The movements of the Planets

Initially I only focused on the different cycles of precession/ obliquity/ inclination/ eccentricity for Earth. The movements of our Moon and the planets are however also added to the model.

It is not enough to just add numbers that are MORE OR LESS in line with the observed orbit. They need to FULLY in line with the observations and the current scientific numbers as well. So e.g. planet movements aligned with all recorded planetary ephemerides, completely in line with oppositions, conjunctions, transits and other periodic interplanetary alignments including all solar and lunar eclipses. For most part they are all available in the model.

As a result the perihelion precession of all planets is now configured in the Interactive 3D Solar System Simulation as well. The perihelion data of the planets comes directly from the 3D model itself. It is calculated in the apparentRaFromPdA function which compares angles between the configured PERIHELION-OF-EARTH point and the other perihelion points of the planets.

There are however assumptions taken as input to the model which off course need to be tested and proven.

For a quick start you can compare the numbers in the model and this overview page . The last column shows the longitude of Perihelion across time coming from this study  by Simon, Bretagnon, Chapront, Laskar et all. I have added the formula’s in the Excel as well.

As a consequence – and I find it very hard to say – Einstein’s theory of relativity is NOT proven by the missing perihelion precession of Mercury. I am definitely not saying there is no theory of relativity. I lack the knowledge for this one. All I am saying is the observed perihelion precession of Mercury is the result of the clockwise movement of the Perihelion point combined with Earth’s wobble. Therefore certain movement is “missing”.

One thing to note upfront is we need to get to a common source for the observed location of the planets. On the internet there are plenty of sources available but they are mostly conflicting with each other.

There is off course NASA with the JPL Horizons  and Webgeocalc  but also these sources have conflicting data.

I am confident we can really create a good source ourselves with the help of the Interactive 3D Solar System Simulation. One that could be verified in time and which is not based upon calculations per epoch (J2000, J1900, J2015, etc.).

In this chapter I will explain the background of the settings that are currently added.

Interactive 3D Solar System Simulation limitations

The Interactive 3D Solar System Simulation has been built in three.js but has however two limitations compared to the movements as described in the current version of the Heliocentric model.

1. Constant speeds

   The movements of Earth, the Sun, planets and Moon orbits can only be added with constant speeds. In other words, Kepler’s second law of variable orbital speeds are not added in the model.

2. Circular orbits

   The movements of the Earth Sun, planets and Moon orbits are mostly added with circular orbits. In other words Kepler’s first law of elliptical orbits  are not added in the model.

   However I have added mostly two orbits to most planets. This is effectively causing a real elliptical orbit. But e.g. the Sun is added with “just” one circular orbit. I will leave it up to experts to determine if the Sun really needs to have an elliptical orbit or a circular orbit fits just fine.

So effectively there is only one real limitation compared to the heliocentric model: The constant speeds. I (again) will leave it up to experts to answer the question if this tool can be used to model all movements correctly or alternatively – if we need to model the speed-differences in as well.

Aphelion and Perihelion of planets

The aphelion/perihelion points are added as orbital points. These orbital points – which are showing as a planet’s PERIHELION - are fully modelled according to Kepler’s third law.

The end result will show these perihelion-points of the planets are actually currently structured according to a Spiral pattern. Let me further explain.

Below you will find a picture that shows the Longitude of perihelion (which technically is the Longitude of the ascending node + the argument of periapsis) placed in a circle with dates of aphelion as a snapshot date on date 21 June 2000 00:00 UTC, the start of the Interactive 3D Solar System Simulation. All data is coming directly from NASA , with the exception of the exact data calculated for the position of the PERIHELION OF EARTH (which is the Earth-Sun perihelion/aphelion point) which is coming from the formula for the Longitude of perihelion precession calculations taken from Meeus, Jean. Astronomical Algorithms. 2nd Ed. Willmann-Bell. 1998 Table 31.A. See also the link  which results in solstice-perihelion alignment in the year 1246 AD.

