The internet is a great way to get facts on just about any subject. However, by its very nature the internet can also include false information about what anyone wishes to publish, and pseudoscience is often promulgated as being science fact.
Surprisingly, one example is the so-called flat Earth hypothesis, which has experienced resurgence in popularity with internet-trolls recently, even though it has been scientifically disproved for several thousand years.
Without going out into space, it is impossible to observe the actual sphere of the Earth directly. After all, no matter the scientific evidence and videos from space, if you put a level on the ground it appears flat, and if you look around the horizon, there appears to be no curvature.
However, from antiquity, early sailors noticed when they observed a ship sail off to sea, as they watched its mast and flag, it did not fade off into the distance, but rather the ships mast and flag appeared to slowly sink into the sea. The ship sailed beyond the point at which you would see it. It’s as if you’re watching it go over to the other side of a hill. This phenomenon can only be explained by a sphere-shaped Earth. And you can always observe this yourself by visiting a harbor or any place with a wide-open view of the ocean. Just to be sure, however, bring a pair of binoculars with you so that you can see details even farther off into the distance.
You can also detect the curvature of the Earth by observing a western sunset over the ocean. Pick a tall building from which you have a clear ocean horizon in front of you. From the building, have a friend observe the sunset from the fourth floor, or higher. Watch as the sun sets from the ground floor, and once it sets just below the ocean, communicate over your cell phones and measure the time difference the added elevation adds to the ground-based setting time. If Earth were flat, the sun would be visible at all elevations at the same time. The setting time will be several seconds later with the added height. Because the Earth is round, the sun will set later the higher you are.
Another method is to pick two locations that are some distance apart (at least a couple hundred miles from each other and on the same north-south longitude meridian). Take two meter-sticks, two tape measures, and a friend. Each of you will take one meter-stick and one tape measure to your location, and stick each meter-stick vertically into the ground, and measure each of the shadows at noon. On a flat Earth, the shadow that is cast by each should be of the same length. However, if you and your friend compare notes, you’ll find that one shadow was longer than the other. That’s because, due to the curvature of Earth, the sun will hit one part of Earth at one angle and another part of Earth at a different angle because of the latitude difference, indicating the Earth is curved.
In 240 BCE, the Greek mathematician and geographer Eratosthenes of Cyrene (276-194 BCE) compared the angle of shadows cast by the sun at both Syene, now Aswan, Egypt, and in Alexandria at noon on the summer solstice when the sun was at its highest point in the sky for the year. (Syene is at latitude 24°05′ north, close to the Tropic of Cancer, which was 23°42′ north around 200 BCE). Eratosthenes knew of a well in Syene where once a year, on the summer solstice, the sun would illuminate the entire bottom of the well and tall buildings and other objects would not cast a shadow. However, he noticed that shadows were being cast on the summer solstice in Alexandria. Using the length of a rod, and the length of its shadow, as the legs of a triangle, he calculated the angle of the sun’s rays to be about 7.2°, or 1/50th the circumference of a circle. Taking the Earth as spherical, and knowing the distance from Alexandria to Syene (5,000 stadia, or about 176.4 km), he concluded that the Earth’s circumference was 50 times that distance, or about 44,100 km, (about 10 percent within the current known value.)
Though Solar Eclipses get all the attention, if you observe a lunar eclipse you can see evidence that the Earth is, indeed round. During a lunar eclipse, the Earth passes between the moon and sun, so that the sun projects Earth’s shadow onto the moon in the night sky. You will observe the round full moon being covered by the projected round shadow of the Earth, something that would not happen if the Earth were flat.
As mentioned earlier, unless you go into space, direct observation that the Earth is round must be induced. However, the curvature of the earth does become somewhat visible at an elevation of 35,000 feet (7 miles) and more easily visible at an elevation of 50,000 feet. So if you’re on the right commercial flight, you might be able to see the curvature of the earth with your own two eyes.