Appendix IV — The movements in the heliocentric model

The current model involves numerous complex movements. Below, I summarize the most significant ones. These movements can be categorized based on the body in motion—Earth, Sun, or Galaxy. Additionally, the motions of these bodies can be divided into three primary types: rotation, linear motion, and precession (also known as nutation). While smaller perturbations also occur, I have not included them in this summary.

Earth movements

1. Rotation Earth: The Earth rotates around its axis

   There are three rotational observations:

   • The Earth rotates 360°on its axis relative to the Sun in one "mean solar day" which is ~86,400 SI seconds (24 hours). The length of a solar day can differ through time. Therefore it is ~86,400 SI seconds.
   • The Earth rotates 360°on its axis relative to the precessing mean vernal equinox in one "Sidereal day". The sidereal day value is fluctuating around 86,164.09053083288 SI seconds, or 23 hrs 56 min 4.09053083288 SI seconds (23.934469591898 hours) or 1.002 737 909 350 795 of Solar day according to a study in 1986. NOTE: The sidereal day is fluctuating in time.
   • The Earth rotates 360°on its axis relative to the International Celestial Reference Frame (ICRF) in one "Stellar day". According to below link this rotation is not affected by precession. The duration is 86,164.0989036905 SI seconds, or 23 hrs 56 min 4.0989036905 SI seconds (23.9344719176918 hours) or 1.002 737 811 911 354 of Solar day. NOTE: The stellar day is ARTIFICIALLY chosen and based upon the length of 86,400 SI seconds a day.

   See e.g. useful constants (opens in a new tab)

   The Earth has a circumference of approximately 40,075 km. The rotation speed of Earth is slow but results in a speed at the equator of ~1,674 km/hr.

2. Motion Earth: The Earth revolves around the Sun once a year

   The Earth's is orbiting around the Sun in an ellipse form and travels at different speeds during the year - slowest at Aphelion (furthest point from the Sun) and fastest at Perihelion (closest point to the Sun) Earth's current orbit (the path) is approximately 940,000,000 km in ~365.24219 days.

   The length of the solar year differs across time. Astronomers use the term Epoch for this. Current calculations are based upon Epoch J2000. This site (opens in a new tab), which also has a downloadable excel sheet (epoch_calc_v2012.xls), helped me a lot in looking at the numbers of past Epoch. Please note: There are theories underneath the calculations of the Epoch, so on shorter term they are more predictable then on longer term.

3. Motion Earth-Moon system orbits a "gravitational center"

   Both the Moon and the Earth orbit a common center of gravity. The mass of the Earth (ME) is 5.9742 * 1024 kg, and the mass of the Moon is 7.349 * 1022 kg - the Ratio of the masses is 81.3 So the center of gravity is therefore located 1 unit from the Earth's center and 81.3 units from the Moon's center

   Earth pivots around this point once every Lunar Month (on average 29.53059 days)

4. Precession1 Earth: The Earth's polar axis direction has a cycle of ~25,771 years

   This Earth’s movement is also called wobbling or “precession of the equinoxes” or “general precession” or “axial precession “ or “lunisolar precession “ or “precession of the equator “ and describes the circular tilting of the Earth’s polar axis, which is the position change of the Earth's North-South rotation axis in relation to the Earth’s orbit around the Sun. The Earth's North-South rotation axis "wobbles" like the slow rotational tilting of a spinning top over a period of 25,771 years (50.3 arcseconds/year).

   The movement is in the negative direction of the calendar, so each year it is a little bit earlier in time. This affects the direction in the sky to which the polar axis points and, in fact, the orientation of the entire orbital path of the Earth.

   The theory is, this precession is caused by the gravitational attraction of the Sun (and the Moon) tugging on the Earth's equatorial bulge.

   Currently the polar axis points to the North star Polaris. The North Star will be Vega instead of Polaris by the year 13,500 AD according to the current heliocentric model.

5. Precession2 Earth: The Earth’s closest approach to the Sun has a cycle of ~21,000 years

   The moment Earth is closest to Sun is called Perihelion. The furthest point is called Aphelion. In year 2000 the perihelion point of our Earth was around 3rd of January and the aphelion point was around 4th of July.

   The movement of the aphelion/ perihelion point in time is called Apsidal precession. Technically Earth's apsidal precession slowly increases its argument of periapsis. The movement is in the positive direction of the calendar so each year it is a little bit later in time. This movement is also known as “apsidal advance” or “precession of the perihelion”.

   The real movement of the apsidal precession compared to the background stars is actually around ~112,000 years. But since the axial precession of 25,771 years is in the opposite direction to the apsidal precession, they meet each other around every ~21,000 years.

   So according to the current theory around year 23,024 AD (2024 AD + 21,000), the perihelion will again by around 3rd of January just like currently in year 2,024 AD – in the heliocentric model.

   There is also a moment in time the aphelion/ perihelion is on the same date as the solstices. The last time this happened was around year 1246 AD. According to J. Meeus, on 14th of December 1246 AD, winter solstice was in line with the aphelion. See e.g. this Wikipedia page about the equation of time (opens in a new tab) or this EarthSky article (opens in a new tab).

6. Precession3 Earth: The Earth’s obliquity (axial tilt) has a cycle of ~41,000 years.

   The axial tilt in year 2000 AD was around 23.43922988 degrees and moves between 22.1 and 24.5 degrees. Currently the motion is decreasing.

   The theory is the higher the obliquity (axial tilt), the more it results in strong seasonal contrasts and therefore is the main driver for climate predictions related to Earth cycles according to the Milankovitch cycles.

