# How much has the earth's rotation been slowed by skyscrapers? **URL:** \ **Category:** Factual Questions\ **Created:** [March 2, 2010, 9:49pm UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042 "2010-03-02T21:49:53Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![spifflog](https://avatars.discourse-cdn.com/v4/letter/s/c5a1d2/32.png) [@spifflog](https://boards.straightdope.com/u/spifflog)\ **Post date:** [March 3, 2010, 3:26am UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/21 "2010-03-03T03:26:47Z")
> [@Daylate](#): > > 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. And people have asked worse questions. Ya don’t like the question, move on to another one. ---
**Author:** ![Duckster](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/duckster/32/1244_2.png) [@Duckster](https://boards.straightdope.com/u/Duckster)\ **Post date:** [March 3, 2010, 3:37am UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/22 "2010-03-03T03:37:31Z")
Still trying to find the cite that says the height and length of the Andes Mountains in South America play a role in the rotational speed of the earth. ---
**Author:** ![Bytegeist](https://avatars.discourse-cdn.com/v4/letter/b/9dc877/32.png) [@Bytegeist](https://boards.straightdope.com/u/Bytegeist)\ **Post date:** [March 3, 2010, 4:12am UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/23 "2010-03-03T04:12:21Z")
> [@Duckster](#): > > Still trying to find the cite that says the height and length of the Andes Mountains in South America play a role in the rotational speed of the earth. It has nothing to do with the Andes in particular, of course. If the mass distribution of the Earth changes, then in general its rotational speed is also going to change, because of the conservation of angular momentum. See the section [here](http://hyperphysics.phy-astr.gsu.edu/Hbase/amom.html) called “Angular Momentum”, and the one [here](http://hyperphysics.phy-astr.gsu.edu/Hbase/mi.html) called “Moment of Inertia, General Form”. Ignoring the vector algebra in **L = I x omega** , notice that the magnitude of the angular momentum (L), which stays fixed remember, is the product of the moment of inertia (I) and the angular speed (omega). So if the mass distribution contracts (because some mass moves closer to the rotational axis), then the moment of inertia _decreases_ and the angular speed _increases_. Vice-versa if the mass distribution expands (when some mass moves away from the axis). ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [March 3, 2010, 5:54am UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/24 "2010-03-03T05:54:32Z")
I saw once a display in the NY Museum of Natural History, I think, on the non-resting “mass” of photons from the sun hitting the earth every second. On this, Dick Plano, Professor of Physics emeritus, Rutgers University, [contributed](http://www.newton.dep.anl.gov/askasci/phy00/phy00644.htm) to Argonne National Lab, writing: An elementary textbook says the sun converts 4.2 x 10^9 kg of mass to energy every second. Using this number, we can estimate the amount of energy (mass) from the sun hitting the earth by calculating the fraction of the entire solid angle the earth intercepts as seen by the sun. Since the diameter of the earth is about 1.3 x 10^7 m and it is 1.5 x 10^11 m from the sun, it subtends an angle of about 8.7 x 10^-5 radians. If we square this angle and divide by 4 pi = 12.6, we get the solid angle fraction subtended by the earth, which I calculate to be about 6 x 10^-10 of the entire solid angle. Multiplying this by the 4.2 x 10^9 kg burned by the sun every second and we obtain\*\* 2.5 kg/s as the mass of the photons (light) from the sun striking the earth every second\*\*\*.[Bold added–Leo] \*During a solar storm, wouldn’t the earth rotate slower? ---
**Author:** ![Random\_Design](https://avatars.discourse-cdn.com/v4/letter/r/58f4c7/32.png) [@Random\_Design](https://boards.straightdope.com/u/Random_Design)\ **Post date:** [March 3, 2010, 12:34pm UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/25 "2010-03-03T12:34:53Z")
Next question: Why do people with pimples not fall over from the added weight and altered centre of gravity resulting from their facial restructuring. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [March 3, 2010, 12:55pm UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/26 "2010-03-03T12:55:13Z")
