Geoid: The Real Shape of the Earth

Until the sixth century BC, when the Greek scientist Pythagoras arrived and claimed that the world was spherical in shape, men considered that the earth was a solid disk that hovered above the surface of the water. The experiment of the Greek scientist Aratustin was the first attempt by scientists to estimate the size or circumference of this sphere. During their voyages in the fifteenth and sixteenth centuries, the explorers Columbus and Magellan supported the earth's sphericity, which is recognized for its rotation around the sun. The famous scientist Newtown created various scientific theories in 1687, the most notable of which was that the balanced form of a homogeneous fluid mass subject to gravity and revolving around its axis is not a completely round sphere, but rather a somewhat flattened shape towards the poles. The French Academy of Sciences conducted two voyages in 1735 to make the necessary measurements to corroborate this concept, and the results confirmed that the Earth is flattened and not perfectly spherical in shape.

Shape of Earth

We live on the planet's surface, and when we want to identify any location on Earth, we must first define this surface - its shape and size - so that we can know exactly where we are. The natural surface of the planet, comprising continents, oceans, mountains, valleys, and seas, as formed by God the Highest, is neither a fluid form nor is it regular enough to be simply articulated. Scientists looked for a less complicated hypothetical form of the Earth and settled on the idea that because the water area in the oceans and seas accounts for roughly 70% of the Earth's area, the shape of the Earth is almost the average shape of the water surface (if we ignore the movement of the water surface due to ocean currents and tides) are the Sea Level, abbreviated as MSL letters, and if we extend this surface under the land to create an integrated shape, this shape will be closer to the true shape of the Earth.

This hypothetical shape was given the name geoid (it should be noted that there is a difference of only 1 meter between both the MSL and the geoid, but in most engineering applications this difference is overlooked and it is considered that both shapes and terms refer to the same body). However, according to Newton's previous principle, the shape of this geoid will not be regular because the geoid's surface is perpendicular to the direction of the earth's gravitational force and is subject to the centrifugal force caused by the earth's rotation on its axis, and both forces differ from one place to another on the earth's surface due to the non-uniform distribution of density. As a result, it was determined that the geoid represents the actual shape of the Earth, but it is also a complex form that is difficult to represent using mathematical equations that allow us to construct maps and establish positions on it.

Geoid vs Ellipsoid

Due to the complexity of the geoid and the difficulty of representing it with mathematical equations, scientists tended to search for the closest known geometric shapes and found that the Ellipse is the closest. If this Ellipse rotates around its axis, it will produce an Ellipsoid or Ellipsoid of Revolution, also known as the Spheroid (the name ellipsoid is the most common). Perhaps they will now come to mind with a question: What is the difference between the ellipse and the circle? Or, in other words, what is the difference between the ellipsoid and the ball? In contrast to the sphere, which is totally spherical, the ellipsoid is somewhat flattened at both poles. Furthermore, the sphere has a diameter that is the same in all directions, whereas the ellipsoid has two distinct axes. To express an ellipse, two elements must be defined (a sphere is represented by only one element, its radius):

•    Half of the major axis (the axis in the plane of the equator) is denoted by the symbol a.
•    Half of the minor axis (the axis between both poles) is denoted by b.

Some express the ellipsoid in another way through the two elements:

•    Half of the major axis (the axis in the plane of the equator) is denoted by the symbol a.
•    The coefficient of flattening is denoted by the symbol f and is calculated from the equation:

f = (a – b) / a or f = 1- (b / a)

Several characteristics distinguish the ellipsoid shape, including:

1- The simplicity with which calculations can be performed on its surface (as it is a well-known geometric shape).

2- The surface of the mathematical ellipsoid and the surface of the geoid are not significantly different (the maximum difference between the two is only 100 meters, which represents the largest geoid height). It is worth noting that the distance between the geoid and the sphere is around 21 kilometers.

Geoid Applications

The geoid is used in the following applications:

1- In Earth satellite remote sensing and geoprocessing data processing, local reference surfaces, such as the normal surface, are determined.

2- In cadastral surveying, the surface of the ground being surveyed is determined (also called a reference surface).

3- In land surveying, to locate high-precision GPS receivers, as well as for other high-precision positioning applications such as 3D mapping and KML processing.

4- To examine Earth surface changes, such as tectonics, landslides, erosion, and so on, in geology and geomorphology.

5- In oceanography to determine local sea level, e.g., tidal datum (not applicable for surveying).

6- In navigation to determine a ship’s position using a satellite system.

7- To determine the mean sea level over the entire Earth in hydrography (not applicable for surveying).