You would have to come up with another force
No, we wouldn't. Zeteticism is a philosophy of empiricism. A Zetetic would say that the sun's yearly movement is visible to us, but its cause is unknown and leave it at that.
A Scientician would imagine that "gravitons/black matter/magnetic photons/higs-bosons did it."
You just posted a link for me to look at which shows a theory of how the planets move. You cannot be 100 percent sure thats how they move, because it is not 100 percent accurate in its predictions of where the planets should be and when they should be there. Thats the problem with Epicycles. Now you are telling me that you cannot support theories, or contemplate what is going on around you unless you have cold hard evidence of truth?
The real truth is that when there is a pretty simple question like "what powers the sun" or "why is the sun moving across the sky" and you don't have a good answer, because it requires the creation of a very special rule set, like Force X only works on object Y, you simply duck behind your Zeteticism. I believe this because you are willing to claim to know the shape of an object so large you cant see it in its entirety unless you view it from space, a place you don't believe that anyone has ever been for an extended period of time. Instead you conduct tests from your house, looking across the bay, you look at pictures and don't see the earth being spherical, in other words, you look at pieces of the puzzle and try to understand the bigger picture like every other scientist.
However, this is not true when you examine other things, for instance, pictures of the earth from space, of it rotating, pictures of men on the moon, men in microgravity, the shape of the moon, retrograde motion. For all of these things, you go into the discussion with the belief that the earth is indeed flat, and so even though there is no evidence of a conspiracy, beyond your belief that the earth is flat(which is not a Zetetic view unless you have seen the whole planet from space) you believe in a NASA conspiracy. See you looked at what you believe ( the earth is flat) then looked at information (NASA) and decided that NASA was just a front organization for money because it contradicted what you believed, not because you saw any direct evidence for it. You jumped to a conclusion! Thats not very Zetetic of you!
Your not a Zetetic in my understanding of the word, which could be wrong, but i am sure that you are being inconsistent in your actions. You claim not to jump to conclusions, you only accept the truth, yet you theorize many things.
Long story short, you engage in what is a clear cut example of Confirmation Bias. You believe the earth is flat, and you look for evidence that supports that theory, and discredit evidence that says otherwise. You support the scientific method, until it leads to conclusions that support a round earth.