> [@Pleonast](#): > > There’s about [50](http://en.wikipedia.org/wiki/List_of_tallest_buildings_in_the_world) skyscrapers over 1000 ft (300 m). > The weight of the Empire State building is about [365 kilotons](http://www.newyorktransportation.com/info/empirefact2.html) (~ 4e8 kg). > The radius of the earth is about [6371 km](http://en.wikipedia.org/wiki/Earth_radius) ~ 6e6 m. > The difference of the [moment of inertia](http://en.wikipedia.org/wiki/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](http://scienceworld.wolfram.com/physics/MomentofInertiaEarth.html). > [Angular momentum](http://en.wikipedia.org/wiki/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. Your estimate assumes all of these buildings were constructed at the equator, which of course is not the case. The real distribution of buildings over the earth’s surface (at latitudes up to/beyond 45 degrees) makes the math painfully complicated, but I’d make a wild-ass guess the time change involved is only about half of what you calculated. ---
**Author:** ![Kiber](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kiber/32/317_2.png) [@Kiber](https://boards.straightdope.com/u/Kiber)\ **Post date:** [March 3, 2010, 3:26pm UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/27 "2010-03-03T15:26:02Z")
What about wind? When I first read the Op, I actually thought that skyscrapers might increase rotation because they basically act as giant sails. And doesn’t most wind, on average, come from the west (at least in temperate zones, which is where most skyscrapers are built)? If so, wouldn’t the pressure of prevailing winds push on the west-facing side of skyscrapers, thereby increasing rotation of the earth? [Here](http://www.met.utah.edu/jhorel/html/wx/climate/windavg.html), for example, is a listing of average wind speed for cities in the US. Hmmmmm - now, looking at [this](http://en.wikipedia.org/wiki/File:Map_prevailing_winds_on_earth.png), I’m starting to wonder about the notion of prevailing winds. Looks like they are a bit more variable than I originally thought. Although it still looks to me like the regions where skyscrapers seem more prominent, typically have winds from the west. ---
**Author:** ![Pleonast](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pleonast/32/1183_2.png) [@Pleonast](https://boards.straightdope.com/u/Pleonast)\ **Post date:** [March 3, 2010, 4:36pm UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/28 "2010-03-03T16:36:26Z")
> [@Daylate](#): > > Exactly 2.48 nanoseconds. there. Now you know. You’re off by something like 4 orders of magnitude. > [@](#): > > And I also know for a fact that somebody has waaaay to much time on their hands. And some of us think time spent thinking about how the world works is well worth it. > [@Joe Frickin Friday](#): > > Your estimate assumes all of these buildings were constructed at the equator, which of course is not the case. The real distribution of buildings over the earth’s surface (at latitudes up to/beyond 45 degrees) makes the math painfully complicated, but I’d make a wild-ass guess the time change involved is only about half of what you calculated. Yeah, I know. I made several crude approximations, which is why I qualified the estimate as rough. But since no one else had even attempted a quantitative answer to the OP, I thought an easily-computed estimate would be instructive. If others are so inclined, they can refine the computation for a better final quantity. ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [March 3, 2010, 4:41pm UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/29 "2010-03-03T16:41:23Z")
> [@Icarus](#): > > 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…) Hey, though, aren’t those planes airborne, and so you still need to factor in their mass? Or does that only apply to treadmills? ---
