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

The speeding up and slowing down of Earth’s rotation is quite a difficult concept. I could not find a clear, understandable description what exactly is going on and how it is related to the Length of Day and Delta-T values. I will give my interpretation in this chapter.

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 is 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 needed 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 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 will indeed further slow down

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

I explicitly mention “seems” because the reason why it shows as the V-shape 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 after that time increased. The value of Earth’s Length of Day is just slowly increasing in time with small fluctuations resulting in this pattern of Delta-T.

The slowing down of Earth rotation in the past century will in my view continue with ups and downs and due to this cyclic effect, there a temperature fluctuations as well.

The trend for the length of day (and therefore Earth’s rotation) is in my view directly related to the perihelion cycle. The 18,636 year cycle starts (and ends) when the PERIHELION-OF-EARTH is aligned with the solstice.

The last time the alignment of the PERIHELION-OF-EARTH with the December solstice happened 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 and therefore on Earth’s rotation.

As shown earlier the PERIHELION-OF-EARTH is not moving at uniform speed. The pattern of the LOD will be exactly inversely.

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 cyclic. My theory is, just like mentioned in several studies above, these cycles are - at least for some part - related to Length of Day/ Earth’s rotation values.

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.

In my view the length of day seems actually to be related to the climate changes (temperature movements) and therefore both these graphs with historic values of Delta-T and the length of day, can’t be correct compared to the temperature graphs.

So the length of day, together with Earth’s rotation (and therefore Delta-T) is fluctuating and as a consequence the temperature changes. But according to above graphs the length of day comes from an absolute zero point and goes up indefinitely. This can’t be right.

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 Delta-T.

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).

The movement that is actually happening:

So to summaries: as the length of day (LOD) increased, the rotation of the Earth is slowing down. The LOD increase moves in cycles and 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.

Let’s have a look at the movements of the moon in the next chapter.