Earth's rotational speed varies.

I have checked the data an found following Peaks; Year 1998, 23.May, the Earth rotated in 86400.0023738 seconds. At 9.July the rotation time of the Earth was 86400.0000159 Seconds. This acceleration happened in just 47 days.

What does this small change means in form of Rotational Kinetic Energy? E-rot = 2.138 x10^29 J I calculated it through the inertia in Excel, and I got a comparable values of Approx 2.12597562 x10^29 J and 2.12597574 x10^29 J, and though you don’t almost see any difference, it’s 11.6 x10^21 J

Is it much? Well, If you wan’t to store this energy with the mass of atmosphere; m-atm = 5.15 x 1018 kg, you need to have the whole Atmosphere to first move with a velocity of 8.2 m/s or 30 km/h and then bring it to the full stop to make this difference.

I don't find this reasonable. Also Sea current's doesn't seem to provide any reasonable explanation.

Another example can be made through long term changes. The slowest rotation speed ever was measured 18.3.1973; 86400.0041340 seconds, the fastest so far was measured at 5.7.2005; 86399.9989263 seconds. This difference means that 25.6 x10^21 J of Kinetic energy was stored for 32 years.

Question; How is physically possible that such a amount of some energy is stored in Earth for such a long time, and could still be retrieved back to a rotational Kinetic energy still having even the correct (same) direction of rotation?

To help the Search; when I put the 1962-2015 data on averages; I got the following diagram; enter image description here

Which proves that the variation seem to have a certain system. Note that this is not calendar Year, it starts on Equinox; 20/21 March. The main thing to see is the +0.45...-0.75 typical annual fluctuation.

  • X-axle is 365 days from equinox to equinox.
  • Y-axle is milliseconds (ms); Cyan Line is average yearly fluctuations. Y zero point is 86400.0017371 Seconds
  • Black lines shows the Sea-Land ratio; Change in Albedo / evaporation under sun Equator, scaled mathematically to diagramm. =(7-(Land/Latitude lenght*10)^2)/10
  • Orange peaks shows she Sun Equator position in Different days; the Highest peak is sommer Solstice, and the lowest winter solstice. 0.1 = 10 Latitudes.

My Answer is; "No Way", And that Earth rotates because of sun.

  • I have calculated the functionality, and I have even found a reasonable Thermodynamical explanation for this, but it's out of the scope of this question.
  • This explanation would also bring this QED theory of Gravity from Feynman back to desk, which means that only Radioactivity remains outside of QED, and thus the probability that also it's explainable with QED is bigger than that it isn't. Which means that QED is probably ToE.
  • $\begingroup$ I'm not sure what your question is. You have to consider the entire solar system with all its bodies if you want to make some kind of conservation argument (of either energy or angular momentum) here since the earth is not a closed system. For a part of some system it's completely possible that its angular momentum fluctuates abit. What's the question about that? $\endgroup$
    – ACuriousMind
    Commented Oct 22, 2015 at 21:17
  • $\begingroup$ Thanks. I do have looked for another Planets too, Mercury and Uranus are really interesting. And I know that Moon and Earth is connected. But I can't see any mechanism through planetal gravitations which could increase the axial rotational speed of Earth. But I sure would be happy to hear one. EdiT; the Question is "Where did this acceleration/energy came from?" $\endgroup$
    – Jokela
    Commented Oct 22, 2015 at 21:19
  • $\begingroup$ One known mechanism for changing rotational speeds is Tidal acceleration. Also, the numbers in your question seem intended to suggest this is a huge effect, but on solar scales, it's really, really small. That it is a "large" effect in the human-made unit Joule means nothing. $\endgroup$
    – ACuriousMind
    Commented Oct 22, 2015 at 21:23
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    $\begingroup$ John R. Told you exactly where the biggest part of it came from. You dismissed his opinion and managed to torque him off enough that he deleted his correct answer--something I have ever seen him do before. $\endgroup$ Commented Oct 25, 2015 at 20:24
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    $\begingroup$ LOD IERS data 1962 2015 gives the LOD graph of WP which is not like the one of the post. What is the link to the source of your data ? $\endgroup$ Commented Oct 26, 2015 at 23:54

4 Answers 4


What does this small change means in form of Rotational Kinetic Energy?

There's a problem with your calculation: You assumed a constant value for the Earth's moment of inertia. The Moon and Sun raise tides on the Earth itself. These Earth tides result in subtle changes in the Earth's moment of inertia. The signature of these tides can easily be seen in the excess length of data for 1998, with the horizontal axis being $(\text{MJD}-50814)/27.32166156-0.15$, where MJD is the modified Julian day number of the day in question. About those numbers: 50814 is the Julian date for 1 January 1998, 27.32166156 is the number of days in a sidereal month, and 0.15 nicely makes the peaks hit the grid lines.

