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### EXAM 3 MATH

Course: BIO 206L 206L, Spring 2012
School: University of Texas
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Word Count: 177

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3 EXAM MATH: //18.1] schwarzchild radius= Rs =2GM/c^2 m M=6.67x10^-11m^3/(kgxs^2); c=3x10^8 m/s Rs= 3 * M/Msunkm Sooo mass 10Msun 3 * 10Msun/ Msunkm= 30km //19.1] Mr= r * v^2/ G mass of milky way wihin suns orbit?? Sun orbital velocity=2.2*10^5m/s 28,000 light years * 9.46*10^15 m/ly so r=2.6^10^20 G=6.67*10^-11 so Mr=1.9* 10^41kg //20.2] Redshift redshift (z) = lambda observed- lambda rest/ lambda rest v=c * z,...

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3 EXAM MATH: //18.1] schwarzchild radius= Rs =2GM/c^2 m M=6.67x10^-11m^3/(kgxs^2); c=3x10^8 m/s Rs= 3 * M/Msunkm Sooo mass 10Msun 3 * 10Msun/ Msunkm= 30km //19.1] Mr= r * v^2/ G mass of milky way wihin suns orbit?? Sun orbital velocity=2.2*10^5m/s 28,000 light years * 9.46*10^15 m/ly so r=2.6^10^20 G=6.67*10^-11 so Mr=1.9* 10^41kg //20.2] Redshift redshift (z) = lambda observed- lambda rest/ lambda rest v=c * z, c=3*10^5 km/s z= 0.010; second z =0.010; redshift much less than 1 so v= c * z = (3*10^5 km/s0 * 0.010 = 3000 km.s //20.3] Hubbles law: v= Ho d * ; Ho=22km/s/Mly so 22km/s/Mly * 10 Mly = 220 km/s away from us d= v/Ho =22,000 km/s / 22km/s/Mly = 1000 Mly //20.4] Ho= 22km/s/Mly= 22 {km/s / 10*6 * (3* 10^5 km/s) x 1 yr] 1/Ho = 1.36 * 10^10 yr or 13.6 billion years If Ho= 44km/s/Mly; universe would be 6.8 billion years old //20.5] 1 + z = lambda observed/ lambda rest redshift of z=1.5 and 1 + z = 1 + 1.5 = 2.5; 2.5 times larger when light we see left galaxy nuclear burning core in high mass star: inert iron core, silicon fusion, magnesium, neon, oxy, C, helium, hydrogen, nonburning hydrogen
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