Answer
$L =6.5\times 10^{10}~m$
Work Step by Step
Let $L_0 = 0.75\times 10^{11}~m$
We can find the distance $L$ according to the astronaut:
$L = L_0~\sqrt{1-\frac{v^2}{c^2}}$
$L = (0.75\times 10^{11}~m)~\sqrt{1-\frac{(0.50~c)^2}{c^2}}$
$L =6.5\times 10^{10}~m$
