# How much has the earth's rotation been slowed by skyscrapers?

So assuming the earth’s weight is more or less constant, surely the building of skyscrapers have directed more mass away from the center and slowed the earth’s rotation somewhat (due to the increase in mass moment of inertia). How much have all these tall structures slowed the earth’s rotation? Or am I missing something?

Yeah you’re missing the fact that those skyscrapers probably represent .0000000000000001% of the mass of the earth re-distributed from the crust to the skies.
Not enough mass to matter, basically. But don’t ask about earthquakes modifying the rotation of the earth because I wouldn’t know how to answer that one.
follow up:

6 × 10^9 kg - Mass of the Great Pyramid of Giza

6.0 × 10^24 kg - Mass of the Earth

But certainly if you add up all the man-made buildings and structures on earth the mass increases a tiny bit more…

But all the mass of all the building was already there.

where did this new mass come from?

From a point lower than the skyscrapers. I think the question is about the redistribution of mass and the effect on rotational velocity.

yes, thank you. Redistribution. Not “if you add up all the man-made buildings and structures on earth the mass increases a tiny bit more”

Yes, if I walk upstairs, the Earth’s rotation slows a little, and if I sit down, it speeds up a little. But not enough to notice.

If we all lie down can we make this day go faster? I want to go home.

ETA: If they catch me lying down at work, they’d probably make me go home anyway. Eureka!

I imagine dams have more effect, by retaining water at a higher elevation than otherwise.

Considerably less than all the reservoirs have increased it, which isn’t much at all to begin with.

I’m sure I remember reading that the earth’s mass increases by some large number of tons every day/year/whatever, due to meteors and space dust entering the atmosphere.

A brief Googling suggests figures between 20,000 and several million tons per year, with the lower end of those figures seemingly more plausible.

Surely that has a much greater effect than building a few office blocks?

And the reverse effect of deforestation? A lot of 50 foot tall trees get cut down to make 20 foot tall houses and 3 foot tall kitchen tables.

There’s also all the carbon that’s removed from underground and released into the atmosphere.

The earth may have recently been sped up.

The Chile earthquake also shortened the day by about 1.26 microseconds.

Yes, moving matter away from the center of the earth will slow down it’s rotation. Here’s a rough estimate of how much.

There’s about 50 skyscrapers over 1000 ft (300 m).
The weight of the Empire State building is about 365 kilotons (~ 4e8 kg).
The radius of the earth is about 6371 km ~ 6e6 m.
The difference of the moment of inertia due to raising that mass from the earth’s surface to skyscraper height is N * M * (R2^2 - R1^2) = 50 * 4e8 * ((6e6+300)^2 - 6e6^2) ~ 7e19 kg-m2.

The moment of inertia of the earth is about 8.034e37 kg-m2.
Angular momentum is L = I * W and is conserved. Since it’s proportional to the moment, we can look at the fractional change ~ 7e19 / 8e37 ~ 9e-19. Multiple that fraction by the length of the day, and we get 9e-19 * 24 * 60 * 60 ~ 8e-14 seconds. That’s 8e-8 microseconds, or 80 femtoseconds.

It’s a small value, but the physics is all freshman-level. Probably make a good homework problem.

Actually, the OP is correct, the building of skyscrapers changes the rotation velocity of the earth. However, interestingly enough, the change is exactly counteracted by the reduced mass of the planet by all of the planes flying around in the air.

I’ve got the number around here somewhere…shuffle…shuffle…(dang, gimme a minute…)

So, if filling the Three Gorges Dam reservoir increased day length by 60 billionths of a second, by what factor does the mass of the water in the reservoir outmass the world’s 50 tallest skyscrapers?

Interesting. The example given in one of the Chile articles today likened it to an iceskater pulling his arms in when spinning to make himself go faster.

What’s the effect of an iceskater getting goosebumps while in a spin? Seems analogous to the skyscraper question - since the scale is so infinitesimally small, despite our perspective of skyscrapers being huge.

Exactly 2.48 nanoseconds. there. Now you know.

And I know for a fact that exactly 21.8 angels can dance on the head of a pin.

And I also know for a fact that somebody has waaaay to much time on their hands.