Answer:
At 99.7% of the speed of light
Explanation:
For the astronaut traveling, the perceived time elapsed [tex]t'[/tex] with respect to the perceived time elapsed [tex]t[/tex] of an observer at rest with respect to the astronaut is:
[tex]t'=t\sqrt{1-\frac{v^2}{c^2}}[/tex]
where c is the speed of light and v is the speed of the traveler.
Solving for v we have:
[tex]v=c\sqrt{1-(t'/t)^2)}\implies \frac{v}{c}=\sqrt{1-(t'/t}^2)}=99.7\%\,c[/tex]
