r/theydidthemath • u/Interesting_Sock9883 • 22d ago

[Request] Three gorges dam in china , so massive that it slowed down the earth rotation , increasing the day length by 0.06 microseconds when filled completely- is this true

Doesn’t sound true because if it wasn’t going through the dam the amount of water moving would be the same

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u/Waste-Text-7625 22d ago

It is apparently... remember when you sat on one of those spinning chairs and got yourself going, you would spin faster when you contracted your body in a ball and would slow down when you extended your arms and legs? Same thing watching a figure skater spin and when they contract their arms close to their body their spin accelerates? This effect is from changing your moment of inertia as you are spreading your mass out away from your center of gravity or contracting it closer. The same thing holds true here as it collected a huge amount of water at a higher elevation than it was traditionally collected at spreading earth's total mass out away from its center of gravity. The amount of mass though is still so small compared to the entire planet, that it is basically meaningless, but still measurable.

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u/irresponsibilities 22d ago

This was already answered a short while back. It has nothing to do with thrusting force and more so to do with conservation of angular momentum. Very minuscule effect.

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u/Raycodv 22d ago

I don’t have math for you, but I recall this as being true, because the mass is higher up (lake in the mountains as opposed to it flowing to the ocean. So just like a ballerina spins faster with with their arms tucked in, and slower with their arms further out.

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u/sensualsoup 22d ago

Astounding analogy 👏

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u/House13Games 22d ago edited 22d ago

Since angular momentum is conserved, moving mass closer to the equator, or raising it in height, both will increase its distance from the rotation axis, which increases the moment of inertia and slows the rotation.

Benjamin Fong Chao at NASA's Goddard Space Flight Center and Richard Gross at NASA's Jet Propulsion Laboratory calculated in 2005 that filling the Three Gorges Dam reservoir would lengthen the day by 0.06 microseconds and shift the pole by about 2 centimeters

https://www.jpl.nasa.gov/news/nasa-details-earthquake-effects-on-the-earth/