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.

There are huge Stars in galaxy which together constitute a very huge mass and centre point of all concentrated mass galactic centre, we assume Star revolve around galactic centre in the same way in which planets revolve around sun we can assume all starts in milky way to constitute one heavenly body assuming all the mass to be concentrated at a single point Galactic centre and other heavenly bodies like stars revolve around galactic centre so we can treat distance of star from milky way as the orbital radius of revolving star

We know If a body orbits around other heavier body due to gravitational force of attraction then we have a relation between mass of heavier body, time period of revolution and, radius of the orbit as

Where M is the mass of heavier body, R is the radius of orbit, G is universal gravitational Constant

G = 6.67 × 10^-11 Nm²Kg^-2

and T is time period of revolution

So rearranging above equation we get time period of revolution as

We are give total mass of Mass of Galaxy as

M = 2.5 × 10¹¹ solar mass

Now 1 solar mass is mass of sun which is

M_s = 2 × 10³⁰ Kg

So total mass of the galaxy is

M = 2.5 × 10¹¹ × M_s

= 2.5 × 10¹¹ × 2 × 10³⁰ Kg

= 5 × 10⁴¹ Kg

we are given distance of star from galactic center which is Radius of Milky way or orbital radius for star that is

R = 50000 ly = 5 × 10⁴ ly

We know that one light year is distance travelled by light in one year

And distance is given as

S = V × t

Where S is the distance covered in time t moving at a speed V

Speed of light is

V = 3 × 10⁸ m/s

Converting time of 1 year into seconds

1 year = 365.25 days

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

So we get time of 1 year as

t = 365.25 × 24 × 60 × 60 s

so we get distance of 1 light year as

S = 3 × 10⁸ m/s × 365.25 × 24 × 60 × 60 s

i.e 1 light year = 9.46 × 10¹⁵ m

Therefore, the radius of milky way is

R = 5 × 10⁴ × 9.46 × 10¹⁵ = 4.73 x 10²⁰ m

So putting values of R, M, G in equation to find time period

= 4.246 × 10¹⁵ s

Converting into years

We already know

1 year = 365.25 × 24 × 60 × 60 s

So 1 s = 1/(365.25 × 24 × 60 × 60) Year

So we get time period in the year as

So star will take 1.34 × 10⁸ Years to complete one revolution