Dark Energy and Atmospheric/Atmolayer Travel

Hello FErs, I've been a lurker around here for a while, personally I am a skeptic/agnostic atheist, and I just have a quick question about the Dark-Energy-bending-light theory that solves the issue of horizon visual.

So, as far as I understand, the reason we have a horizon of which there is no end in sight is because our atmosphere/atmolayer contains dark energy and influences the vertical acceleration of light to give the illusion that we have a curved Earth. This makes sense as a valid explanation, but I have a quick question about it. (This may sound a little demeaning and condescending, but I don't want it to sound that way.)

Do we have any mathematical equations to explain the curving of light due to dark energy? The reason I want to know an equation of this is because if light has the tendency to curve upwards from our disc/globe, then there should be a certain height at which our globe will no longer "exist" visually, an "event horizon" of sorts if you will. Which also brings up another point. The curving of light must mean that light has the natural tendency (due to dark energy) to curve upwards toward the Sun or star from which it originated (which could also solve the issue of the sun looking smaller than it is because this curvature will act as a lens and magnify the sun due to a larger radius of curved light hitting the Earth.

However, does this curvature have any effect on light traveling directly up and down? As in, if light is followed from the sun perpendicular to our Earth, will it exhibit any curving or slowing due to the acceleration effect of Dark Energy?

And I will leave this thread open with one more thought. I'm becoming interested in astronomy and physics because I love science. And just to be clear, a flat Earth implies that satellites are falsified objects and are not possible because of the acceleration of our disc. So what exactly causes the stars to "rotate" out of our view similar to how the sun does. And how does the sun "rotate" out of our view?

EDIT: I forgot to add my second point. And that is, I am going to be an airplane pilot, and as far as I am concerned, there is no need for course correction when you are traveling around the globe/disc to falsify and make it seem like we live on a curved Earth. As in, if we were to fly from South America to Asia, we do not need to turn the plane as long as we follow a straight path from one airport to the next, yet our path does not take us over the Arctic area. So will it be covered, do you think, in my flight training that my instructors will have to impose the idea of a "Curving Hoax" and show me how to turn the plane very stealthy as to not be noticeable, so that it may seem I have taken a straight path, but rather I have curved along the disc of the Earth to reach my destination?

You will curve on an east-west course. It isn't a conspiracy.

I'm confused. What's your standpoint here? That the flat Earth is true and I must compensate for the radial spacing of the Earth, or the globe Earth is true and I wouldn't have to?

Your GPS instruments (via satellites programmed by US Air Force)  will compensate for you... And the "straight and level" flight is very hard to discern from "very slightly curved and tilted" by a slope of 1/10000 or so).

East-West is a curved direction on the earth. Even were it a globe.

East-West is a curved direction on the earth. Even were it a globe.

What you call a direction is not a direction. It is a route, made up of an infinite number of directions. If you are moving in a curve it is because you are changing directions all the time. Moving East, for example, starts you on a straight line that would eventually take you to outer space on a round Earth. But as soon as you start moving in that direction the curvature of the floor under your feet makes you change direction. Also, if you are following a compass the needle immediately starts showing a different direction and you start changing your direction to follow it.

The one thing that is not affected by the floor or the needle of the compass is light. And light in general does not follow an Eastern "direction" for long. Nor does it follow the shape of the floor. (Of course, we are talking about places where gravitation is not strong enough to bend light significantly).

Ok. From the top. If I fly a plane on a globe across the circumference, it is a straight line that is the shortest distance between two points on that line. If I fly on a flat disc and want to follow the shortest distance for a flight, it will go straight. I don't exactly have a picture, but mimicking the circumference of a circle on a flat disc produces a curved path. That means that if I were to fly straight from South America to Asia, I would travel along the equator for the shortest distance, a straight line. However, if Earth is a disc, I would have to either travel directly over the Arctic (following the "Arctic Center" model) which would logically be the shortest, straightest path, or I would follow in a circular path that would follow the equator of the Earth.

So, if I were to attempt to fly the shortest distance between these two continents, it would have to be straight over the Arctic if the Earth were a disc, or along the equator if the Earth were a globe. Now logically, planes do not fly over the Arctic unless their destination is somewhere up in those northern regions. So that means either the Earth is in fact a globe and they are taking the most logical path around the Earth, or it is somewhat of a conspiracy in which airline pilots follow a curve around the Arctic at a distance similar to the Equator to feign the illusion that the Earth is a globe. Otherwise, the shortest distance the plane would take is directly north, hence proving a flat disc Earth.

And on my other topic, I suppose that Dark Energy in the atmosphere/atmolayer is either undetectable enough to avoid mathematical grappling, or some other explanation will suffice.

East-West is a curved direction on the earth. Even were it a globe.

Think of it this way. If the Earth were a globe, traveling along the Equator would be going East or West without any change in physical direction other than, of course, following the curvature of the surface of the Earth. If it were a disc, however, the Equator would be like a giant ring halfway between the center of the Disc (the Arctic) and the Ice wall (Antarctica).

So, although it is a curved surface, you would not need to adjust any flight paths if the Earth were a globe, but you would if the Earth were flat.

East-West is a curved direction on the earth. Even were it a globe.

Yes, many round-earthers have trouble with this concept. On a round earth, the number of places a person can begin a circuitous trip around the globe is only infinite. However, round-earthers are generally surprised to find how few places there actually are to strike this journey.