First I will tell you how the height of the mountains was initially measured. Two centuries ago, to do this, atmospheric pressure anisotropy was used. For example, in 1802, Alexander von Humboldt measured the height of the Chimborazo volcano in Ecuador. To do this use a barometer. Climb to the top and simply using Torricelli’s Laws, where pressure decreases with height not in a perfectly linear way but roughly, he was able to calculate the height even though it is only an approximation. The problem with this method is that local weather conditions also cause pressure variation to be inaccurate.

Later there was a whole stream that belonged to George Everest, the British surveyor who gave the Himalayas its name in the 1950s, and in which the triangulation began. How does this work? If you are at a point at the foot of a mountain and you know exactly the distance between you and it, with a device that measures angles very precisely called a goniometer, you can find out the angle formed by the line connecting the summit of the mountain with the point where you are and the horizontal. Thus, knowing one side of the triangle (the horizontal distance of the mountain or the adjacent side) and the tangent of the angle, by trigonometry, you can calculate the height of the mountain (the opposite side). But this method also had problems because the further away from the foot of the mountain, the more inaccurate the calculated height. To get more reliable measurements, what they did was a series of small and medium right triangles to get the total height.

But in this case also there might be an argument because where do we put 0? That is, you are measuring the height with respect to the signal. In the past, it was already known that sea level, which can be a perfect zero, fluctuates. What was done was an average between the maximum and minimum tides. Currently, we know a few things. The first is that the Earth is not perfectly spherical. It is an oval that is flattened at the poles and is wider at the equator just to rotate. This affects the measurements of the mountains. If you measure Everest with respect to the center of the Earth, it is lower than Chimborazo because Everest is not at the equator, while Chimborazo, relative to the center of the Earth, is higher than Everest by about 1,800 meters.

We now also know that sea levels vary within a hundred meters due to the difference in gravity caused by the heterogeneous distribution of masses within the planet. This effect must be added to the gravitational pull of the Moon which is responsible for the tides… So where do we put zero to measure mountains? It is called a geode. We imagine that under Mount Everest, or any other mountain, the waters of the oceans follow. The height of this assumed circumference would adopt what is called the isogravitational potential. This means that the gravity will be the same all over that surface. This is calculated based on gravity. Taking gravity at various points, it is possible to find out the theoretical height of the imaginary sea level, the geoid: this is the reference surface for calculating the height of the summit.

But this step is avoided using GPS, which is the method we use today to measure the height of mountains. In this case it is also measured by triangulation, but the difference is that we have an external reference. GPS satellites act as a kind of reference network. With respect to this reference grid, the various points are measured with astonishing accuracy, on the order of millimeters over distances of hundreds of kilometres.

**Anna Crespo ***She is a professor in the Department of Geodynamics at the University of Granada.*

*Question sent by email ***Paula Garcia**

*Formatting and writing: ***Victoria Toru**

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