What is really nice - and for which I could not find any reference it has ever been done before - now we have the degree coordinates, we can also add the approximate dates next to these coordinates.

The picture shows the approximate date for the planets to reach it’s aphelion/ perihelion position. With these dates we can determine the DIRECTION of the location of the perihelion.

So e.g. Mars perihelion is around 26th of August 21:48 UTC and aphelion is around 23rd of February 06:25 UTC. This does not mean that each year Mars is closest to Earth on these dates but it means, the THEORETICALLY CLOSEST Mars could come to Earth is around these approximate dates. So e.g. in year 2003 AD Mars has one of the closest approaches. See for instance here 

By studying the provided NASA values of eccentricity and knowing the location-direction of the Perihelion, we can also calculate the location position of the Perihelion.

The below picture shows the EXACT LOCATION of all planet Perihelion with the dots plotted. These dots are (off course) also in the Interactive 3D Solar System Simulation:

To see the Perihelion in the Interactive 3D Solar System Simulation for yourself:

• Go to the 3D model (link in right top corner)
• Open “Perihelion Planets”
• Press “Perihelion Spiral”

Or if you want to see the individual points:

• Go to the 3D model (link in right top corner)
• Open “Settings”
• Open “Objects show/hide””
• Select ALL planets which mention “PERIHELION” (so e.g. “PERIHELION Mercury”

• Select the option “1 second equals” “1000 years”
• Press “Run”

And see the planet Perihelion points turn clockwise in a period of one holistic year of 298,176 years around Earth. Initially it starts more or less as a golden spiral, but the structure changes across time if we take all currently accepted scientific numbers as input.

The perihelion values of the planets are mostly in line with the formula. For Mercury they are quite exact.

Ascending and Descending nodes of planets

This website  helped me to explain the way the ascending & descending nodes need to be looked at.

I also created some pictures of all planets where the ascending and descending nodes are located.

The Ascending and Descending nodes are added in the code with formula’s based upon the “Orbital Inclination” and the “Longitude of ascending node” values as provided by NASA/ Formula’s.

How are these planet settings calculated?

In the Interactive 3D Solar System Simulation all calculations are based upon the following three principles:

• All the calculations are grounded with scientific data (e.g. the ascending/ descending nodes, eccentricity values, etc).

• The locations of the perihelion points are calculated clearly. You cannot cheat by adding calculation onto calculation in the Interactive 3D Solar System Simulation.

• The orbital elements of the planets are fully calculated based upon Kepler’s 3rd law.

  ”Kepler’s Third Law of Planetary Motion: The square of the period of a planet’s orbit around the sun is proportional to the cube of the size of its orbit”

So although the current heliocentric model sees some connection between the time of the orbit and the size of the orbit according to the Kepler’s 3rd law, in the Interactive 3D Solar System Simulation there is a DIRECT CONNECTION modelled.

In the code you can dive into how all elements are exactly calculated. To help you I have also created a mindmap  where you can see how the calculations are build up.

Below an example how Jupiter’s calculations are structured:

barycenterEarthAndSun.pivotObj.add(barycenterPLANETS.containerObj);
barycenterPLANETS.pivotObj.add(jupiterPerihelionFromEarth.containerObj);
jupiterPerihelionFromEarth.pivotObj.add(jupiterbarycenterPLANETS.containerObj);
jupiterbarycenterPLANETS.pivotObj.add(jupiterPerihelionFromSun.containerObj);
jupiterPerihelionFromSun.pivotObj.add(jupiter.containerObj);

It works like this:

• All calculations start at the location of the PERIHELION OF EARTH ”= barycenterEarthAndSun” in the code.

  The PERIHELION OF EARTH is the base of the Sun and all planet calculations and as mentioned before, the PERIHELION OF EARTH is moving across time:

• From the PERIHELION OF EARTH, the speed of the planet’s perihelion is added as the barycenterPLANETSXX.

  Now the location of the Perihelion point can be set:

• From the barycenterPLANETS, the planet’s perihelion location is set.

