Who exactly is behind the conspiracy? I've searched through many of the sources the FE'rs have provided. The FAQ states:
"Q: "Why do the all the world Governments say the Earth is round?"
A: A Conspiracy among world Governments claiming to have space programs has disseminated the lie to the other governments of the world, as well as to the media and the general public.
Q: "What about NASA? Don't they have photos to prove that the Earth is round?"
A: NASA is part of the conspiracy too. The photos are faked."
Likewise yet more specifically, the Conclusive Categorical Conspiracy Compendium explains, and quite logically I must admit, that not every one in the government needs to know about the conspiracy. NASA, public relations people, RASA, and China are the real culprits.
Now I have serious problems with both the FAQ and the CCCC. First of all, NASA and RASA are government agencies. This means that they both hire and remove people from office, and that high positions in NASA and RASA and public relations people and GPS manufacturers and people who have "been in space" and (I'll add this one) the developers of Google Earth--change constantly. Which means that keeping the about forty five conspirators (calculated by the CCCC) organized is extremely difficult. And what about when they die? Who will take their place and discover their secret? Surely, new people previously unknown to them will be assigned to those positions. How will they keep the conspiracy going? I am likewise confused about the history of the conspiracy, seeing as the ancient Greeks had no motive for a conspiracy, so in the spirit of debate I will say that they had a reason to tell people such false information. Now, this "secret" would have to be carried on through centuries. How would this be possible? These problems lead me to believe that you should revise your conspiracy theory about governments and begin considering a third party being involved.
The circular shadow in a lunar eclipse would only show that the shadow object is circular, since in FE the Earth does not eclipse the moon.
There are equally valid explanations for the other things as well. I'm not a certified FExpert so I don't know them all.
The Greeks must surely be the founders of the conspiracy.
Um....I'm not too familiar with the Greeks' space exploration program, did they ever get to Mars or something? 
What kind of motive did they have? And you still havent answered my previous question....
Motive is irrelevant, the conspiracy exists, the reason for it doesn't affect that fact. It's probably money.
Lastly, I took this quote from user Government Agent to further question the conspiracy. Reason definitely affects the
theory (do not forget that the conspiracy is a theory, not a fact) because without motive there is no point, no gain, and therefore no reason for existence. And I do not consider "the motive is
probably money" and "the government is lying when they say the Earth is round (because you do not have sufficient evidence for the FE)" as evidence of the conspiracy.