Regardless of the stories told in many elementary and middle schools, when Christopher Columbus set sail across the Atlantic Ocean, he wasn't trying to prove the world was round; in fact, virtually nobody had thought Earth was flat. In the 3rd century BCE, the ancient Greeks calculated that the planet had to be spherical, among many other facts about Earth.
Despite long-standing scientific knowledge about the planet's shape, however, there are still people who believe Earth is flat, including some famous flat-Earthers. Mathematical calculations, astronomical observations, and standard geological processes associated with a spherical planet can't convince flat-Earthers otherwise; instead, these supposed pieces of evidence are instead a part of a grand political conspiracy orchestrated among every governmental institution in the world.
It may be puzzling as to why there would be a political conspiracy covering up the real shape of the planet, but it is rather innocuous to consider it. And, for those who disagree, what naturally comes from the Flat Earth theory is the question, "What would be the physical implications if the Earth were actually flat?"
Part of the Flat Earth theory states that Earth does not have gravity; it is instead accelerating upward in the universe at a rate equal to the rate scientists claim gravity pulls, thus creating the perception of gravity. Along with a constant upward motion, the sun and moon float and orbit above the Earth's surface.
Both of these theories together present a fundamental problem: if this were the case, there would neither be a force to keep the sun and moon from crashing into Earth, nor a force to keep the sun and moon orbiting Earth. These two theories presuppose there is no gravity, but it is precisely gravity that makes orbiting possible and prevents the moon, Earth, and sun from colliding.
Orbiting can be understood like any centripetal force: the object in orbit is being pushed perpendicularly to the central figure, while it is also being pulled down towards that same figure. Because the orbiting object is both falling away from and towards the center, it circles it, thus establishing a constant orbit. It is also this combination of forces which prevents Earth from falling into the sun from its immense gravitational pull.
If there is no gravity, then there is no force causing the moon and sun to revolve in a circular pattern. Furthermore, if there is no gravity or orbital movement, and Earth is continuously accelerating upward, then the sun would crash into Earth.
Earth's core plays an important part in many of the planet's systems. The 5,700°C (~10,000°F) ball of condensed magma sits at the center of our planet, beneath the much-cooler liquid mantle made from different metals, including iron.
According to the Dynamo theory, the convection currents and Earth's rotation causes the liquified iron to move great distances and flow under Earth's crust, creating an electrical current and magnetic field from that current. Iron continues to move through the magnetic fields, generating more electrical currents in a never-ending cycle.
The resulting magnetic field spans the entirety of the globe, and though it fluctuates and changes, it remains constant enough to protect Earth's atmosphere from high levels of radiation generated by the sun, solar wind, and cosmic rays. The magnetic field acts as a shield and keeps Earth's atmosphere in place, thus allowing life to thrive on the planet.
A flat Earth would not have a core (or perhaps it would have a center that acts dissimilar to our own); thus, there would be no current under the crust to generate a magnetic field. The atmosphere would dissipate, and life would be unsustainable.
Under Earth's surface are the hot liquid mantle and the even hotter solid core. The heat differentiation between the two layers is theorized to cause a convection current in the mantle, which brings hotter materials up closer to Earth's crust where they subsequently cool again and drop towards the core. This natural process circulates great amounts of liquid rock and magma below the surface and slowly moves the tectonic plates above it. When the tectonic plates push into one another, separate, or slide past each other, they create seismic activity that we experience as earthquakes and volcanoes.
Because a flat Earth would not have a core (or maybe a center that functions entirely differently from a spherical planet's core), tectonic movement and subsequent seismic activity wouldn't be present. At first glance, this may seem like a benefit since both earthquakes and volcanoes have had such a devastating effect on human life, but not having these natural processes would have even greater consequences.
Firstly, volcanoes, though immediately detrimental, have a beneficial long-term advantage: they provide essential gases to generate and sustain a stable atmosphere. Without the tectonic activity provided by a spherical planet, Earth would not be livable. Around 4.6 billion years ago, volcanoes began growing above water and released gases necessary for life from the planet's interior. These new gases converted an atmosphere made up primarily of hydrogen sulfide, methane, and carbon dioxide into one comprising gases necessary for life, including oxygen, nitrogen, and water vapor.
Earthquakes, which have proved direr than volcanoes in the last century, also have a regenerative function. Both earthquakes and their natural by-products are ultimately restorative against general erosion. Waves and ocean tides gradually degrade coastlines, but these events create new sand deposits, bringing back much of the sand lost through attrition.
If there were a flat Earth, water would not be retained in the atmosphere, rendering the planet dry. Without water, there would be no erosion, making the need for new sand deposits ultimately unnecessary. Earth would still be self-sustaining, but lifeless.
Gravity is one of the fundamental reasons why the solar system functions the way it does. The sun's mass and gravitational pull, combined with the lateral movement of planets, causes planets to orbit around the sun. The Flat Earth theory argues there is no such thing as gravity, but what we experience as gravity is due to Earth accelerating upwards at 9.8 m/s² (32 ft/s²).
This claim thus puts into question gravity on a universal scale. Earth would continuously move laterally away from the sun at a constant speed and never stop, but if Earth doesn't have a gravitational pull, there is no reason to believe any other cosmic object has any gravitational pull either. Our solar system would no longer remain intact. Because there is no gravitational pull between the sun and any of the planets, they would all move laterally - maybe in differing directions or not - but, regardless, all celestial objects in the universe would disperse outwards from the origin of the Big Bang, but not congregate in systems.