Answer:
The time is 1206 years.
Explanation:
Given that,
Distance = 27000 ly
[tex]1\ ly =9.47\times10^{15}\ m[/tex]
Speed = 0.9990c
We need to calculate the time
Using formula of speed
[tex]v = \dfrac{d}{t}[/tex]
[tex]t=\dfrac{d}{v}[/tex]
Put the value into the formula
[tex]t =\dfrac{27000\times9.47\times10^{15}}{3\times10^{8}}[/tex]
[tex]t=8.523\times10^{11}\ sec[/tex]
We need to calculate the time dilation the clock on the spaceship
Using formula of dilation time
[tex]t'=t\sqrt{1-\dfrac{v^2}{c^2}}[/tex]
[tex]t'=8.523\times10^{11}\times\sqrt{1-\dfrac{( 0.9990c)^2}{c^2}}[/tex]
[tex]t'=8.523\times10^{11}\times\sqrt{1-(0.9990)^2}[/tex]
[tex]t'=3.8106\times10^{10}\ sec[/tex]
The time convert in years
We know that,
[tex]1\ yr= 3.16\times10^{7}\ sec[/tex]
So, the time is
[tex]t'=\dfrac{3.8106\times10^{10}}{3.16\times10^{7}}[/tex]
[tex]t'=1206\ years[/tex]
Hence, The time is 1206 years.