1998 excess length of day vs sidereal month

Those tidal variations account for about half of the 2.5 millisecond change in LOD from 23 May to 9 June. Those tidal effects need to be removed when analyzing length of day variations. The remaining variation is mostly attributable to the atmosphere. There are strong annual and quasi-biennial variations in length of day, and almost all of these variations are due to the atmosphere. (The oceans also play a lesser role.) The correlation between length of day and atmospheric angular momentum is very strong, depicted below.

Strong correction between AAM and tidally-adjusted excess length of day http://hpiers.obspm.fr/eop-pc/analysis/excitactive1.php?IB=1&term=1&AAM=1&option=1&dimx=600&dimy=450&langue=1&sel_option1=1&choix=3&trend=1&filter=Select+band+above&P0=1&tr=95&spec=0&freqmin=-10&freqmax=10&choixspec=4&chi_g=1&chi_f=1&TC=433&QC=100&SUBMIT=Submit+request&an1=2009&mois1=1&jour1=1&an2=2013&mois2=12&jour2=31

The annual and quasi-biennial happened to be in phase during the summer of 1998. In addition, 1997/1998 was a very strong El Nino year. This transferred excess mass in water vapor to the atmosphere during the summer of 1998. The El Nino made the northern hemisphere subtropical westerly jet turn into a subtropical easterly jet. To make matters even strong, 1998 marked the start of a strong La Nina. The combination of these events made for a very abrupt change in length of day.

Question; How is it physically possible that such a amount of some energy is stored in Earth for such a long time, and could still be retrieved back to a rotational Kinetic energy still having even the correct (same) direction of rotation?

You should look instead to angular momentum. This is the answer to your question. External torques do act on the Earth, sometimes speeding it up, other times slowing it down (see the first graph). In addition to this cyclical behavior, these tidal interactions have a smaller secular effect that increase the length of a day by about two milliseconds per century. After accounting for these known interactions, what's left is essentially a torque-free system in which angular momentum is conserved. (Energy is not.) The primary components of this system are the inner core, the outer core, the crust and mantle, the oceans, and the atmosphere.

As described above, rapid (a couple of years or faster) variations in the rotation rate of the crust and mantle are largely a consequence of exchange of angular momentum between the crust and the atmosphere, with the oceans playing a reduced role. Longer term variations (several years to several decades) are generally assumed to be a result of exchanges of angular momentum between the mantle, the outer core, and inner core. There are good (but not yet great) correlations between long-term variations in length of day and variations in the Earth's geomagnetic field, and there are signs that the inner core is currently rotating slightly faster than is the crust and mantle.


Jianli Chen, "Global mass balance and the length‐of‐day variation," Journal of Geophysical Research: Solid Earth (1978–2012) 110.B8 (2005).

John Gibson and Chopa Ma, "Signature of El Nino in Length of Day," in IERS Technical Note 26, 1999.

Richard Holme and Olivier De Viron, "Characterization and implications of intradecadal variations in length of day," Nature 499.7457 (2013): 202-204.

Philip Livermore, Rainer Hollerbach, and Andrew Jackson, "Electromagnetically driven westward drift and inner-core superrotation in Earth’s core," Proceedings of the National Academy of Sciences 110.40 (2013): 15914-15918.

Richard Ray and Svetlana Erofeeva, "Long‐period tidal variations in the length of day," Journal of Geophysical Research: Solid Earth 119.2 (2014): 1498-1509.

Kevin Trenberth and Lesley Smith. "The mass of the atmosphere: A constraint on global analyses," Journal of Climate 18.6 (2005): 864-875.

