In 1610, Galileo Galilei observed the moons of Jupiter rotating around it. He described them as small planets orbiting a larger planet—a description (and observation) that was very difficult for the church to accept, as it challenged a geocentric model where everything was supposed to revolve around the Earth. This observation also showed that the planets (Jupiter, Neptune, and later Venus was observed too) are all spherical, and all orbit the sun.
81) The distance from which various lighthouse lights around the world are visible at sea far exceeds what could be found on a ball-Earth 25,000 miles in circumference. For example, the Dunkerque Light in southern France at an altitude of 194 feet is visible from a boat (10 feet above sea-level) 28 miles away. Spherical trigonometry dictates that if the Earth was a globe with the given curvature of 8 inches per mile squared, this light should be hidden 190 feet below the horizon.
51) Antarctica is by far the coldest place on Earth with an average annual temperature of approximately -57 degrees Fahrenheit, and a record low of -135.8! The average annual temperature at the North Pole, however, is a comparatively warm 4 degrees. Throughout the year, temperatures in the Antarctic vary less than half the amount at comparable Arctic latitudes. The Northern Arctic region enjoys moderately warm summers and manageable winters, whereas the Southern Antarctic region never even warms enough to melt the perpetual snow and ice. On a tilting, wobbling, ball-Earth spinning uniformly around the Sun, Arctic and Antarctic temperatures and seasons should not vary so greatly.
20. The common sense of man tells him - if nothing else told him - that there is an "up" and a "down" in -nature, even as regards the heavens and the earth; but the theory of modern astronomers necessitates the conclusion that there is not: therefore, 'the theory of the astronomers is opposed to common sense - yes, and to inspiration - and this is a common sense proof that the Earth is not a globe

The most commonly accepted explanation of this is that the space agencies of the world are involved in a conspiracy faking space travel and exploration. This likely began during the Cold War's 'Space Race', in which the USSR and USA were obsessed with beating each other into space to the point that each faked their accomplishments in an attempt to keep pace with the other's supposed achievements. Since the end of the Cold War, however, the conspiracy is most likely motivated by greed rather than political gains, and using only some of their funding to continue to fake space travel saves a lot of money to embezzle for themselves.