There is a lot of evidence that demonstrates the **sphericity** of the Earth, although it should be noted that **our planet is not perfectly round**. In fact, depending on the degree of approximation that one wishes to maintain, the Earth can be considered a **ball**a** geoid**or a **rotation ellipsoid**. Let’s see in detail what these shapes are and why all of them, in some way, can be associated with the Earth.

## The study of the shape of the Earth: geodesy

There **geodesy** It is the discipline that studies the** physical and mathematical aspects of the Earth**. Its aim is to define the shape and size of the Earth, how to measure it and how to represent it. The shape of our planet, however, is very complex and geodesy has the task of studying it by creating **models that allow it to be represented** at best in a mathematical way.

To represent the Earth “in a mathematical way”, geodesy tries to identify which **geometric solid** It is more similar to the real shape of the Earth, so that it can be used in calculations on the Earth’s surface. Geometric solids are figures whose points are in a three-dimensional space, and are therefore characterized by three dimensions: height, width and depth. Therefore, each solid has a surface area and a volume.

At this point the question might arise: **Why is it necessary to use a geometric solid to make calculations about the Earth’s surface?** Because each geometric solid corresponds to a formula that defines it, so that its characteristics can be calculated. In fact, each geometric solid has a respective formula to calculate its volume and surface area. The Earth, on the other hand, has a **too complex shape** to be defined mathematically, for this **it is necessary to approximate it** to a geometric solid, so that its dimensions can be calculated mathematically and the exact position of points on its surface can be determined.

## The Earth from sphere to geoid

A first approximation of the shape of the Earth proposed by geodesy is the **ball**. Already **from the 3rd century BC** Some scholars had argued that the Earth was spherical. In support of this thesis they also brought **numerous tests**. For example, the progressive disappearance of elements on the horizon or, vice versa, the appearance on the horizon of the highest elements, such as mountains, first, and only from a lesser distance that of the lowest elements, such as buildings.

Actually **the Earth is quite far from being a perfect sphere**: its shape depends on multiple forces at play, including forces related to the motions of the planet. For example, due to the **Earth’s rotation motion**that is, the motion that the Earth makes as it rotates on itself, our planet is slightly **flattened at the poles and bulging at the equator**. In fact, the Earth’s radius at the equator is **6378 km**while at the poles it is **6356 km** with a difference of 22 km. Furthermore, the surface of the Earth is not perfectly smooth, but there are mountains and ocean depressions. The shape of the Earth is therefore unique and very irregular and for this reason the solid that best represents it is defined **geoid**.

Given the very complex and irregular shape of the Earth, the solid that best describes its shape is the **geoid**. The geoid is defined as “the mean surface of the oceans which tends to arrange itself according to an equipotential surface of the gravitational field”. This very complex definition simply indicates **a solid that follows the distribution of masses** on the Planet: where there are mountains the geoid rises, while where there are depressions it descends, always maintaining its surface perpendicular to the direction of the gravitational force.

So, the geoid is the solid **less approximate and more precise** to represent the shape of the Earth, being able to better adapt to its irregularities. However, although conceptually it is quite simple to understand, the geoid is very **hard to define** mathematically: there is no mathematical formula that defines its characteristics. This means that there is no formula that can calculate its volume or surface area.

This is a problem for geodesy, because it makes it impossible to use it as a solid to make measurements on the Earth’s surface. So, although very accurate, **the geoid is too complex** and the shape of the Earth is represented by another solid: **the rotation ellipsoid**.

## The Earth as a rotational ellipsoid

THE’**rotation ellipsoid**unlike the geoid, is a solid that **it can be described in geometric terms**Therefore:

- it is possible to define it through a mathematical formula;
- There are formulas to calculate its volume and surface area.

In particular, the rotation ellipsoid is the solid describable in geometric terms that best approximates the Earth’s surface. As can be understood from the name, this solid is a rotation solid: that is, it is the result of the rotation of a plane figure, which therefore rotates on itself to create it.

Although the geoid is more similar to the real shape of the Earth, the rotational ellipsoid is often used to describe the Earth’s shape because it is much simpler to define and approximates the shape of the Earth better than the sphere, as it takes into account the flattening at the poles and the bulging of the equator: the reference ellipse is the one with the **equatorial semi-axis longer than the polar one**.

For these reasons it was adopted by geodesy as **solid representing the shape of the Earth**. In fact, being simpler to define, it is possible **use the ellipsoid to make calculations and measurements of our planet**For example, you can measure the extent of the Earth’s surface or locate its points precisely by creating geographic coordinates.

## The Earth’s size and geographic coordinates

The use of a mathematically definable geometric solid to represent the Earth has allowed geodesy to calculate its dimensions. Obviously we are talking about very large numbers: the Earth’s surface is about **510.100.000 km ^{2}**while its volume is approximately

**a thousand billion cubic kilometers**The rotation ellipsoid also allowed the development of a

**coordinate system**on the Earth’s surface: Knowing the formula that best approximates the Earth’s surface, it was possible to draw a grid on the Earth’s surface made up of lines called

**meridians**And

**parallels**Counting these imaginary lines allows us to use angular coordinates that can be used to establish a unique correspondence for every point on Earth.