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    $\begingroup$ Thanks for interesting contribution. I still miss the calculations about the energy amounts. Energy is always conserved. But Earth is not a closed system, it receives and transmits heat (or Electromagnetig radiation, if you like). But only that. It rotates around its axis freely. The article about "Earth tides" is really interesting. I will do the missing calculations, Though the long term vertical amplitude of "Lunar node" 17 mm and the Period of 18.6 Years might not fill the needed scale. The diurnal /semi-diurnal changes might allready be neutralized in the measured rotation time it self. $\endgroup$
    – Jokela
    Commented Oct 26, 2015 at 8:29
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    $\begingroup$ Well, hmm,, I checked the 2015 data. It seams that these slow rotation peaks goes near the new moon. (+/- 5 days) And about the Earth tides, they seem to be similar as the water tides; the raise is always compensated, (pics on your link, red&blue). I cant see any physical calculation which could cause this 1 ms order change. And I would expect these planetal-variations to be really accurate. But I can see how the shade of new moon reduces the power of the sun causing quite random, weather dependent decelaration approximately at the time of new moon. -I thank you very much about this input. $\endgroup$
    – Jokela
    Commented Oct 26, 2015 at 9:47
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    $\begingroup$ @JokelaTurbine - When doing your energy calculations, you should be using the moment of inertia of the crust and mantle ($7.13\times10^{37}$ kg·m$^2$) rather than of the Earth as a whole ($8.04\times10^{37}$). A one millisecond change in the crust+mantle's rotation rate is about $4.4\times10^{21}$ joules. Spread that across the 47 days from 23 May to 9 July is just about one terawatt. That's tiny compared to the 174 terawatts the Earth receives from the Sun. $\endgroup$ Commented Oct 26, 2015 at 12:44
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    $\begingroup$ Yes. Thanks, I do agree. But If the official cause for Earth's rotation is nowadays that it rotates because of "it has always rotated" Then you are not aloud to count the 174 TW's from sun. en.wikipedia.org/wiki/Earth%27s_rotation#Origin But, I can easily agree with You from this part of my Question; My Answer is; "No Way", And that Earth rotates because of sun. :-) Cause I can't found this One terwatt nowhere else than from Sun. $\endgroup$
    – Jokela
    Commented Oct 26, 2015 at 14:10
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    $\begingroup$ @JokelaTurbine - Hold on! The Earth is indeed rotating because it always has been (and because the torques are small). There's a huge difference between the Sun providing energy to make the atmosphere and crust+mantle rotate at slightly different rates and between the Sun making the Earth rotate. $\endgroup$ Commented Oct 26, 2015 at 16:06

The most abrupt changes in the Earth's rotation rate are due to interactions between the mantle and the core. These changes are correlated with a phenomena known as geomagnetic jerks - sudden changes in the Earth's magnetic field.ref1 The mechanism is unknown, but one theory is that Taylor columns in the outer core become entrained with lumps/protuberances in the mantle.

There also is a recently discovered 5.9 year cycle believed to be caused by the mantle "wobbling" on the liquid core.ref2

The length of day is also affected by the Sun's activity (sunspot) cycle.ref3

Decadally detrended LOD data (with 6-month running average), plotted with 5.9-year oscillation fit (dashed line) Decadally detrended LOD data (with 6-month running average), plotted with 5.9-year oscillation fit (dashed line)

  • $\begingroup$ Thanks for this answer. I have thought also a lot about the interactions between the Mantle and the core, and even the Magnetic field. One known thing is that the Mercury has no atmosphere and a really weak magnetic field. Quickly studied, these Jerks; en.wikipedia.org/wiki/Geomagnetic_jerk doesn't jump out from this diagram; upload.wikimedia.org/wikipedia/commons/5/5b/… I am awere, and agree your comment about the Sun's activity and it's affection on LOD. Well, I do claim that the whole rotation origins from sun. $\endgroup$
    – Jokela
    Commented Oct 26, 2015 at 20:20

As Earth rotates, the Moon's gravity causes the oceans to rise and fall. (The Sun also does this, but not as much.) There is a little bit of friction between the tides and the turning Earth, causing the rotation to slow down just a little.

Since the amount of water in the Ocean varies this too will impact the rotational effect of tides. I can not take the time to do the calculations but this seems reasonable.

This may be the basis for spin but I am sure that ionic difference of 300,000 volts of potential between the ionosphere and the negative ground earth while rotating through the suns magnetic field will create a Lenz drag of sorts that also needs to be taken into the calculations. I will address this last point when I have some free time.

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    $\begingroup$ Thanks for the answer. The tides goes twise a day. If we calculate that the whole Ocean Surface of the world (3.6 x 10^14 m2) is raised for one meter (speks for 2 m tide) we will have 3.53 x 10^18 Joule, which is approx 0.03 % of the deeded Energy. Your idea about Magnetic field is new and interesting though,,, Thanks for that! $\endgroup$
    – Jokela
    Commented Oct 25, 2015 at 17:38
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    $\begingroup$ I calculated the 300 000 Volts potential; if it could do the work with 100% efficiency; this 47 day (4060800 Seconds) acceleration would need continuous current of 9 521 933 281 Amperes. But I am hardly seeing any mechanism how this would function. $\endgroup$
    – Jokela
    Commented Oct 25, 2015 at 20:17

I want to answer to my own Question to simply summarize the various answers;

  • 47 days change at 1998 was 2.3579 ms. Energy 11.6 x10^21 J. Needed power 2857 Terawatt.
  • 32 Year change 1973-2005 was 5.2077 ms Energy 25.6 x10^21 J. Needed power 25.4 Terawatt
  • Typical yearly Change from 24.4. to 1.7. 1.19 ms, 68 days, Energy 5.85 x10^21 J. Needed Power 1000 TW

And Both changes increased the rotation speed of Earth!

