While it seems like those who believe the earth is flat are some adamant about their fact, these questions below will throw them off their feet.
Part A: Movement on the Earth Problems
A1. Distance. Quantas has a flight from Sydney to Buenos Aires every day (week?). It's about 9000 miles, takes 14 hours at 640 mph. On a flat earth, the distance between eastern Australia to Buenos Aires is enormous. They are on opposite sides, exactly, of the flat earth map, more than 12,000 miles apart, and the flight between them would take at least 20 hours. These flights take 14 hours. Explain. A2. Flights over the south pole. Flights travel from South Africa to New Zealand by going over Antarctica. On a flat earth, this is impossible. You would fly off the disc of the earth. Yet these flights happen. Explain.
A3. Shipping. Shipping regularly sails due south, going around the "bottom" of the globe, and comes north again, without making a 180 degree turn. This is impossible on a flat earth, if you look at the map. You can't be pointing due south and then be pointing north again without making a turn, however gradual, of 180 degrees. Explain.
Part B: Astronomical Problems
B1. The Seasons. It is summer in the southern hemisphere when winter in the northern hemisphere, and vice versa. The sun diagram I've seen does not allow the sun extra time over the "summer" hemisphere. That's why it's warmer in summer -- owing to the tilt of the earth toward or away from the sun, the sun is up longer, and the rays are more direct, in the summer, heating the surface for longer and more directly. This is not accounted for on the flat earth map. Explain how this happens. B2. Polaris. Currently, the earth's axis points more or less directly at Polaris, the pole star in the northern hemisphere. At the north pole, Polaris is directly overhead. When you travel south, Polaris gets lower and lower to the horizon, until finally it disappears. It does not appear at all above the horizon for most southern observers. Explain.
B3. Constellations. Same as for Polaris. The southern hemisphere has different constellations than the northern. On a flat earth, everybody would see the same constellations all the time. Constellations are also upside down in the southern hemisphere. Orion is standing on his head in Australia. The moon and planets, and the sunspots which are visible, are all "upside down" in the southern hemisphere. On a flat earth, they would look the same everywhere.
B4. Changing size of the Moon vs. Sun. The sun and moon both measure about 1/2 of a degree of arc in the sky. The moon is about 400 times smaller than the sun, but it's also 400 times closer, so by a coincidence it exactly covers the sun during a total solar eclipse. The moon's orbit around the earth is not a perfect circle. Part of the orbit is closer to the earth than the other. So the moon is visibly, measurably bigger for part of every month, when it is closest to the earth. BUT THE SUN IS NOT. The earth's orbit around the sun is more or less circular, with neither semimajor axis much longer than the other, so the sun is always about the same size. In the flat earth model, the sun and moon are always the same distance away. There is no explanation for the change in the moon's size.
B5. Changing size of Venus. Venus is much closer to earth when it is on the same side of the sun as the earth in its orbit. When it's on the other side of the sun from earth, it is almost twice as far away. So Venus looks noticeably, measurably bigger for the part of the year it's on the same side as us. Same for Mercury, but the change in size is smaller, because the orbit of Mercury is much closer to the sun. So there are Mercury, Venus, and the Moon, all changing apparent size at different times and for different lengths of time. The flat earth model cannot explain this.
B6. The size of the sun. In the flat earth model, the sun is 32 miles across and 3000 miles away from the earth, which is 24,000 miles across. So the sun one thousandth the size of earth, roughly. Yet it is hot enough to warm the earth. A star of that size cannot make enough heat through nuclear fusion to light and warm the earth according to the flat earth model. What is the power source of the sun, and how does it produce the power it produces?
B7. Sun's rays. Flat earthers like to cite crepuscular rays as evidence that the sun is really close to the earth. They don't understand them, but ignoring that for now -- you see crepuscular rays coming from a cloud and striking the earth. You are really seeing a column of light going from the cloud to the ground, reflected by dust in the atmosphere so it hits your eyes. You are seeing the side of a column of light. In the flat earth model, the sun is a flashlight. Day and night are explained by the flashlight shining on different parts of the earth. However, if that were true, observers in the night half would be able to see, in the distance, the column of light illuminating the day half.
B8. More sun's rays. Before you see the sun rise, the clouds above the horizon are lit up from below, because the sun, below the horizon is illuminating them. The same is true after sunset. Twilight is the time when the sun illuminates the sky overhead but no rays hit the ground directly. No matter how you slice the flat earth model, there is no way for the sun to light the clouds without illuminating the earth at the same time.
B9. Viewing the constellation Octans. The south celestial pole is in the constellation of Octans. From any given point in the southern hemisphere it is seen by looking due south, (at various altitudes, depending on the observer's latitude). It is always in the same position in the sky from a given point, all day, all night, all year long. Here we see the directions observers at A, B and C would have to look in order to see it, looking due south from their respective locations. It is clearly impossible for people in all these positions to look due south and see the same thing in the sky. (Note, Octans does rotate on the celestial polar axis, depending on date, time, and location, but it would always be due south.) B10. Full moon. Put a flat earth map in front of you. Imagine the moon is in a full moon position, as seen from New York. But someone in Chile would see a new moon. People in Mexico would see the left side of the moon lit and people in West Africa would see the right side of the moon lit. And these would all be at the same time. This is not what we see. Also, notice how it is night in England but day in South Africa. Flat Earthers claim that the reason we have night is because the sun is too far away to be seen. Yet here it is closer to England than it is to South Africa. Finally, if the sun can light up the moon at that distance, then all of North America would be in daylight.
B11. Lunar eclipse. This is a very big problem for flat earthers. Total lunar eclipses are a fact, visible fairly regularly, by billions of people, and videotaped. There is no way that a flat earth can cast a circular shadow on the moon. Also, there is no scenario in the flat earth model in which the earth comes between the sun and the moon. In any case, the moon and sun in the flat earth model are 32 miles wide, so the earth would totally obscure them, and nothing like an "eclipse" would ever be possible. Please explain. Part C: Curvature Problems C1. Setting sun. Flat earthers like to say "I saw such and such and it should have been below the horizon." It is true, refraction sometimes makes it possible to see things a little below the horizon. But suppose refraction doubles the amount you can see: if the horizon on the curved earth is normally 6 miles away for a 6 foot person on the ground, refraction makes it possible to see things 12 miles away. But eventually, curvature wins. Here's proof. The setting