Saturn


The illustration on the right side of this page shows the Dendera Zodiac in its natural state with no rotations applied to the stones and with the God that represents Saturn, already identified by scholars in the past from its hieroglyph inscription, highlighted in the night sky circle. The decryption rotations need to be applied to the stone circles to be able to start to analyse the manner in which Saturn is encoded into the carving, which can be performed by clicking the next button, noting that the decryption rotation places the staff of the Saturn God perfectly aligned with the Y axis of the sculpture.


The starting lines and circles for the formation geometry of Saturn can now be added to the illustration using the experience from the previous planet systems where the principal astronomy angle lines of the previous planet, Jupiter, are moved to the Jupiter planet system's secondary orbital focal point. In addition to the three primary astronomy angle lines the GM alignment line for Jupiter, which was explained on the previous page, can also be added to the display and these features can be shown on the illustration by clicking on the following button.




1) RESOLVING THE FRAMEWORK OF SATURN



The first intersection point of the geometry is the point where the yellow GM line of Jupiter crosses the circle that defines the inner ridge of the outer hieroglyph circle at the top of the illustration, which is perfectly in line with the vertical staff of the Saturn God. The intersection point and the staff line can be displayed by clicking the following button.


As well as providing the starting geometry for Saturn, this geometry also confirms that the Jupiter geometry on the previous page was correctly understood with the GM line of that planet being the principal alignment feature of system.

The formation geometry then uses a construction line that is the E-W celestial axis of the Jupiter system rotated clockwise by 33+1/3 degrees, the angle used at the start of Dendera Zodiac for the initial rotation, to form the intersection with the staff line at the hand of the Saturn God. This line and the intersection point at the hand of the God can be added to the illustration using the following button.


The celestial axes can now be animated into their new position with the origin located at the hand of the Saturn God and the north axis pointing towards the bottom of the screen.

2) SOLVING SATURN USING NASA DE441 DATA



The construction lines and circles used in the formation geometry can be removed from the illustration by clicking the next button, leaving just Saturn's celestial axes and the Saturn God on the illustration.


It is now possible animate the three principal astronomy angles onto the illustration in the same manner as was done on all previous pages. In order to do this the NASA ephemeris data is required for the Saturn planet system, which includes Saturn and its numerous moons rotating around a common barycenter, at the moment given in DE441 for the geometric winter solstice of 2729 BCE.
Saturn system Barycenter
Standard Gravitational Parameter (GM):

Ephemeris:

Event:

Date:

System center:

Reference frame:

Reference plane:
Osculating elements
e
Orbit eccentricity

QR
Periapsis distance (AU)

IN
Orbit Inclination (deg)

OM
Longitude of ascending node (deg)

W
Argument of periapsis (deg)

TP
Time of periapsis (JD)

N
Mean motion (deg/day)

MA
Mean anomaly (deg)

TA
True anomaly (deg)

a
Semi major axis (AU)

b
Semi minor axis (AU)

AD
Apoapsis distance (AU)

PR
Orbit period (day)
State vectors
X
X (AU)

Y
Y (AU)

Z
Z (AU)

Table 15 - The data for the Saturn planet system at the DE441 geometric winter solstice in the year 2729 BCE


The first of the astronomy angles that needs animating is the longitude of the ascending node angle of the Saturn planet system's orbit projected from the ICRF reference plane onto the plane of the orbit of The Moon, which is the plane of the Dendera Zodiac. This can be shown on the illustration by clicking the following button.


The argument of periapsis is the next angle that can be plotted by clicking the following button.


The focal points of the orbit of the Saturn planet system can now be marked onto the green apsis line.


The final of the three principal astronomy angles is the true anomaly and this can be animated onto the illustration by clicking the next button.


The coloured arcs can be removed from the animation to leave just the celestial axes and the three principal astronomy angles of Saturn by clicking the next button.


The way that the system's geometric alignments can be verified is to use the value of GM for Saturn and make sure that this has a clearly defined carved feature on the sculpture. This can be checked by taking the value of GM for Saturn from the raw NASA DE441 data in table 15, 37940584.8418, splitting it into its component parts that will be used in the next section when the data is being extracted, 37, 94, 58, 48, 41 and 8, adding these together to give 286 degrees. This angular value can be plotted onto the illustration as a line rotated clockwise around the celestial axes center point starting from the north direction, and the resulting location of that line can be seen by clicking the following button.


