The radius of the Earth, that is, the distance from the center to the surface, is 6,371 kilometers, with a margin of error of two meters. Yes, it’s just two meters of uncertainty, without computing the imperfections caused by the terrestrial topology. But since when do we know this?
The oldest known measurement was made by Eratosthenes of Cyrene in approximately 240 BC. In a simplified way, the Greek mathematician considered the Earth a perfect sphere, and used basic concepts of geometry to calculate its dimensions.
Let’s take a basketball with a stick attached to its surface, pointing towards the center of the ball. When lighting a flashlight and pointing it at the stick, if the alignment between the two objects is perfect, there will be no shadow on the surface of the ball. If, on the other hand, there is an angle between the incident light and the rod, we can see a small shadow, which will be greater the greater the inclination of the rod.
Let us now imagine two sticks, one of them aligned with the flashlight. The angle between the two — and consequently the length of the shadow caused by the second — depends on the distance between them and the diameter of the ball. The closer together, or the larger the sphere, the smaller the shadow of the second rod.
Eratosthenes used this same reasoning on a grand scale, substituting the earth for the ball. According to this hypothesis, at the exact moment when the Sun was directly above a city (Siena, in the stories told), it would measure the extent of the shadow in Alexandria caused by a certain rod. Knowing the size of the rod and the distance between the two cities, he could calculate the size of the Earth.
The challenge was to measure the distance between cities. Eratosthenes would have asked for the collaboration of bematistas, specialists in carrying out such measurements by counting steps or some kind of rudimentary odometer. It is impressive that the value found for the Earth’s circumference was 39,425 kilometers, while the official current measurement is 40,008 kilometers.
Today our knowledge of the Earth is more advanced, of course. It is not a perfect sphere, for example, but an ellipsoid, flattened at the poles due to the movement of the Earth’s rotation — a difference between the radii of about twenty kilometers. Satellites and lasers enable measurements with precision of less than one meter, in some cases. But the end result is still very close to that found more than 2,000 years ago.
An excellent example of the success of the scientific method, this experiment is still used as a way of thinking about the production of scientific knowledge. Eratosthenes formulated a hypothesis and developed a practical experiment to confirm it, based on observational data. This is the foundation of the production of discoveries and new knowledge in modern science.
Flat Earth is an absolutely distorted view of this model. Based on alleged experiments carried out by the English inventor Samuel Rowbotham in the 19th century, its defenders claim that the Earth would be flat, in an attempt to invalidate the knowledge that already existed since the 3rd century BC Discussions with flat-Earthers boil down to false debates: the argument is based on on hypotheses created after observations, just to justify their own model. It is the typical fallacy used in conspiracy theories such as the alleged falsification of the arrival of human beings on the Moon.
Deniers do not propose experiments to confirm or reject a hypothesis: they adapt observations to their personal beliefs. If the data contradict the claim, discard the data and keep the hypothesis. For science to be open to new evidence and paradigm shifts, everyone needs to follow the same rules.
Knowing the size and shape of the Earth allows us, for example, to predict the location and time of a solar eclipse tens of years from now, with the precision of minutes. The moon’s shadow on the Earth depends on the curvature of the planet, and — contrary to flat-Earther arguments — prior knowledge allows us to make accurate predictions of the future behavior of nature. Serious alternative models should be able to make similar predictions and, even more, point out flaws in the predictive performance of previous models.
We have known the dimensions of the Earth for over 2,000 years, but the debate about the importance of the scientific method is more current than ever. In years of pandemic and discussions about vaccines and proven ineffective treatments, it is essential to understand how this knowledge is produced within the scope of scientific research.
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Thiago Gonçalves is an astronomer at the Valongo Observatory/UFRJ and a science communicator.
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