Answer
$L'=0.0087ly$
Work Step by Step
To find relativistic energy, use the equation $$E=\gamma mc^2$$ First, convert 1533 MeV to joules to get $$1533 MeV \times \frac{1.602\times 10^{-19}J}{1.000eV}=2.456\times 10^{-10}J$$ Solving for $\gamma$ and substituting known values yield $$\gamma=\frac{E}{mc^2}=\frac{2.456\times 10^{-10}J}{(9.11\times 10^{-31}kg)(3.00\times 10^8m/s)^2}=2995$$ Relativistic length is calculated using the formula $$L'=\frac{L}{\gamma}$$ Substituting in the value of $\gamma=2995$ and $L=26ly$ yields $$L'=\frac{L}{\gamma}=\frac{26ly}{2995}=.0087ly$$