The geometric system finishes with the movement of the astronomy lines and celestial axes that was seen on the previous pages and are moved to the western focal point of the planet system's orbit. As with the previous system for Mars and Jupiter, the geometry lines are also rotated by 90°, but this time in an anticlockwise direction, during the translation of their center point onto the focal point. This transition can be animated onto the illustration by clicking the following button.


The alignment carvings appear at this stage and can be highlighted by clicking on the following button.


The principal alignment is that the apsis line of the Saturn system aligns with the apsis marker carving on the intermediate stone circle. Additionally, the true anomaly line aligns with the base of the northern standing Goddess in the top left of the illustration. The GM line, which is drawn using the raw NASA data and which will contain some numerical discrepancy from the true value, passes through the second of the two Gods on the Decan ring, parallel to its staff line, and therefore this is the first of the numerical values that needs to be extracted from the carving to confirm that the geometry is now correctly positioned.

3) EXTRACTING THE EPHEMERIS DATA FOR SATURN


The illustration can now be set up with the celestial axes and the gravity marker point so that it is ready for the extraction of the numerical data from the Dendera Zodiac sculpture. The gravity marker is the mini planet system at the bottom left of the sculpture which has been used on all the previous pages.


GMearth (km3 s-2)
DE441 value: 37940584.8418000
Corrected value : 37940584.84520446
NASA:    DENDERA:

The GM value for Saturn uses three alignment mechanisms to ensure that the value can be extracted to the required precision. The first is a tangent to the large circle object on the Decan ring, the second is to the back of the standing God in the inner night sky ring and the final alignment, as is always the case for every planet, is with the Standard Gravitational Parameter marker. The first two alignment markers deliberately draw your attention to these carvings, which are used again on a later page.

Longitude of the ascending node (deg)
DE441 value: 4.8859893499393310
Corrected value : 4.8859893499393295
NASA:    DENDERA:
These angles are projected onto the Dendera Zodiac from the reference plane.

Argument of periapsis (deg)
DE441 value: 64.26181493863810
Corrected value : 64.26181493863794
NASA:    DENDERA:

Mean anomaly (deg)
DE441 value: 160.53128425206120
Corrected value : 160.53128425206116
NASA:    DENDERA:

Orbit eccentricity
DE441 value: 0.0656123098196329100
Corrected value : 0.0656123098196329059
NASA:    DENDERA:

Orbit inclination (deg)
DE441 value: 22.2023336586995400
Corrected value : 22.2023336586995345
NASA:    DENDERA:

Semi minor axis (AU)
DE441 value: 9.5538652619824460
Corrected value : 9.553865261982443
NASA:    DENDERA:

Orbital period (days)
DE441 value: 10819.5767469115100
Corrected value : 10819.5767469114883
NASA:    DENDERA:

4) THE DENDERA EPHEMERIS DATA FOR SATURN

The full ephemeris data for the Saturn planet system at the moment of the geometric winter solstice in 2729 BCE, taken entirely from the Dendera Zodiac, is shown below in table 16. The values in the table that were not directly extracted from the stonework have been calculated from the extracted values using the software than runs this website by applying standard celestial mechanics formulae.
Saturn system barycenter
Standard Gravitational Parameter (GM):

Ephemeris:
(DE441 conditions)

Event:

Date:

System center:

Reference frame:

Reference plane:
Osculating elements
e
Orbit eccentricity

QR
Periapsis distance (AU)

IN
Orbit Inclination (deg)

OM
Longitude of ascending node (deg)

W
Argument of periapsis (deg)

TP
Time of periapsis (JD)

N
Mean motion (deg/day)

MA
Mean anomaly (deg)

TA
True anomaly (deg)

a
Semi major axis (AU)

b
Semi minor axis (AU)

AD
Apoapsis distance (AU)

PR
Orbit period (day)


State vectors
X
X (AU)

Y
Y (AU)

Z
Z (AU)

Table 16 - The corrected data for the Saturn system at the time corrected geometric winter solstice in the year 2729 BCE



Saturn is the last of the planets that is carved into the Dendera Zodiac with an accompanying hieroglyph inscription which allows the planet to be identified. The system for extracting its data has used celestial axes that are parallel to the sculpture's axes, the very first angle of 33+1/3 degrees that was used on the first page has has been reused in Saturn's formation geometry. These facts all point to this being the last of the planets to be shown on the sculpture, added to the fact that it is also the last of the planets that can be seen with the naked eye.

There are, however, more planets and their ephemeris data contained in the Dendera Zodiac.