so if we got a mirror to orbit around earth at light speed, would we be able to see the future 
If a mirror orbited the earth at light speed, certain parts of the earth would sometimes have rapid flashes of light because of reflections from the sun.
That's it.
I don't think so. Think of it like boom the mirror appeared, then light is being traveled to the mirror, from earth, at the same time, light from the mirror is being traveled to earth. So you'll be seeing the the mirror display 1 year ago I believe.
That doesn't make sense at all. If there was suddenly a mirror 1 light year away, then the light would have to travel from earth all the way to the mirror (which would take one year) and then travel all the way back to earth from the mirror (which would take another year).
So you would see two years into the past.
Think of it like this. If the mirror is
x lightyears away from earth, then it would take light
y years to make the round-trip to the mirror and back.
Distance is
x and the time it takes is
y.
X is doubled, because not only does the light have to reach the mirror, but it also has to travel all the way back to earth.
y = 2x
So if the mirror was
two light years away instead of one, then you could look back four years into the past.
y = 2(2)
y = 4
