Question

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)`

Answer 1

Here, `r=50000ly=50000xx9.46xx10^(15)m=4.73xx10^(20)m`
`M=2.5xx10^(11)` solar mass =`2.5xx10^(11)xx(2xx10^(30))kg=5.0xx10^(41)kg`
We know that
`M=(4pi^*2(r^(3))/(GT^(2))`
or `T=((4pi^(*2)r^(3))/(GM))^(1//2)=[(4xx(22//7)^(2)xx(4.73xx10^(20))^(3))/((6.67xx10^(-11))xx(5.0xx10^(41))]^(1//2)`
`=1.12xx10^(16)s`.