**Author:** ![Marley23](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Marley23](https://boards.straightdope.com/u/Marley23)\ **Post date:** [March 3, 2010, 4:45pm UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/30 "2010-03-03T16:45:33Z")
> [@Hero\_From\_Sector\_7G](#): > > The earth may have recently been sped up. > > [The Chile earthquake also shortened the day by about 1.26 microseconds.](http://www.nowpublic.com/environment/chile-earthquake-earth-axis-quake-changes-axis-shortens-day-2585178.html) [And the 2004 Indian Ocean quake did twice that much. But it doesn’t really matter because each year, the day gets 15 microseconds longer.](http://en.wikipedia.org/wiki/2004_Indian_Ocean_earthquake) > [@](#): > > because of tidal effects of the Moon, the length of a day increases at an average of 15 µs per year, so any rotational change due to the earthquake will be lost quickly ---
**Author:** ![Munch](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/munch/32/5281_2.png) [@Munch](https://boards.straightdope.com/u/Munch)\ **Post date:** [March 3, 2010, 5:07pm UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/31 "2010-03-03T17:07:12Z")
> [@Kiber](#): > > What about wind? When I first read the Op, I actually thought that skyscrapers might increase rotation because they basically act as giant sails. Yeah, but proportionally speaking, they’re ridiculously tiny, tiny little sails. The earth is [slightly more rough than a billiard ball](http://www.bautforum.com/astronomy/33-earth-smooth.html#post416) - and given a perfectly smooth billiard ball, a proportionally-sized Mt. Everest bump on it would be hardly noticeable. Skyscrapers are a mere fraction of Everest. Just goes to show how the vastness of the size of this planet is hard to comprehend. ---
**Author:** ![Daylate](https://avatars.discourse-cdn.com/v4/letter/d/9dc877/32.png) [@Daylate](https://boards.straightdope.com/u/Daylate)\ **Post date:** [March 3, 2010, 5:29pm UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/32 "2010-03-03T17:29:59Z")
> [@](#): > > And some of us think time spent thinking about how the world works is well worth it. I knew my comment would be sort of like poking a wet bear. ---
**Author:** ![Kiber](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kiber/32/317_2.png) [@Kiber](https://boards.straightdope.com/u/Kiber)\ **Post date:** [March 3, 2010, 5:41pm UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/33 "2010-03-03T17:41:36Z")
> [@Munch](#): > > Yeah, but proportionally speaking, they’re ridiculously tiny, tiny little sails. The earth is [slightly more rough than a billiard ball](http://www.bautforum.com/astronomy/33-earth-smooth.html#post416) - and given a perfectly smooth billiard ball, a proportionally-sized Mt. Everest bump on it would be hardly noticeable. Skyscrapers are a mere fraction of Everest. > > Just goes to show how the vastness of the size of this planet is hard to comprehend. This is certainly true and a good point. However - proportionally speaking, skyscapers also make a ridiculously tiny, tiny impact on any change to the mass moment of inertia for the planet. So it seems to me that the proportionality argument cancels out - as long as your are comparing any (tiny) increase in rotation due to wind, with any (tiny) decrease due to moving mass further from the center of rotation. None of this is to say that wind makes any impact whatsoever - but IF it does, it should only be compared to whatever tiny impact changing the moment of inertia would have. ---
**Author:** ![Snarky\_Kong](https://avatars.discourse-cdn.com/v4/letter/s/a183cd/32.png) [@Snarky\_Kong](https://boards.straightdope.com/u/Snarky_Kong)\ **Post date:** [March 3, 2010, 5:49pm UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/34 "2010-03-03T17:49:11Z")
> [@Kiber](#): > > This is certainly true and a good point. However - proportionally speaking, skyscapers also make a ridiculously tiny, tiny impact on any change to the mass moment of inertia for the planet. So it seems to me that the proportionality argument cancels out - as long as your are comparing any (tiny) increase in rotation due to wind, with any (tiny) decrease due to moving mass further from the center of rotation. > > None of this is to say that wind makes any impact whatsoever - but IF it does, it should only be compared to whatever tiny impact changing the moment of inertia would have. Something to note is that wind isn’t caused by the rotation of the Earth, so a fair amount of the sails would be pushing the Earth while others are slowing it down. Heck, you have different wind directions at different elevations. Finding the average lateral force at buildings’ foundations… good luck. ---
