Answer
To a stationary observer, the length of the rocket is $~~14.5~m$
Work Step by Step
We can find the velocity of the rocket:
$\frac{v}{c} = \frac{\Delta \lambda}{\lambda}$
$\frac{v}{c} = \frac{520~nm-700~nm}{700~nm}$
$\frac{v}{c} = -0.257$
$v = -0.257~c$
The speed of the rocket is $0.257~c$
We can find $\gamma$:
$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$
$\gamma = \frac{1}{\sqrt{1-\frac{(0.257~c)^2}{c^2}}}$
$\gamma = \frac{1}{\sqrt{0.933951}}$
$\gamma = 1.035$
We can find the length of the rocket to a stationary observer:
$L = \frac{L_0}{\gamma}$
$L = \frac{15~m}{1.035}$
$L = 14.5~m$
To a stationary observer, the length of the rocket is $~~14.5~m$
