Earth’s Rotation cycles = Length of Day (LOD) cycles causing ΔT

This topic took me a while to wrap my head around. The speeding up and slowing down of Earth’s rotation is quite a difficult concept, and I could not find a clear, understandable description of what exactly is going on and how it relates to the Length of Day and Delta-T values. Let me share my interpretation.

Earth’s Rotation determines the Length of Day (LOD)

According to scientific research Earth’s rotation has gradually been slowing down in the past century .

This resulted in a slight increase in the length of a day (LOD)  in the past century on average around 1.7 milliseconds per day.

Earth’s rotation is not slowing down at a uniform rate, so it might differ per year AND it can move in cycles across centuries. This slowing down of Earth’s rotation has implications for timekeeping systems on Earth.

Two major time keeping systems

There are basically TWO MAJOR definitions of time keeping systems but - just for you to be aware - there are lots  of  more . The two major timekeeping systems are :

• TT is a fixed length of time, artificially chosen as 86,400 SI seconds a day.

  “Terrestrial Time (TT) is a theoretical uniform fixed time scale which coincidentally aligned to the mean Solar day around 1820 AD which was 86,400 SI seconds”

• UT is time as eventually actually experienced on Earth. Sometimes it is longer than 86,400 SI seconds and sometimes it is shorter than 86,400 SI seconds.

  “Universal time (UT) represents the observed rotation angle of the Earth relative to an inertial reference frame”

So – according to the current theory - the length of day (LOD) as measured on Earth (UT), has increased compared to the length of day (LOD) fixed TT value of 86,400 SI seconds a day in the past century The TT value can be considered as the IFRS time/ atomic time. Independent on the LOD changes. That is why TT it is more suitable for the predictions of astronomical events. The TT LOD is however set to 86,400 SI seconds as the mean value and ** EVENTUALLY** should be set to the real mean value.

Delta-T changed due to the difference between TT and UT time

The difference between TT and UT results in Delta-T 

If the Earth rotates slower (i.e. LOD > 86400), UT falls behind, and ΔT increases over time. So If LOD > 86400: ΔT increases (positive trend).

Delta-T has been increasing over time as the Earth’s rotation slowed down. As a result we sometimes need to add additional leap seconds to Coordinated Universal Time (UT) to maintain synchronization with atomic time.

We can also decide not to add/ subtract any leap seconds but the result will eventually be noon will no longer be at the exactly the middle of the day.

The value of Delta-T around 1900 AD has been ~0 and as of 2020, TT was ahead of UT by ~69 SI seconds.

“ΔT is the time difference ΔT = TT − UT between Universal Time (UT, defined by Earth’s rotation) and Terrestrial Time (TT, independent of Earth’s rotation), which results in a drift in the length of a day as experienced on Earth”

The following graph can be found on the Wikipedia page  about the historic values of Delta-T from 1650 AD.

The institution responsible for maintaining global time is the ”International Earth Rotation and Reference Systems Service” (IERS) . On their website  you can find a lot more information as well.

Explanation Earth’s rotation is slowing down in the past centuries

Here’s where the Delta-T graph becomes revealing. Earth’s rotation has not slowed down at a uniform rate, as shown in the Delta-T picture from 1650 AD till 2020 AD. The Delta-T value first seems to went down, and then up again.

I explicitly mention “seems” because the reason why it shows as the V-shape for the Delta-T value is because UT reached exactly the 86,400 seconds a day at that moment in time. Before ~1800 – 1900 AD TT was ahead of UT and after that time UT was ahead of TT. So Delta-T decreased before ~1800 – 1900 AD and afterwards increased.

The value of Earth’s Length of Day is just slowly increasing in time with small fluctuations which crossed the 86,400 seconds a day point somewhere around 1850 AD resulting in this pattern of Delta-T.

The slowing down of Earth rotation / longer length of a solar day, is not moving forward in a straight line but goes with up’s and down’s. Sometimes the length of day is behind the trend-line and sometimes it is further than the trend-line.

There is however a trend which just shows Earth’s length of day is increasing / Earth’s rotation is slowing down, over the past centuries.

