There Three Gorges Dam is currently thelargest hydroelectric plant in the worlda mammoth engineering work built in the province of Hubei, China, along the Yangtze River, which came into operation in 2012 with a capacity of 22,500 MW. His dam, high 181 meterscreates a basin of water that extends well 1080km2. Well, according to a NASA calculation the plant would accumulate so much water that slow down (albeit imperceptibly) the earth’s rotation. This is a truly minimal decrease, estimated at just an extension of the day 0.06 millionths of a second. But why does this happen?
The answer has to do with the fact that the length of the day varies continuously: in the long run the length of the day tends to increase, but in recent decades the days are getting shorter. One of the many factors on which the length of the day depends is the distribution of land mass. The classic example given in these cases is that of a skater who rotates on herself: when he brings his arms closer to his body he accelerates, while when he tenses them he slows down. This is a general fact: the more the mass of an isolated rotating body is distributed away from the rotation axis, the more the rotation slows down, and vice versa, the more the mass is distributed closer to the rotation axis, the more the rotation increases (this is a manifestation of what in physics is called conservation of angular momentum).
But what does this have to do with the Three Gorges Dam? Well, being a dam it accumulates water where there was none before, and therefore actually changes – even if slightly – the distribution of the earth’s mass, which is a rotating body. According to available estimates, the Three Gorges Dam basin would contain approximately 42 billion tons of waterwhich can be raised up to 175 metersthus accumulating mass further away from the Earth’s rotation axis than it would be without the dam.
Furthermore, the facility is located at a latitude of approximately 30°therefore the accumulation of mass occurs at a certain distance from the Earth’s rotation axis (remember, however, that the Earth is slightly flattened at the poles, so places at low latitudes are further away from those at high latitudes). Conceptually, therefore, the Three Gorges basin acts like a skater who holds out her arms: the consequence is that the Earth slows down and the length of the day increases. Now, 42 billion tons is a lot, but it is very little compared to the mass of the Earth (6000 billion billion tons), so the increase in the length of the day is completely imperceptible and completely negligible for any practical purpose. But we can estimate it through our knowledge of physics and some calculations!
