Finally, pay dirt. I was able to find some data outlining the transporter theory. It strengthened my understanding of how the gravitational fields effect the transporter grid. This was essential.
It seems using this transporter to go anywhere outside of this solar system would be extremely difficult to with any level of accuracy. Our data on gravitational fields outside of our solar systems is good in some cases but it is no where near the level of understanding that we would need to go a greater distance. This seemed to put a hole in my theory that this machine was responsible for the populations disapperance from Terra Durom. Where would they go if they couldn't leave the solar system? But I couldn't focus on that right now.
It seems we'll still need to stick with a lot of hard science and invest a lot of money into computer power in order to organize the data, and make the necessary calculations.
My first impression was that distance would be related to power output. But that didn't seem to be the case at all. According to the theory, it takes the same amount of power to transport something anywhere in the galaxy. It's the accuracy that is the hard part.
The theory seemed to indicated a relationship between gravity and parallel worlds. This would probably explain why we were able to find an earth like world so easily after coming through the rift. Our two planets are tied to each other somehow through gravity. The rift is in the same position relative to the sun in both our universes. The rift is also in the same position relative to each of our planets. The observational power of their instruments is incredibly advanced.
Everything is tied together. But that would mean.....