The trend of the length of day is inversely to the movement of the PERIHELION-OF-EARTH

And this is what ties it all together: the trend for the increasing length of day is directly related to the perihelion cycle. The 18,636 year cycle starts (and ends) when the PERIHELION-OF-EARTH is aligned with the December solstice.

The last time the alignment of the PERIHELION-OF-EARTH with the December solstice occurred was at the start of year 1246 AD. You can check it in the Interactive 3D Solar System Simulation. On JD 2176142 the value of the PERIHELION-OF-EARTH is at 6:00:00.

By the year 10,564 AD the PERIHELION-OF-EARTH will align with the June solstice. The flow from solstice alignment to solstice alignment has an impact on the length of day / Earth’s rotation.

The pattern of the trend of the LOD will be exactly inversely to the movement of the PERIHELION-OF-EARTH.

So the PERIHELION-OF-EARTH movement has been slowing down in the past centuries resulting in a longer Length of days.

The fluctuations to the LOD trend might explain the smaller temperature cycles

This connection has fascinating implications. In the picture below coming from this paper , which you can find on several sites, the temperature cycles on the northern hemisphere for the last 10,000 years are presented.

You can clearly see these temperature changes are fluctuating.

Now let’s zoom into the last little ice age which ended around 1880 AD . Since then we are living in a relatively warmer period.

I found below graph on this website  which provides an overview of the fluctuation LOD values.

You can clearly see the LOD changes are fluctuation as well.

As mentioned above, the trend of the LOD also has a pattern. We can create a zoomed in picture to show the pattern from year 0 to 3000 AD.

We can plot these two patterns in the same picture. Additionally I have added the graph of the global temperature in it which can for instance be found over here .

So the current expected value according to the trend-line is ~86,400.003 seconds a day but we are now well below the trend. That might explain why Earth’s global temperature had become severely warmer in the past century.

Earth current values of the Length of day well below the trend of the LOD seems to reach a minimum stretched value and as a result I expect it will reach the turning point IN OUR LIFETIME.

This is not a new theory. The Length of Day (LOD) cycles and climate cycles might be related to each other as also stated in several studies like this one from 2006 , this one in 1976  and this one in 2010 . There are a lot more websites and studies that mention this same link.

Why does the Delta-T graphs extrapolate exponentially into history?

I also found some graphs about the historic values of Delta-T from longer periods. This graph comes from this website 

On the IERS website  and in the same document mentioned above you can also find the Length of Day (LOD) historic values from 2000 BC to 2500 AD.

You can clearly see both graphs are inversely correlated with each other. The longer the length of day, the more the value of Delta-T declines and vice versa.

Historic values of Delta-T are based upon Moon observations, either via eclipses or occultations , which can be explained by Earth’s movement on its Axial Precession Orbit (APO). You can have a look at the Interactive 3D Solar System Simulation on the effect.

Earth is slightly turning on its orbital path around EARTH-WOBBLE-CENTER, causing the Moon to slightly turn as well, which had an impact on the observed point in time which shows as an increase in ΔT.

The graph about the historic values of Delta-T from 720 BC coming from this site , seems to show a circle, which has most probably a “furthest left point” in year 3411 BC and a most “furthest right point” in year 5903 AD. Just like the perihelion cycle. But what this actually shows is Earth’s movement on its Axial Precession Orbit (APO).

I don’t think this is correct. The movement that is actually happening:

The trend of the length of day had a turning point around year 1246 AD and as a result the extrapolation is not correct.

So to summarize: The length of day (LOD) increase / the rotation of the Earth is slowing down, is moving in cycles. The LOD increase does not only move in cycles compared to a trend-line, but also on cycles ON this trend-line. As a consequence we sometimes have warmer periods and sometimes have colder ones.

I think there is a dance going on between UT and TT: Sometimes UT is ahead of TT and sometimes UT is behind on TT. In the long run however it is levelling out on the UT value of the mean length of day (LOD).

I created below graphs with some more background on the dance between UT and TT. All data is in the Excel based upon the Interactive 3D Solar System Simulation.

Now that we understand how Earth’s rotation cycles connect to climate patterns, let’s explore the movements of the Moon in the next chapter.