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### A star of mass 2-0 - 1028 kg that is 1-4 - 1020 m from the center of a.docx

• 1. A star of mass 2.0 ? 10 28 kg that is 1.4 ? 10 20 m from the center of a galaxy revolves around that center once every 1.2 ? 10 8 years. Assuming that this star is essentially at the edge of the galaxy, each of the stars in the galaxy has a mass equal to that of this star, and the stars are distributed uniformly in a sphere about the galactic center, estimate the number of stars in the galaxy. (Do not round your answer to an order of magnitude.) ________________stars Solution given m = 2.0*10^28 kg r = 1.4*10^20 m T = 1.2*10^8 year = 1.2*10^8*365*24*60*60 = 3.78*10^15 s let M is the mass at galaxy center we know, T = 2*pi*r^(3/2)/sqrt(G*M) T^2 = 4*pi^2*r^3/(G*M) M = 4*pi^2*r^3/(G*T^2) = 4*pi^2*(1.4*10^20)^3/(6.67*10^-11*(3.78*10^15)^2) = 1.137*10^41 kg so, no of stars in the galaxy, N = M/m
• 2. = 1.137*10^41/(2*10^28) = 5.685*10^12 stars <<<<<<<<<<-------------------Answer
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