Yes. That's what NASA should do.... send out a big unmanned space probe with a big mirror on it. Why?... so we can look at ourselves.... in the past!
Immediately I will say that I don't know for sure that someone isn't already doing this genius idea, as it seems quite an obvious one to me. But perhaps my idea is unique for the possible future applications a big space mirror would have.
I believe there are already space probes and space telescopes that are on a mission into to leave our solar system and head out into deep space. These send back more detailed pictures of the universe than we would get from out planet.
My proposal is such a space probe that will not only be able to transmit pictures from afar, but also have a telescope pointed back at the earth, with an incredible amount of detail. This amplified image will be reflected back in our direction by a giant space mirror on the craft. It needs to be pretty big because of the vast distance it will travel, so we can see it from earth.
Now here's the clever application. If the space craft/mirror goes far enough we will eventually be able to see back in time! It'll take a few decades (probably) but the accuracy of telescopic technology on earth should be able to keep up with the distance the craft will travel. The further from our solar system it gets the further back in time we will see the earth. ...to the point that we will be able to see past events from a certain amount of time ago.
Initially this could be used to solve crimes, maybe by pinpointing an individual's position at a certain time on a certain day. Eventually... (and maybe we're talking hundreds of years time) we'll be able to use this technology for historical research.
For every light-year the craft travels away from us, we will be able to see 2 light years into our past... as the light from earth has to travel to the telescope and back to the earth again.
And obviously it'll have duel use, it can also be used to view deep space. (when it's not solving Columbo style mysteries)
How will it be powered? ... Initially, solar power. There should be enough power as it passes our sun to get up to a pretty amazing speed. ...Then so long as it doesn't crash into a planet or moon, it will keep going at this speed forever. Laws of inertia state that if nothing's there to slow it down, it'll just keep going. With our next nearest star just over 4.2 light-years away, it won't be long before any loss in speed is regained. Nothing can go wrong.
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