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
= 1.137*10^41/(2*10^28)
= 5.685*10^12 stars <<<<<<<<<<-------------------Answer
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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
