“So Hyperion we have thus concluded that the pod is from the Binary star system Zeta Reticuli.” Anstor looked across the elongated table to see that Hyperion was judging the information that he had just received.
“Well,” Hyperion began, “I would think that you are right, seeing as the machine said this. After all, why would it be wrong?” he looked to the back of the room where sat a gargantuan machine. “An Interstellar Fragment Device. One of the greatest inventions in the history of man. Yet, this is the only one, and we and Ted respectively are the only ones who know of it.”
“So well Hyperion, we now need to discover how to get to Zeta Reticuli. If we can build an IFD, we can build a rocket, all with private funds.

 

I would venture to say that is too much information.

You are falling into the trap where want us to know as much as the characters about the IFD and the pod. In this case, if we need to know, NOW, then tell us rather than have the characters tell eachother stuff that they both already know.

Your dialogue is not very natural sounding. I suspect this is because you are trying to use the dialogue for exposition. As it is, I read that Anstor is Hyperion's teacher or commander.

Your PoV is Anstor but this is barely established. More time thinking with Anstor about the situation would cure that.

For dialogue to sound more natural, keep the sentences short. People talk in short simple sentences or fragments 90% of the time. More than 1-2 sentences before bouncing back to the other speaker seems odd.

Why is the word "respectively" there? It does not apply to "know". "Respectively" implies an order, and "know" is boolean in this situation unless it is important in what order they learned of the IFD.