# What is the actual shape of the Earth?

Planet Earth may appear round when viewed from space, but the reality is that the shape of the Earth is more like a spheroid (ellipsoid of revolution) with a uneven surface.

Today determining that the Earth is not flat seems obvious. Also that it is not a perfect sphere, but is flattened at the poles. But determining the exact shape and topography of the Earth's surface remains a challenge, so approximate mathematical models are often used.

## Earth shape and geodetic models

Models to represent the Earth vary in complexity and accuracy with which they represent the shape and size of the Earth. Even a flat model, far removed from the actual shape, can be useful for local reference and work.

Geodesy is the branch of Earth sciences that deals with the study of shape and size of our planet, along with its orientation in space and variations in the gravitational fieldincluding both natural and artificial forms.

Its calculations and measurements are used in other geological sciences and coordinate systems for navigation, positioning, cadastres, surveying, etc.

### Sphere

The simplest model of terrestrial morphology is the sphere. This hypothetical sphere would have an average radius of 6,371 km from the planetary center to the surface, although it can vary from the minimum of the poles (6,357 km) to the maximum at the equator (6,378 km).

The radius is a characteristic of a perfect sphere, but the rotation of the planet on itself generates a centrifugal force that causes a distribution of mass with greater accumulation in the equatorial zone, and this is what causes flattening at the poles.

The deviation of the sphere from the true terrestrial form is estimated at 0.3%, a deviation that in the dimensions of the planet can become important, but at the same time it is small enough so that the model of a spherical Earth can be used in many contexts.

### ellipsoid of revolution

Since the terrestrial sphere is flattened at the poles, its most exact geometric shape would be a oblate spheroid. The spheroid is the geometric shape that is obtained by rotating an ellipse on itself, that is, a spheroid is an ellipsoid of revolution.

The ellipsoid is also an approximate shape, like the sphere, but with a higher degree of accuracy. There are different spheroid models, including the terrestrial spheroid WGS 84 (World Geodetic System 1984) used in the GPS system.

The WGS 84 ellipsoid is defined by:

• Semi-major axis (a): 6378137.0m
• Semi minor axis (b): 6356752.31424m
• Flattening (f): 1/298.257223563
• Product of the Gravitational Constant (G) and the Mass of the Earth (M): GM = 3.986004418×1014m3/stwo
• Angular Velocity (ω): 7.292115×10-5 rad/s

### Geoids

The spheroid in the previous section is defined through a mathematical model that represents a planet with a regular terrestrial surface, so it is considered an ideal mathematical representation.

But the distribution of mass and density on the planet is not homogeneous, so neither is the gravitational field distribution.

Geoids are mathematical models that use measurements of the gravitational field to represent the shape of the Earth. Although in the topography there are peaks of almost 9 km (Mount Everest) and depressions of more than 11 km (Mariana Trench), the different geodetic models vary from +85 m in Iceland to -106 m in South India.

Theoretically, a geoid coincides with the shape the Earth would have if the oceans completely covered it, extending over the continents and if they were only affected by the attractive force of gravity and the centrifugal force of rotation, without the effect of the tides, winds and other meteorological phenomena.

Also, keep in mind that the shape of the Earth is constantly changing. To keep track of these changes, outside of geodetic models, scientists use thousands of Global Positioning System (GPS) receivers capable of detecting changes in your altitude of just a few millimeters.

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