  1. Body Tides Summarize

    • 0.3 ms for a 14 day period.
    • 0.16 ms for a 28 day period
    • 0.14 ms for 1/2 year period
    • 0.02 ms for a year period.
    • 0.126 ms for Lunar node period; (18.6 years)
  2. Ocean Tides

    • Max 0.05 ms for a 14 days period
    • 0.026 ms for a Years period
    • 0.024 ms for lunar node period
  3. Earthquakes Sumatra 0.0068 ms

  4. Geomagnetic Jerks;

    • Magnitude of change almost 0.1 ms (Holme & Viron 2013)
  5. Ionosphere potential;

    • I don't understand this, or the paper of Livermore & Hollerbach 2013. Does it mean that they are meaningless. -NO, but atleast nobody can't even clearly say if this is cause or effect, and what is the Magnitude.
  6. Core and Mantle of the Earth

    • Power needed complete the 32 year acceleration; 25.4 TW.
    • Earths internal Heat 47 TW
    • The mass of the core is 30 % of the Earth's mass.

All above can be estimated to cause following difference to yearly fluctuation of LOD; - Body tides; 0.4-0,5 ms - rest, max 0.1 ms This means that approx 0.6 ms change in 68 days, which needs 2.9 x10^21 J energy and 500 TW Power remains unexplained.

  1. Atmosphere and Sun.

Hadley cell's Produces 198 TW of kinetic energy to Atmosphere in yearly average, but Ferrel cells consume's 275 TW, so we end up having -77 TW of kinetic power loss in system.

Madden-Julian oscillation, MJO rains with factor 5 compared to Hadley-Cell, and it's Hight is also 15 km, compared to 10-15 km hight of Hadley. I didn't found Information about the Energetics of Madden-Julian, but if we scale it with factor 5, based on the rain amount, we would have (5 x 198 TW ~) 1000 TW. Due to the nature of MJO, It can easily have even many times higher power. Obvious is also, that the MJO pushes and pulls the air in approx 13 000 km distance 1/3 of earths Circumference, and there is a simultaniously a mass transfer to an greater radius in order of 7-10 km. Thus acceleration of LOD is possible.

Further conclutions about the Sun's affect to LOD are;

  • Sun spots influence detected, (Lihua Ma, 2015.)
  • Needed power is easily available; 173 000 Terawatt
  • 30 % of the power is used to produce water steam/rain;
  • 1.38 x 10 ^15 kg / day, needed power atleast 26 118 Terawatt
  • Volume expansion 2.3 x 10 ^15 m3 (ie. 10 km x 482 km x 482 km)
  • Raises high during day, rains at evening. (Tropical rain belt)
  • Moves to east with 5 m/s (Reference), which means 432 km/ day
  • 1.38 x 10 ^15 kg mass is lifted up in a daily basis up to 10 km high, moves 400 km's to east and rains back down.
  • Note that the direction of the push is given by air density, which comes form air temperature. The morning 6 o'clock is the coldest point, and the afternoon at 15 0'clock is the hottest.

According to Jianli Chen, 2005, Global Mass balance and the Length-of-day Variation, Summary;

However, when a full mass balance is applied, the seasonal oceanic and hydrological exictations become too small to explain the residual LOD changes.

According to Richard S. Gross, "Earth Rotation Variations - Long Period." Page 20;

The fluctuation in the length-of-day of 1500-year period is currently unknown origin. However, given its large amplitude which is too large to be caused by atmospheric and oceanic processes but which is comparable in size to the amplitude of the decadal variations, it is probably caused by the same core-mantle interactions, such as gravitational coupling, that are known to cause decadal variations in the lenght-of-day. Decadal LOD variations

It can be concluded, that the internal energy production of Earth can't provide the needed power to the accelerating variations of LOD. It can further concluded, that only the 77 TW energy consumption of Ferrel- and Hadley Cell combination is enough to reduce the LOD around 15 ms in just 30 years. Sea-current's and other losses would only increase this. Thus, it must be concluded, that the only source for the rotation can be the sun. There is already many 4-5 ms observed accelerations in the past, happened in only 20 Years. To put these on scale, it means that the 86400 s rotation time could be achieved in only approx 20 Million years. Look other planets; Rotation of Uranus? Magnetic field of Venus?

  • $\begingroup$ I agree that there are a number of forces causes the rotational change in momentum, Tidal variations, Crust and Mantel vs Inner Core, and Magnetic Field varitations between earth and atmosphere, I would also think atmospheric turbulence would also play a role, large typhons and hurricanes as well. $\endgroup$
    – StarDrop9
    Commented Oct 28, 2015 at 13:46

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