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 105ly.
Mass of our galaxy Milky Way,M=2.5×1011 solar mass 1 Solar mass = Mass of Sun=2×1030 kg Mass of our galaxy,M=2.5×1011×2×1030=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 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 =6.67×10−11×5×10414×3.142×4.733×1060 =1.12×1016 s =365×24×60×601.12×1016 years =3.55×108 years
