Regarding the "traveling at the same speed" idea. When in an aircraft, two people can toss a ball to each other. From the POV of those Inside, the ball is moving at normal ball tossing speed. From the POV of those outside, the ball is being gently tossed to over 500kph and the catcher catchers it without problem. If this is the "everything on the planet moving at the same speed" idea in action. Which does make it possible to travel in either direction.
“1 In the beginning God created the heaven and the earth. And the earth was without form, and void; and darkness was upon the face of the deep. 2 And the Spirit of God moved upon the face of the waters. 3 And God said, Let there be light: and there was light. 4 And God saw the light, that it was good: and God divided the light from the darkness. 5 And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day.
Aristotle (who made quite a lot of observations about the spherical nature of the Earth) noticed that during lunar eclipses (when the Earth’s orbit places it directly between the Sun and the Moon, creating a shadow in the process), the shadow on the Moon’s surface is round. This shadow is the planet's, and it’s a great clue about the spherical shape of the Earth.
At the end of the day, I think the one single proof of FE or Ball E, will be the irrefutable circumnavigation of Antarctica. As it is, we have no modern attempt. We have no attempt to travel across its middle, and no one wants to take on the challenge of a North South circumnavigation of the planet, the last great achievement (which is odd to me). All three of these things Not being done are Very strange indeed.
14 And God said, Let there be lights in the firmament of the heaven to divide the day from the night; and let them be for signs, and for seasons, and for days, and years: 15 And let them be for lights in the firmament of the heaven to give light upon the earth: and it was so. 16 And God made two great lights; the greater light to rule the day, and the lesser light to rule the night: he made the stars also. 17 And God set them IN THE FIRMAMENT of the heaven to give light upon the earth, 18 And to rule over the day and over the night, and to divide the light from the darkness: and God saw that it was good.

38) To quote Reverend Thomas Milner, “In the southern hemisphere, navigators to India have often fancied themselves east of the Cape when still west, and have been driven ashore on the African coast, which, according to their reckoning, lay behind them. This misfortune happened to a fine frigate, the Challenger, in 1845. How came Her Majesty’s Ship ‘Conqueror,’ to be lost? How have so many other noble vessels, perfectly sound, perfectly manned, perfectly navigated, been wrecked in calm weather, not only in dark night, or in a fog, but in broad daylight and sunshine - in the former case upon the coasts, in the latter, upon sunken rocks - from being ‘out of reckoning?’” The simple answer is that Earth is not a ball.
47.) In consequence of the fact being so plainly seen, by everyone who visits the seashore, that the line of the horizon is a perfectly straight line, it becomes impossible for astronomers, when they attempt to convey, pictorially, an idea of the Earth's "convexity," to do so with even a shadow of consistency: for they dare not represent this horizon as a curved line, so well known is it that it is a straight one! The greatest astronomer of the age, in page 15 of his "Lessons," gives an illustration of a ship sailing away, "as though she were rounding the top of a great hill of water;" and there – of a truth – is the straight and level line of the horizon clear along the top of the "hill" from one side of the picture to the other! Now, if this picture were true in all its parts – and it is outrageously false in several – it would show that Earth is a cylinder; for the "hill" shown is simply up one side of the level, horizontal line, and, we are led to suppose, down the other! Since, then, we have such high authority as Professor Richard A. Proctor that the Earth is a cylinder, it is, certainly, a proof that the Earth is not a globe.
6) If Earth were a ball 25,000 miles in circumference as NASA and modern astronomy claim, spherical trigonometry dictates the surface of all standing water must curve downward an easily measurable 8 inches per mile multiplied by the square of the distance. This means along a 6 mile channel of standing water, the Earth would dip 6 feet on either end from the central peak. Every time such experiments have been conducted, however, standing water has proven to be perfectly level.
Roger Hodgson left the band in 1983 and the Supertramp that most people know has not existed for over 30 years. The music of Supertramp totally changed after Roger left to match Rick’s musical influence, which is more jazz and blues. Rick Davies and his wife have trademarked the name Supertramp, yet the band only consists of one original member – Rick.
In the next photograph (Figure 6), the lettering on the hull is no longer visible. The layer of gray containers is even more visible in the inferior mirage, and the first layer of multi-colored containers is now beginning to appear in the inferior mirage. In the next photograph (Figure 7), the light from the gray layer of containers and its inferior mirage are beginning to merge. The first layer of the multi-colored containers above it is clearly visible in the inferior mirage. The white of the bridge castle is starting to show up in the inferior mirage. In Figure 8, the layer of gray containers no longer is visible. The bottom of the bridge castle and its inferior mirage have merged. None of the hull is visible. In the next photograph (Figure 9), the ship has turned, so we see the back of the bridge castle and containers on the stern. Much of the bottom of what appears to be the ship is an inferior mirage of the upper containers. At any rate, the hull is clearly not visible. Finally, in Figure 10 none of the containers are visible. All that we can see is the back of the bridge castle, merged with the upside-down inferior mirage. Notice the symmetry between the two.
15.) The idea that, instead of sailing horizontally round the Earth, ships are taken down one side of a globe, then underneath, and are brought up on the other side to get home again, is, except as a mere dream, impossible and absurd! And, since there are neither impossibilities nor absurdities in the simple matter of circumnavigation, it stands without argument, a proof that the Earth is not a globe.
Light travels at a finite speed, with the speed depending upon the medium. With mirages, the medium is air. In air, the speed of light is only slightly less than it is in a vacuum, and the speed of light in air depends upon the temperature of the air. Simply put, the speed of light is slightly greater in warmer air than it is in cooler air. In physics, we usually express this behavior reciprocally as the index of refraction, n:

178) People claim Google Earth somehow proves the ball model without realizing that Google Earth is simply a composite program of images taken from high-altitude planes and street-level car-cameras superimposed onto a CGI model of a ball Earth. The same could be just as easily modeled onto a square Earth or any other shape and therefore cannot be used as proof of Earth’s rotundity.
25.) The surveyor's plans in relation to the laying of the first Atlantic Telegraph cable, show that in 1665 miles – from Valentia, Ireland, to St . John's, Newfoundland – the surface of the Atlantic Ocean is a LEVEL surface – not the astronomers' "level," either! The authoritative drawings, published at the time, are a standing evidence of the fact, and form a practical proof that Earth is not a globe. 
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