In the summer, many people like to go to the mountains. And there you will find not only beautiful views, cows and mountain huts with cold beer, but also a lot of scientific questions. For example: What is the height of the highest mountain on earth? How high can the mountain reach? Does the mountain go further than the surface of the earth? There are answers to all of these questions, and some of them are quite surprising.
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Let’s start with the last question. The English astronomer and mathematician George Airy developed this formula for them:
h indicates the height of the mountain above sea level; With ρ the density of the rock, times for the Earth’s crust («c») and the Earth’s mantle («m»). If you use the usual values - about 3.3 g/cm³ for the mantle and 2.75 g/cc for the crust, then one gets the base b for the mountain, that is, the depth of its “root”, with b ~5 h. A mountain like Zugspitze, which is about 3 kilometers high, reaches 15 kilometers deep inside the Earth. Since the material of the lithosphere, the outermost layer of the Earth, is less dense than that in the mantle, there are gravitational anomalies under the mountains – a mass less than one would expect.
Airy based his model on Archimedes’ principle: just like an iceberg that floats on water and is partially immersed in it, the rock of a mountain range descends into the sublithosphere. Unlike mountains, it is not solid, but is more elastically deformable. The higher the Berg thrust from above, the deeper the lithosphere at this point.
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