“You can ask John where is father and mother are. And then he will tell you where they are.”
Gatot Soedarto
1

“Asking” John is a metaphor for “using your access to John as a gateway to his parents”, whether “John” is alive or not is irrelevant.

“Invisible” is just another word for “Undetectable using light in the optical spectrum”.

If there is a medium outside the earth’s atmosphere, then it may well be invisible, but it cannot be “undetectable”, because any effect it has on the earth is a means to detect it. If it has no effect at all, it is indistinguishable from non-existing, so then I reject it as non-existing.

You say there has to be a medium through which the earth travels. I say there is none. You say that the medium must put up resistance so that the earth doesn’t fall into the sun. I say that the earth falls towards the sun all the time, but the sideways motion makes it miss the sun all the time. It’s (weak spacetime curvature, so I can make the approximation) Newton: The earth is massive, and the force the sun exerts causes it to accelerate towards the sun. But it also has “sideways” velocity. So the sideways velocity and the acceleration towards the sun combine, and pull the earth on a path that always curves towards the sun, but also always misses it. No medium necessary.

The fish analogy is correct, but actually serves as a point against your argument: The medium doesn’t just put up a force because it’s Tuesday. It puts up a “force”, because to move the fish through water requires the energy to put displace the water. If you want to move the fish, the water that is in the way must be pushed aside. 
If the earth had to move through a medium, it would constantly have to displace the medium, as well. That would cost energy, as well. So the earth would constantly lose energy, and the orbit of the earth could not be constant, because the kinetic and potential energy of the earth on its orbit must decrease to give energy to the medium. Analogy: If you “throw” a stone under water, it won’t travel far, because it loses its energy of motion to the medium.
If there is no medium outside the earth, on the other hand, then the earth doesn’t lose energy, and the orbit stays stable over long time. The orbit of the earth is stable over long periods of time, because we measure it to be that way, so there is no medium.

Seriously, you should put a bit more effort into your ideas. It took me less time to find out why your idea is wrong than it took me to read your post.

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