Earth’s Axial tilt and Inclination tilt are related

When I started my journey my initial thesis was based on the assumption the Axial tilt & Orbital Inclination tilt were related to each other. Initially I thought they were just the same kind of value but expressed in a different manner. That turned out to be wrong. It took me quite some time to figure out how exactly they were related but in the end I was finally able to get all numbers working together.

In the Excel sheet in TAB “Chapter 5 Obliquity” you can find the calculations behind the relation between the Axial tilt and the Orbital Inclination tilt.

1. Current Obliquity (which is actually Axial tilt + Inclination tilt)

   My theory is the Axial tilt & Orbital Inclination tilt are related to each other.

   Currently the terms ”Axial tilt” and “Obliquity” are used interchangeable to describe the same behaviour: The angle between Earth’s rotational axis and its orbital axis. To make a distinction of what is really happening I propose to use the term “Axial tilt” to describe the angle between Earth’s rotational axis and its orbital axis but to use the term “Obliquity” to describe the RESULT of the Axial tilt and Orbital Inclination.

   I have added the OBLIQUITY formula of Chapront et al . (2002) and J. Laskar  in the excel.

   The obliquity is however defined by both an Axial tilt factor AND an Inclination tilt factor. So let’s first have a look at the current Inclination tilt value.

2. Inclination cycle

   The Wikipedia page about orbital inclination  only mention the CURRENT inclination value of ~1.57° and the Wikipedia page about Earth  also only mentions the more specific ~1.57869° as the CURRENT value, same as this website . The J2000 value has a startdate of 1 January 2000 12:00 UTC. The start of the 3D model is however 21 June 2000 00:00 UTC, so we need to take this into consideration as well.

   It was very hard to find any graph to show what is happening on a longer term with the orbital inclination of Earth.

   I could however find one source paper with a combination of the eccentricity and inclination figures across time. See below graph  coming from this paper  for more details. It seems to come from a solar system model by Varadi Runnegar and Ghil  which mentions Earth’s inclination varies between 0 and about 0.05 radians (or about 3 degrees). Just to make it clear, It is a model and nothing is confirmed. We could however derive the current trend so the values need to be in line with this paper.

   It clearly mentions the Orbital Inclination in the past was higher so we are currently decreasing across time.

   

   The Orbital Inclination picture in this paper shows the maximum and minimum degrees. I have modified the picture to show what is actually happening.

   

   As can be seen, there are three differences compared to the current model:

   • The inclination cycle has a mean value of ~1.4951°
   • The inclination cycle moves from ~0.9311° to ~2.0591°.
   • The inclination cycle is repeating the same pattern with a duration of 99,392 year years.

   Although there are some small differences between the two pictures, we can also confirm the values for Inclination tilt are fully in line in the current timeframe.

3. What are the values for the Axial tilt?

   There are several formula’s available for the Axial tilt. The value on 1 January 2000 AD 12:00 UTC was ~23.43929083°.

   Currently there is no mean value known yet. I expect however the MEAN value of the Axial Tilt to be ~23.42723° and oscillating by +/- ~0.564° (above and below).

4. What are the values for the Inclination tilt?

   The value of Earth’s Inclination to the invariable plane on 1 January 2000 AD 12:00 UTC was ~1.57869°.

   Currently there is no mean value known yet. I expect however the MEAN value of the Inclination Tilt to be ~1.4951° and oscillating by +/- ~0.564°.

5. What are the effects on Earth’s obliquity of both Axial tilt and Inclination tilt?

   Both the Axial tilt and Orbital Inclination tilt have the same angle of ~0.564°. The result is ~23.42723° +/- 2 * ~0.564°.

   The total result of the Axial and Inclination Tilt resulting in the experienced Obliquity Tilt of Earth compared to the Sun path will therefore oscillate in a period of 298,176 years between ~22.36° and ~24.58°.

   

   Now we have shown how Axial and Inclination are related to each other on the LONGER TERM values, let’s also plot them on the SHORTER TERM.

