Question

The observable universe contains about 2 trillion galaxies. Our solar system belong to one of these galaxies and is called the Milky Way galaxy. Like the Earth revolves around the sun, the sun also revolves around the center of our galaxy, once every 2.5 × 108 years. Assume that each of the stars in our galaxy has the same mass as our sun and the stars are uniformly distributed in a sphere about the galactic center, find the number of stars in our galaxy. Assume our sun is at the edge of that sphere and the mass of the sun is given to be 2.0 × 1030 kg and the distance of the sun from the galatic center is 2.2 × 1020 m.

Answer 1

let,

mass of the sun(star) is , m1=2*10^30 kg

the total mass of the galaxy is m2

total no of stars in the galaxy is N

===> m2=N*m1

and

time period is T=2.5*10^8 years

distance between the sun and galatic center is r=2.2*10^20 m

use,

T^2=4pi^2*r^3/G*m2

(2.5*10^8*365*24*60*60)^2 = 4pi^2*(2.2*10^20)^3/(6.67*10^-11*N*m1)

(2.5*10^8*365*24*60*60)^2 = 4pi^2*(2.2*10^20)^3/(6.67*10^-11*N*2*10^30)

===> N=5.0696*10^10 or N=5.07*10^10

no of stars in the galaxy is, N=5.07*10^10