8000 years in future. I do not think so.
Sirius sector is 8.6 +- 0.4 light years from Milky.
So,if you travel at speed of light,it would take you max 9 years. Lets...say that sleeper ships could traval at 1/4 of Light speed. Then you would need max 36 years to Sirius.
In intro movie,it says,it was 23rd century. 816 + 200 + 9-36 = 1025 - 1052
816 as..I think,present year,200 as 23 century, 200 years from now, and min 9 years,max 36 years for sleepers to travel to Sirius.