6. Obliquity broken down into Axial and Inclination with J. Laskar paper

   The first picture is a coming from the paper “Secular Terms of Classical Planetary Theories Using the Results of General Relativity” as created by Laskar  which that shows the (expected) obliquity of the axial tilt in the years 8,000 BC to 12,000 AD.

   This famous picture can be found on a lot of websites  and shows the obliquity across time.

   It shows the Obliquity to be ~23.44° around year 2000 AD.

   

   Just to make it clear, this is a theoretic model and there are (off course) no measurements outside the small timeframe around our age:

   

   I have updated the picture with the numbers as mentioned above (mean value of ~23.42723° and oscillating by twice ~0.564°) in Green. The data is compared to formula’s provided by “Chapront et al. (2002)” and “J. Laskar’s Mean Obliquity Formula” as added in the Excel sheet. The theoretically numbers of J. Laskar are completely in accordance with the measurements FOR 1000 OF YEARS around the current age (year 2000 AD). However on the longer term the predictions from J. Laskar differ from the numbers in the Holistic Universe Model.

   

   The break-down of what is actually happening is added in the next picture. In Blue the Axial Precession. In Red the Inclination precession. In Green the result of both (which was shown as “dotted Green” in the previous picture).

   NOTE: I have changed the horizontal axis in the next picture to the years according to the BC and AD values instead of counting the years from 2000 AD as shown in the previous J. Laskar pictures AND I have added the start year of 12,000 BC instead of 8,000 BC as shown in the previous J. Laskar pictures. I have done this to make the Perihelion precession cycle a little more visible (from 8,072 BC to 10,564 AD).

   

   The Axial tilt & Orbital Inclination tilt are related to each other: They work upon each other. Therefore the currently experienced ~23.44° does not only contain the axial tilt factor but also contains the inclination-tilt factor.

7. Where is the invariable plane tilted to?

   The PERIHELION-OF-EARTH orbits the Sun in in one Inclination precession period which moves Earth on its path on the invariable plane. Currently Earth is tilted ~1.57869° to the invariable plane. The mean tilt is ~1.4951°.

   The Aries-Pisces point is the highest point and the Virgo-Libra point is the lowest point.

   

   This feature of a mean value is currently not mentioned anywhere. If some astronomer could confirm it, it will be a great find to confirm the correctness of the model.

   So beside our solar system in total being tilted ~60 degrees to the galactic plane, also the PERIHELION-OF-EARTH has a specific tilt on its orbit around the Sun.

8. Comparing the Obliquity values to the current formula’s around 2000 AD

   

9. Behaviour of the Inclination tilt around 2000 AD

   

10. Long term fluctuation of Axial, Inclination & Obliquity

    To show the movements along the 298,176 year cycle, I have created an overview.

    

    We can also separate the Axial and Inclination movements

    

11. Summary inclination movement

    To close off, this is a picture of the movement of the PERIHELION-OF-EARTH as experienced from Earth. Due to Earth’s movement around the EARTH-WOBBLE-CENTER the eccentricity changes and therefore we experience it as the BLUE pattern.

    

    In PURPLE you see the dates where Inclination precession meets Axial precession (see date 1245-12-14).

    In GREEN the current date and Inclination. In year 29,200 AD we will reach the minimum and in year 78,896 AD it is maximum again. This inclination tilt compared to the stars stays fixed.

    NOTE there are only 16 FIXED PURPLE POINTS in the sky compared to the fixed stars where EVERY TIME the inclination precession meets axial precession on its 298,176 year cycle! It is a 16 spoke wheel of time!

    NOTE this does not mean automatically the experienced Inclination precession or Axial precession or Perihelion precession is always the same across time. These are average values. The reason why there could be small differences experienced on Earth is because the Axial and Inclination tilt also work upon each other and there are other smaller movements at play.

Let’s also look at the Eccentricity effect in the next chapter.