Let us assume that our galaxy consists of 2.5 × 1011 stars each of o

1.	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» Answer: Mass of our galaxy Milky Way, M = 2.5 × 1011 solar mass Solar mass = Mass of Sun = 2.0 × 1036 kg Mass of our galaxy, M = 2.5 × 1011 × 2 × 1036 = 5 × 1041 kg Diameter of Milky Way, d = 105 ly Radius of Milky Way, R = 5 × 104 ly 1 ly = 9.46 × 1015 m ∴r = 5 × 104 × 9.46 × 1015 = 4.73 ×1020 m SINCE a star REVOLVES around the galactic centre of the Milky Way, its time period is given by the relation: T = ( 4π2r3 / GM)1/2 = [ (4 × 3.142 × 4.733 × 1060) / (6.67 × 10-11 × 5 × 1041) ]1/2 = (39.48 × 105.82 × 1030 / 33.35 )1/2 = 1.12 × 1016 s 1 year = 365 × 324 × 60 × 60 s 1s = 1 / (365 × 324 × 60 × 60) years ∴ 1.12 × 1016 s = 1.12 × 1016 / (365 × 24 × 60 × 60) = 3.55 × 108 years.

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»

Mass of our galaxy Milky Way, M = 2.5 × 1011 solar mass

Solar mass = Mass of Sun = 2.0 × 1036 kg

Mass of our galaxy, M = 2.5 × 1011 × 2 × 1036 = 5 × 1041 kg

Diameter of Milky Way, d = 105 ly

Radius of Milky Way, R = 5 × 104 ly

1 ly = 9.46 × 1015 m

∴r = 5 × 104 × 9.46 × 1015

= 4.73 ×1020 m

SINCE a star REVOLVES around the galactic centre of the Milky Way, its time period is given by the relation:

T = ( 4π2r3 / GM)1/2

= [ (4 × 3.142 × 4.733 × 1060) / (6.67 × 10-11 × 5 × 1041) ]1/2

= (39.48 × 105.82 × 1030 / 33.35 )1/2

= 1.12 × 1016 s

1 year = 365 × 324 × 60 × 60 s

1s = 1 / (365 × 324 × 60 × 60) years

∴ 1.12 × 1016 s = 1.12 × 1016 / (365 × 24 × 60 × 60) = 3.55 × 108 years.