Everyone knows that the earth is spherical. All… aside from for some marginal exceptions. The traditional Greeks already knew concerning the sphericity of our planet. Amongst different proof, they spotted that once a boat disappears over the horizon, the very last thing to vanish is the mast. It used to be Aristotle who first compiled a listing of empirical proof for this sphericity. Later, Eratosthenes of Cyrene calculated the Earth’s circumference with exceptional precision, estimating it at about 40,000 km.
having a look on the sky
That the Earth is a sphere is rather obtrusive when having a look on the night time sky. The placement of stars noticed on the similar time varies with latitude. Inside of Spain, if we take a look at the sky from Granada or Santander (each towns of more or less the similar longitude), the sky appears to be like other on the similar time of night time.
View of the sky from Granada (left) and Santander (proper), 13.11.2025. at 11:30. Flat Earthism within the Center Ages?
Right through the Center Ages, the approximate sphericity of the planet used to be additionally approved. For instance, within the library of Merton School, Oxford, there’s a e-book summarizing the paintings of 14th-century schoolmen appearing that the Earth is spherical. The shadow it casts at the moon right through an eclipse permits us to deduce its form. For instance, the form that the shadow would have if our planet have been triangular, sq. and even hexagonal is proven.
Peter Appian, Cosmography (Antwerp, 1545). Merton School Library, Oxford. Juan Antonio Aguilar Saavedra
The knowledge that the Earth is spherical led Christopher Columbus to suggest his voyage to India, crusing west, assured that he may achieve Asia on the different finish of the sector. As of late we all know that the calculations that Columbus offered to justify his expedition have been incorrect, which is why the counselors of the King of Portugal rejected his proposal. Even if it’s debated whether or not it used to be a planned mistake to get royal popularity of his shuttle.
Math vs flat earth
The large dimension of the planet, in comparison to our on a regular basis scales (at the order of a meter), along side the irregularities of the relaxation, makes the curvature of the Earth almost imperceptible to the bare eye. This is to mention: without delay watching that the Earth is spherical is very tricky. Until one is an astronaut and watches it from area, or perhaps whilst flying over the sea? We got here up with the solution the usage of ESO-level math.
Epic/NASA
Industrial airplane fly at cruising altitudes between 10 and 12 km. At that top, it’s simple to calculate how some distance the attention can see. If we name “h” the peak, and “d” the gap to the horizon, it is sufficient to observe the Pythagorean theorem, assuming that the Earth is round with a radius of “R”, which is 6,370 km.
The result’s roughly:
d = √(2Rh)
Taking R = 6370 km and h = 10 km, we get a viewing distance of 357 km. Now not unhealthy for the view from the window!
At upper altitudes, for instance 12 km, the gap will increase to 391 km.
Representation of the calculation of the viewing distance to the horizon, from the peak h.
The principle lenses of many cellphones (now not wide-angle, which distorts the picture) quilt a box of view of about 70–80 levels. The use of somewhat geometry, we will estimate the curvature of the Earth comparable to that viewing perspective. If the required perspective is θ, the horizon line has duration θ·d and corresponds to an arc of circumference of θ·d/R.
For θ = 70°, the arc visual at the horizon spans about 4°. Even if it won’t appear to be a lot in comparison to 360° of whole circumference, it is sufficient to make the curvature noticeable!
Simply take a look at the image beneath. For θ = 80° and h = 12 km, the arc will increase to 4.9°.
Blue, the visual arc of the horizon for θ=70°, from a top of 10 km. The fairway strains prohibit, in point of view, the sphere of view.
So the solution to our preliminary query is: sure. In just right stipulations, with out clouds and with just right visibility, the curvature of the planet may also be noticed with the bare eye from an aircraft. It’s in point of fact thrilling to look, first-hand, a phenomenon this is as acquainted as it’s tricky to look at. And it invitations us to suppose.
Within the phrases of Apollo 11 astronaut Michael Collins:
“Apparently, the overriding feeling I had once I checked out Earth used to be, ‘My God, that little factor is so fragile available in the market.’
At 10 km altitude in an aircraft, we will revel in, even on a small scale, a glimpse of that very same feeling.