  The speed of the perihelion is moving and as a result we need to add the counter movement:

• From the planet perihelion, the counter movement of the barycenter movement is set.

  Now we will move from Earth location to the Sun location because the movements are compared to the Sun:

• From the counter movement you go to one mean distance to the Sun (+100 in the model) including the tilt of the orbit.

  And lastly the orbital parameters of the specific planet can be added:

• The orbital elements are added + the ascending and descending nodes numbers are set ”= jupiter” in the code.

The most important orbital elements of our planets can be found in the 3D model.

Let’s focus per planet how they are modelled.

MERCURY

Mercury is fully in line with the transit data by NASA.

Input: Mercury transit data 

VENUS

Venus is fully in line with the transit data by NASA.

Input: Venus transit data 

MARS

Mars is fully in line with the opposition data as provided in the below mentioned input sources.

Here’s the observed sequence of Mars-Deneb Algedi conjunctions - between the years 2005 and 2020 (i.e. a 15-year Martian cycle):

An interesting consequence of the eccentricity of the orbit of Mars is that when Mars comes closest to Earth (every ~779.926) its distance from us can vary significantly. As a result, its angular size at closest approach will vary significantly and so determine the amount of surface detail that we can see from Earth.

Mars is closest to us when it is on the opposite side of the sky to the Sun. Mars will be seen with the smallest angular size at opposition when Mars is furthest from the Sun (at aphelion) and the Earth is closest from the Sun (at perihelion). Picture © NASA

Input: Mars opposition data1 
Input: Mars opposition data2 
Input: Long term MARS positioning 

JUPITER

In the Excel TAB ”Chapter 9 Planets start” I have added the Saturn/ Jupiter alignments that I could find in Stellarium and the data in the interactive 3D solar system simulation (check it for yourself).

Input: Jupiter-Saturn data 
Input: Jupiter-Saturn data 
Input: Jupiter-Neptune data 

SATURN

Jupiter and Saturn are ”mostly” in line with the alignment data as provided in the below mentioned input sources.

Input: Jupiter-Saturn data 
Input: Jupiter-Saturn data 

URANUS

NEPTUNE

Input: Jupiter-Neptune data 

Input: other data 

OTHER SOLAR SYSTEM OBJECTS

The orbit of asteroid 433 Eros  has been added as well. I couldn’t find any historic records so that could be refined further as well.

The basics for Pluto and 1P/Halley a.k.a. Halley’s Comet  are added as well but need further detailing to be correct. I didn’t just want to add random orbital numbers but it needs to be based on scientific input data (e.g. eccentricity numbers).

Recommendation before continuing

Before we add all other bodies I think we first need to agree on the correctness of all calculation formula’s and how they are added in the configuration.

In my view there are – at least - 3 type or orbits we need to add in the model, and for which there are different formula’s:

1. Solar system Bodies between the Sun and Earth with a Synodic period smaller than a year (e.g. Mercury, Venus, etc.)
2. Solar system Bodies that can go around Earth with a Synodic period greater than a year (e.g. Mars, 433 Eros, etc.)
3. Solar system Bodies that do not go around Earth with a Synodic period smaller than a year (e.g. Jupiter, Neptune, etc.)

I am calling the community to step in and bring the model further.

It is very hard to elaborate on all individual settings in the Interactive 3D Solar System Simulation on paper. There are too many connections that take a lot of time to explain fully. It is best to just have a look at the setting, and look in the Excel how and why this setting is set as it is. You can study the model for yourself.

I have updated the code of the Interactive 3D Solar System Simulation as such, so it is quite easy to play with certain settings. You can for instance play with eccentricity to see e.g. what will happen with perihelion movements or what will happen with the planet position in time, etc. This is a very nice feature which is created for the first time in history.

You can also just fill in individual numbers yourself and see if you can create a better version of the model. Up to you.

For all planet characteristics, see Excel sheet “Holistic-Universe-Model.xls” TAB ”Input 3D Model”. & all “Chapter 09” planet TABs.