Let us consider that our galaxy consists of `2.5xx10^(11)` stars each of one solar mass. How long will this star at a distance of `50,000` light year from the galastic entre take to complete one revolution? Take the diameter of the Milky way to be `10^5ly. G=6.67xx 10^(-11) Nm^(2) Kg^(-2). (1 ly= 9.46xx10^(15)m)`

Explanation

Here, `r = 50,000 ly = 50,000 xx 9.46 xx 10^(15) m = 4.73 xx 10^(20) m`
`M = 2.5 xx 10^(11)` solar mass `= 2.5 xx 10^(11) xx (2 xx 10^(30)) kg = 5.0 xx 10^(41) kg`
We know that, `M = (4 pi^(2) r^(3))/(GT^(2))` or `T = ((4 pi^(2) r^(3))/(GT))^(1//2) = [(4 xx (22//7)^(2)xx(4.73 xx 10^(20))^(3))/((6.67 xx 10^(-11)) xx (5.0 xx 10^(41)))]^(1//2) = 1.12 xx 10^(16) s`