Respuesta :
Answer:
Time taken by the spacecraft to cross milky way, [tex]T = 6.147\times 10^{4} years[/tex]
Given:
Actual length, l = [tex]1.2\times 10^{5} ly[/tex]
speed of the aircraft, v =0.890 c
Solution:
From the Einstein's theory of relativity, using length contraction:
[tex]l' = l\sqrt(1 - \frac{v^{2}}{c^{2}})[/tex]
[tex]l' = 1.2\times 10^{5}\sqrt(1 - \frac{(0.890 c)^{2}}{c^{2}})[/tex]
l' = [tex]5.472\times 10^{4} ly = 5.472\times 10^{4}c yrs[/tex]
Time taken by the spacecraft to cross milky way, T:
[tex]T = \frac{l'}{v}[/tex]
[tex]T = \frac{ 5.472\times 10^{4}c}{0.890 c}[/tex]
[tex]T = 6.147\times 10^{4} years[/tex]
