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

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
7 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:

$T = (\frac{4π^2 \,r^3 }{ GM})^{\frac{1}{2}}$
$= (\frac{4 × (3.14)^2 × (4.73)^3 × 10^{60} }{6.67 ×10 ^{-11 }× 5 × 10^{41}}) ^{\frac{1}{2}} =\frac{ 39.48 × 105.82 ×10^{30} }{33.35 }) ^{\frac{1}{2}}$

$=(125.27 × 10^{30} )^{\frac{1}{2}} = 1.12 × 10^{16}$ s
1 year = 365 x 324 x 60x60 s
$1s = \frac{1}{365 ×324 × 60×60}$ year
$∴ 1.12 × 10^{16}s = \frac{1.12 × 10^{16} }{365 × 324 × 60×60}$
$= 3.55× 10 ^8$ years