7. Precession4 Earth: The Earth’s orbital inclination changes every ~70,000 years.

   Currently the “orbital inclination” is around 1.57869°. This type of precession is also known as “Planetary precession” or "Precession of ecliptic" and has a duration of around 70,000 years and is making the Earth’s path on the ecliptic orbit around the Sun to modulate in amplitude from 0.7° to 2.4°. As mentioned by Wikipedia (opens in a new tab) when measured independently of Earth's orbit, but relative to the invariable plane (ICRF), this type of precession has a period of about 100,000 years.

8. Precession5 Earth: The Earth’s polar location changes slightly every 14 months.

   The Earth’s spinning top wobbles causing the location of the North and South Poles to vary by 3 to 15 m. This Chandler Wobble causes the latitude of any position on the Earth to move a few metres in this 14 month cycle and therefore affects GPS readings

Please note the precession period: 1/25,771 - 1/70,000 = ~1/41,000.

Sun movements

1. Motion1 Sun: The Sun (and Earth) revolve around the Solar System "gravitational center"

   The Sun's mass is 1.9891 * 1030 kg it is 332,950 times heavier than our Earth. The Earth does cause the Sun to wobble but it is a very tiny motion. On the other hand, Jupiter (the heaviest planet in the Solar System) causes a much more appreciable wobble in the Sun. Sun wobbles around a point just outside its surface every 11.859 years (the length of Jupiter's orbit).

2. Motion2 Sun: The Sun revolves around the Galaxy once every 250 million years

   The Sun's position in the Milky Way Galaxy is about 2/3 of the way out from the center to the edge of the galactic disk, (and about 20 light years north of the galactic plane). Estimates of the Sun's distance from the center of the Milky Way Galaxy range from about 25,000 to 28,000 light years (a light year is around 9,461,000,000,000 km)

   The speed of our Sun around the Milky Way galactic centre is about 230 km/s (828,000 km/h)

   

Milky Way Galaxy movements

1. Motion Galaxy: Our Galaxy is moving through the Universe

   The universe has been expanding ever since the Big Bang started, about 13.8 billion years ago. All galaxies are moving away from each other at a speed proportional to the distance that separates them. We can’t measure our speed relative to our starting point because the universe has no center or edge. If there were nothing to disturb this motion, we would be stationary relative to the radiation left over from the big bang, the cosmic microwave background radiation. However, we are moving towards the Leo and Virgo constellations, pulled there at more than 600 km/s by a group of galaxies dubbed the Great Attractor (opens in a new tab).

   The search for the exact role of the Great Attractor and the fate of our galaxy is off course not fully known yet The mysterious Great Attractor that’s pulling us in (opens in a new tab)

   There is also a theory for Dark Flow (opens in a new tab) that contradicts with the Great Attractor.

   There are more motions between our Milky Way Galaxy and other nearby galaxies at play, but I will not go further into details. The net result – according to the current theory - is we are moving towards the constellation Leo at a speed of ∼600 km/s (2 160 000 km/h or about 0.2% of the speed of light)

As can be concluded our solar system is definitively not a flat disk that is hardly moving with some planets revolving around them. If you only consider the Sun movement, it looks more something like this This is how we move through space (opens in a new tab).

The universe is full of motions, rotations, and precession forces, with countless fluctuations at play. The ones mentioned above are the most significant, but even they are only part of the picture. What we observe can never be perfectly captured by a formula. All motions are approximations because everything is constantly in motion.

As a result of all the Earth motions, the eccentricity, axial tilt and therefore insolation of sunlight on Earth’s surface changes over time which (partly) causes the climate on Earth to change. One of the first to describe these effects, was Milutin Milanković. He created what is now called “The Milankovitch cycles”.

The Milankovitch cycles show the effects of all Earth movements

Milankovitch cycles describe the collective effects of changes in the Earth's movements on its climate over thousands of years. The term was coined and named after the Serbian geophysicist and astronomer Milutin Milanković. In the 1920s, he hypothesized that variations in eccentricity, axial tilt, and precession combined to result in cyclical variations in the intra-annual and latitudinal distribution of solar radiation at the Earth's surface, and that this orbital forcing strongly influenced the Earth's climatic patterns. He performed highly accurate calculations which recreated Earth’s insolation history.

As shown above, the date of perihelion does not remain fixed, but in ~21,000 years, slowly regresses (moves later) within the year. There is strong evidence that this long-term change in the date of perihelion influences the Earth's climate.

For further explanation, please take a moment to have a look at the wikipedia article (opens in a new tab)

Earth’s historic ice ages can largely be explained by Milankovitch cycles, but gaps remain in this theory. For example, the observed ~100,000-year cycle of Earth’s temperature peaks does not align with the calculated Milankovitch cycles. However, the existence of these cycles at least suggests that periodic forces are at play.

In the current heliocentric model, the movements of Earth, the Moon, planets, Sun, and galaxy are seen as unrelated. For instance, Earth’s axial wobble is not connected to its apsidal precession, and we are thought to be rushing through space at tremendous speeds, never returning to the same point. Gravity is the main force holding everything together, while dark matter binds galaxies and dark energy drives cosmic expansion.

Creating a comprehensive 3D model of the universe using these heliocentric parameters —one that can stand the test of time— is challenging, if not impossible. I have yet to find a fully predictive model. Most existing studies isolate one factor and attempt to forecast future behaviour, but I question the completeness of such approaches.

The model described in this book aligns with current scientific observations but suggests that precession movements are interconnected. In this view, the enormous galactic speeds we perceive are more conceptual than actual. If we consider the Sun as orbiting Earth (or a point near Earth), and Earth as slowly moving along its own precession orbit, the dynamics change significantly.