Question

Let us assume that our galaxy consists of 2.5 × 10¹¹ stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution ? Take the diameter of the Milky Way to be 10⁵ ly.

Answer 1

Given: Total number of stars in Galaxy is 2.5× 10 11 , mass of each star is 1 solar mass and the diameter of the Milky way is 10 5  ly.

We know that,

1 ly=9.46× 10 15  m

1 solar mass=2× 10 30  kg

Radius of the Milky way is,

r=50000 ly

The time taken by a star to complete one revolution is given as,

M= 4 π 2 r 3 G T 2 T= ( 4 π 2 r 3 GM ) 1 2

Where, r is the radius of the Milky way, G is the universal gravitational constant and M is the total mass of Galaxy.

By substituting the given values in the above equation, we get

T= [ 4 ( 3.14 ) 2 × ( 50000×9.46× 10 15 ) 3 ( 6.67× 10 −11 )( 2.5× 10 11 ×2× 10 30 ) ] 1 2 = [ 4× ( 3.14 ) 2 × ( 4.73× 10 20 ) 3 ( 6.67× 10 −11 )×( 5.0× 10 41 ) ] 1 2 = [ 4173.52× 10 60 33.35× 10 30 ] 1 2 =1.12× 10 16  s

We know that,

1 s= 1 365×24×3600  year

Therefore,

1.12× 10 16  s= 1.12× 10 16  s 365×24×3600 =3.55× 10 8  years

Thus, the star takes 3.55× 10 8  years to complete one revolution.