**Author:** ![Munch](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/munch/32/5281_2.png) [@Munch](https://boards.straightdope.com/u/Munch)\ **Post date:** [March 3, 2010, 6:51pm UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/35 "2010-03-03T18:51:46Z")
> [@Kiber](#): > > This is certainly true and a good point. However - proportionally speaking, skyscapers also make a ridiculously tiny, tiny impact on any change to the mass moment of inertia for the planet. So it seems to me that the proportionality argument cancels out - as long as your are comparing any (tiny) increase in rotation due to wind, with any (tiny) decrease due to moving mass further from the center of rotation. > > None of this is to say that wind makes any impact whatsoever - but IF it does, it should only be compared to whatever tiny impact changing the moment of inertia would have. You know, I didn’t even notice the post I was responding to was talking about wind - I took the “sails” comment more as a metaphor. Either way, I think it’s hard for a lot of people to comprehend how very tiny we are (the other thread regarding the poles tilting 3 inches shows this as well), and what a vastly insignificant effect skyscrapers have on the earth’s momentum. It would be like the difference a marathon runner sees after trimming their fingernails. ---
**Author:** ![Colophon](https://avatars.discourse-cdn.com/v4/letter/c/f05b48/32.png) [@Colophon](https://boards.straightdope.com/u/Colophon)\ **Post date:** [March 3, 2010, 7:52pm UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/36 "2010-03-03T19:52:28Z")
I don’t see how, even if they weren’t so tiny, “sails” could speed up the rotation of the earth. Surely the movement of the atmosphere is already part of the rotating system of the earth? For a sail to speed up the system, surely it would have to poke out of the atmosphere and pick up some kind of notional external push (like a solar sail, say). It seems to me that expecting a skyscraper, no matter how big, to give a push to the earth is like trying to make a sailing dinghy go faster by putting a fan on the deck pointing at the sail. If I’m wrong, please put me right… ---
**Author:** ![lissener](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lissener/32/6139_2.png) [@lissener](https://boards.straightdope.com/u/lissener)\ **Post date:** [March 3, 2010, 7:58pm UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/37 "2010-03-03T19:58:24Z")
> [@Daylate](#): > > I knew my comment would be sort of like poking a wet bear. Nah, more like picking your nose in public. Only one person comes off as rude. ---
**Author:** ![Munch](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/munch/32/5281_2.png) [@Munch](https://boards.straightdope.com/u/Munch)\ **Post date:** [March 3, 2010, 8:05pm UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/38 "2010-03-03T20:05:36Z")
n/m ---
**Author:** ![Dickerman](https://avatars.discourse-cdn.com/v4/letter/d/8baadc/32.png) [@Dickerman](https://boards.straightdope.com/u/Dickerman)\ **Post date:** [March 3, 2010, 8:40pm UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/39 "2010-03-03T20:40:08Z")
There is a lot of rockfall (and icefall) in the worlds mountains. I would imagine they yearly amount would far offset the yearly building rate, but alas, I have no cite. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [March 3, 2010, 9:09pm UTC](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042/40 "2010-03-03T21:09:50Z")
> [@Dickerman](#): > > There is a lot of rockfall (and icefall) in the worlds mountains. I would imagine they yearly amount would far offset the yearly building rate, but alas, I have no cite. Never mind the rate at which buildings are erected - I’d guess that the rockfall is cancelled out by the amount of geologic upthrust, since many/most/all mountain ranges are undergoing both continous erosion _and_ continuous growth. Likewise with icefall, which is offset by snowstorms near the summit. OTOH, glaciers are disappearing in many places, so that’s a definite trend toward high-altitude mass reduction… [Previous page](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042.md?page=1) [Next page](https://boards.straightdope.com/t/how-much-has-the-earths-rotation-been-slowed-by-skyscrapers/531042.md?page=3)