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

Hii dear,

◆ Answer- 3.55×10^8 years.

◆ Solution-
# Given-
M = 2.5×10^11 solar mass
M = 2.5×10^11×2×10^36 kg
M = 5×10^41 kg
r = 5×10^4 ly
r = 5×10^4×9.46×10^15 m
r = 4.73×10^20 m

# Solution-
Time period of a star revolving around milky way is given by,
T = √(4π^2r^3 / GM)
T = √[(4×3.14^2 × 4.73^3×10^60) / (6.67×10^-11 × 5×10^41)]
T = 1.12×10^16 s
T = (1.12×10^16) / (365×24×60×60)
T = 3.55×10^8 years

Time taken to complete one revolution is 3.55×10^8 years.

Hope that was useful...

Answer 2

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.