The planets of the Solar System, as well as the various exoplanets detected so far, all have a spheroid (quasi-sphere) structure, and the Earth is no exception. However, this mostly common form does not imply that it is physically impossible for a planet to possess a certain degree of flatness.
For hundreds of years, humans have known that the Earth is not flat. There are many ways to demonstrate this, from the masts of ships disappearing as they pass the horizon, to extended vision at higher levels of altitudes, to the longer shadows of the Sun at higher latitudes, by studying the shape of the Moon's shadow cast on the Earth during a solar eclipse, or by observing the Earth directly from space.
However, the fact that all the planets we have observed so far are not flat, does not prevent a planet from presenting a certain flatness. Moreover, some observations taken in isolation could correspond to a flat and circular Earth.
How to achieve the flattest planet possible? One possible strategy would be to consider a solid block of material — stone, steel, or something harder like diamond or graphene — and build the largest flat disc possible. Using conventional materials like these, it would be possible to form a thin, flat, stable disc, hundreds of kilometers in radius. A flat world larger than any object in the asteroid belt and possibly even similar in size to the Moon.
But in this case, it would technically not be a planet. In 2006, when the status of planet was withdrawn from Pluto, the International Astronomical Union set three criteria for a body to be considered a planet:it must orbit the Sun or a host star; it must have sufficient mass for its gravity to keep it in hydrostatic equilibrium, i.e. in a quasi-spherical, oblong or prolate shape (in the case of rotation); it must clear its orbit of any other body of comparable size.
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Thus, a totally flat body would not satisfy the second criterion requiring hydrostatic equilibrium, and therefore could not be classified as a planet. Nevertheless, it is still possible to achieve a high degree of flatness while satisfying this second criterion:rotation.
The Earth has a relatively slow rotation:it rotates 360° in 24 hours. This means that a person living at the equator (the maximum distance from the earth's axis of rotation), experiences an additional speed of 464 m/s compared to another living at the poles. This "surplus" of speed shapes the shape of the Earth by causing it to elongate, causing the planet to adopt an oblong spheroid shape:a quasi-sphere flattened at the poles and elongated at the equator.
The diameter of the Earth at the equator is 12,756 km, while at the poles it is only 12,714 km. Thus, one is 21 km closer to the center of the Earth at the North Pole than at the equator. If this rotation is slow for our planet, it turns out to be much faster for others, particularly among the gas giants. For example, the poles of Saturn are flattened by 10% compared to the equator.
However, according to current planetary models, this rotation may be much higher, and the flatness more pronounced. While no known planet currently has strong flatness, some Kuiper Belt objects exhibit impressive properties. The dwarf planet Haumea holds the record for flatness, with an equatorial diameter along its major axis being twice as large as its minor axis. This 2:1 ratio makes it the object known to have the most extreme hydrostatic balance.
Astronomers believe that Haumea's rotation comes from a collision, along with its two moons:Hiʻiaka and Namaka. Hiʻiaka, the more massive of the two, exerts a strong gravitational influence on Haumea, further complicating the system. Haumea is not just a world with an equatorial bulge and compressed poles; it has three distinct axes of different lengths, making it a triaxial ellipsoid.
Higher rotation speeds are possible; the denser and faster a planet is, the more flattened it is. The maximum limit being that from which the equator begins to disintegrate in space, the gravitational and electromagnetic cohesive force being overcome by rotation. For a planet like Earth, the limit would be a ratio of about 3:1. For a denser planet, like a uranium planet, this ratio could go up to 5:1.
In any case, the more a body is flattened, the more difficult it is for it to maintain its rigidity, because the internal forces lead to phenomena of friction and differential rotation of its peripheral layers. In the same way that the outer regions of Saturn's rings rotate more slowly than the inner regions, a flat planet would face the same forces. Ultimately, there may be planets flatter than Earth, but physics puts a limit to this flatness.
