s) / (71 km/s/Mpc) d = 152 Mpc = 152 x 10 6 pc = 496 x 10 6 LY 2b. if H o < 70 km/s/Mpc then d would increase if H o > 70 km/s/Mpc then d would decrease 3. H o = v / d = (7500 km/s) / (1.4 x 10 2 Mpc) = 54 km/s/Mpc 4. ( M 1 + M 2 ) = a 3 / P 2 = [ (600 x 10 3 pc) (206265 AU/pc) ] 3 / (40 x 10 9 yr) 2 = (1.89 x 10 33 ) / (1.6 x 10 21 ) = 1.2 x 10 12 solar masses 5. H o = 80 km/s per Mpc v = 3600 km/s v = d H o d = v / H o = 3600 km/s / 80 km/s/Mpc = 45.0 Mpc

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6. d = 2 pc v = 100 km/s P = 2 π d / v = (2 π x 2 x 206265 x 1.5 x 10 8 km) / 100 km/s = 3.9 x 10 12 s = 1.23 x 10 5 yr M = d 3 / P 2 = (2pc x 206265) 3 / (1.23 x 10 5 yr) 2 = 4.6 million solar masses 7. T = 1 / H o H o = 40 km/s per Mpc T = 1 / { [40 km/s/Mpc / (10 6 x 206265 x 1.5 x 10 8 km/Mpc)] (3600 x 24 x 365.25s/yr) } = 1 / { ( 40 / 3.1 x 10 19 ) ( 3.2 x 10 7 ) } = 1 / 4.1 x 10 -11 /yr T = 24.5 x 10 9 yr (= 7.7 x 10 17 s) 8. T = 20 billion year
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Unformatted text preview: H o = 1 / { (20 x 10 9 yr)(3600 x 24 x 365.25s/yr) / [10 6 x 206265 x 1.5 x 10 8 km/Mpc)] } = 1 / { (20 x 10 9 ) ( 3.2 x 10 7 ) / (3.1 x 10 19 ) } = 1 / 2.04 x 10-2 Mpc/s/km H o = 49 km/s/Mpc 9. v / c = [ (z + 1) 2 – 1 ] / [ (z + 1) 2 + 1 ] = [ (5.8 + 1) 2 – 1 ] / [ (5.8 + 1) 2 + 1 ] = [ (6.8) 2 – 1 ] / [ (6.8) 2 + 1 ] = [ 46.2 – 1 ] / [ 46.2 + 1 ] = 45.2 / 47.2 v = 0.958 c = 2.87 x 10 5 km/s 10. v / c = [ (z + 1) 2 – 1 ] / [ (z + 1) 2 + 1 ] = [ (8 + 1) 2 – 1 ] / [ (8 + 1) 2 + 1 ] = [ (9) 2 – 1 ] / [ (9) 2 + 1 ] = [ 81 – 1 ] / [ 81 + 1 ] = 80 / 82 v = 0.976 c = 2.93 x 10 5 km/s 11. R sch = 2 G M / c 2 = 2(6.67 x 10-11 N m 2 /kg 2 ) (10 9 ) (1.989 x 10 30 kg) / (3 x 10 8 m/s) 2 = 2.95 x 10 12 m = 2.95 x 10 9 km = 19.6 AU The average Sun-Pluto distance is 39.5 AU. Problems 1, 2a, 5, 9, and 11 are each worth 1 point. Problems 6 and 7 are each worth 2 points....
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Solution_Set_10 - H o = 1(20 x 10 9 yr(3600 x 24 x...

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