Astronomers didn't need a transporter mishap to find a mirror solar system, just new gravitational lensing techniques. They spotted two gas giants analogous to Saturn and Jupiter orbiting a star in Sagittarius that's about 5,000 light years away. Getting there would involve a five-year trip at Warp 8, in case you were wondering. This mirror solar system is like a mini-version of our own, with a star half the mass of our sun and tighter orbits than our own gas giants.
Micro-lensing is a refinement of techniques used to spot objects that would normally be invisible to us. In this case, astronomers at St. Andrews University in Scotland detected the two planets as the light reflected from them was deflected by the gravity of a star. This refraction brightened and magnified the image. Even planets with less mass than Earth can be found by astronomers using this method.
Dr. Martin Dominik of St. Andrews told the BBC:
"It looks like this may have formed in a similar way to our Solar System. And if this is the case, it looks like [our] Solar System cannot be unique in the Universe. There should be other similar systems out there which could host terrestrial planets."
Solar System's 'look-alike' found. [BBC News]