Earth’s Eccentricity cycles

Now let’s look at the eccentricity. In the previous chapters, I showed how Earth orbits the EARTH-WOBBLE-CENTER clockwise over ~22,937 years, while the PERIHELION-OF-EARTH moves counter-clockwise in 99,392 years. They meet every 18,636 years — and this meeting has a fascinating consequence for how we experience eccentricity.

1. What is the current orbital eccentricity value?

   The Sun has a J2000 eccentricity value of 0.01671022 AU compared to Earth according to this NASA website . So in year 2000 AD the PERIHELION-OF-EARTH was at a mean distance of 2,499,813.33 km (149,597,870.698828 km * 0.01671022) compared to Earth.

   There is also a VSOP87 formula which calculates the value to be 0.0167089 AU : Eccentricity time series, Nautical Almanac, 1974, page 75 in this book .

   The Interactive 3D Solar System Simulation is completely aligned to the JPL value of 0.01671022 AU on 1 January 2000 AD 12:00 UTC (see also excel sheet chapter 6).

2. What is the eccentricity cycle?

   There are a number of graphs available on the internet showing how the eccentricity moves across time. See e.g. this graph on the Wikipedia page .

   In the previous chapter I have also added below graph coming from this paper 

   
   NOTE: Both these graphs are coming from models and are not described in formulas.

   So at least to confirm: we KNOW the value of the eccentricity is currently DECREASING in time. However according to the current model it will decrease to ~0 by year ~27,000 AD. I do not think that is correct. Let me explain.

   Initially my intention was to model the orbital eccentricity in the Interactive 3D Solar System Simulation completely in line according to the current theory. So with eccentricity cycles of ~100k and ~400k as described in the Milankovitch cycles.

   NOTE: The mentioned ~100k year cycle of eccentricity is actually not calculated by Milankovitch. He calculated a ~95k year cycle, a ~125k year cycle and a ~400k year cycle but a lot of sources combine the 95k and 125k into a ~100k year cycle. See e.g. here  or here  or here  for more details.

   I explored a lot of options but was unable to fit in ~100k and ~400k year cycles correctly and understandable from a functional point of view. Additionally, in my view is not needed at all because such a pattern would be strange.

   My conclusion is the current model to explain eccentricity doesn’t take into consideration that the eccentricity will decrease and increase in the perihelion precession cycle of 18,636 years. So there are no ~100k and ~400k year cycles, but only a 18,636 year cycle.

   Off course I tried to find the source for these cycles but they seem to be theorized and not based upon hard data .

   So here’s where it gets interesting. There are five reasons why I believe the current Milankovitch-based orbital eccentricity theory needs revision:

   1. There is no ~100k year eccentricity cycle theorized at all (but ~95k and ~125k) while this ~100k year pattern is showing up in reconstructed historical geologic temperature records of Earth.
   2. There is no ~400k year pattern in the geological temperature record over the past 1.2 million years 
   3. The eccentricity changes do not have sufficient effect on the total change in global annual insolation . So the theory doesn’t explain the result.
   4. The theorized ~95k, ~125k, ~400k year cycles are really.. theorized. There is no data at all. It is mainly based upon Jupiter-Saturn gravitational resonance .
   5. Milankovitch did not study planetary precession. It was discovered more recently and measured to have a period of about ~70k years against ecliptic and ~112k years against ICRF. With this missing crucial movement you cannot calculate Jupiter-Saturn gravitational resonance correctly at all.

   The most simple explanation is therefore: Because of the motion of Earth around the EARTH-WOBBLE-CENTER and the PERIHELION-OF-EARTH around the Sun in opposite direction, the distance from Earth relative to the PERIHELION-OF-EARTH changes and therefore the eccentricity of Sun-Earth distance changes in a cycle of 18,636 years.

3. What is the MEAN distance from the PERIHELION-OF-EARTH to EARTH-WOBBLE-CENTER?

   Here’s the puzzle. We can’t calculate this value directly from available data, but we can derive it by adding the proper numbers into the Interactive 3D Solar System Simulation because we know these three elements:

   1. The minimum eccentricity value was reached in 8072 BC when perihelion was aligned with the summer solstice.

   2. The maximum eccentricity value was reached in 1246 AD when perihelion was aligned with the winter solstice.

   3. The currently experienced eccentricity is a value between the max eccentricity and min eccentricity values and since it is decreasing, the MEAN value needs to be – at least - below 0.01671022 AU.

   You can use these three elements in the Interactive 3D Solar System Simulation and you will come to a MEAN distance of 0.01370018 AU.

   The eccentricity has a cycle similar to the 18,636 year Perihelion precession cycle. The maximum eccentricity in this period is 0.01370018 + 0.00308211 AU which is ~0.01678229 AU. The minimum eccentricity in this Perihelion precession period is 0.01370018 - 0.00308211 AU which is ~0.01061807 AU.

4. Visualize the Eccentricity cycle

   Let me show you what the current theory predicts versus what I propose. The first picture comes from this physics document  and shows eccentricity values across time according to the current model.

   Again to remind: These are theoretically models and not measured (apart from the small period from ~1,500 AD to the current era).

   

   I have modified the picture with values as presented in this chapter to visualize the eccentricity movement. You can also have a look at the Interactive 3D Solar System Simulation and you should see the same behaviour.

   

5. Comparing the Orbital Eccentricity values to the current formulas

   Let me walk you through the different timescales to show how these values compare.

   First, here’s the expected Eccentricity cycle ~25,000 years in both directions around our lifetime:

   

   The same picture as above including existing Eccentricity formulas showing close agreement in recent millennia:

   

   And focusing on tens of thousands of years around our current era:

   
   NOTE: The trend of the orbital eccentricity can be modelled but modelling it exactly like theorized with cycles of ~100k/ ~400k is in my view not needed. Both from a functional point of view as from a technical point of view, cycles of 18,636 years are just as valid. After all we do not know the historic values.

Now that we understand how eccentricity cycles work in this model, let’s explore the values of Earth’s rotation (ΔT) in the next chapter.