The Moon
The primary design criteria that dictates the position of the principal carved elements of the Dendera Zodiac is the numerical astronomy data of The Moon and its orbit from the year 2729 BCE.
The technical knowledge that is presented within the carving is comparable to our own, and the Dendera Zodiac can only be understood if the reader is furnished with an understanding of celestial mechanics.
If you have no knowledge of celestial mechanics then an introduction to the subject, written in an easy to understand non-technical manner, can be displayed in a new tab by clicking on the following button.
The 'key' from the Great Pyramid's lower northern shaft is essential to the design of the Dendera Zodiac because it provides an exact time and date from which the analysis of the sculpture can be commenced, that being the moment of the geometric winter solstice (when the Earth's axis and north pole is pointing directly away from The Sun) which occurred on January 14th 2729 BCE 17:29:25.6958 TDB at Julian Day 724669.228769627. Using NASA's DE441 ephemeris via the online portal, five numerical values can be extracted from the data at this moment in time which are required at the outset to start to solve the sculpture's design, and are shown in table 1 below.
If you have no knowledge of celestial mechanics then an introduction to the subject, written in an easy to understand non-technical manner, can be displayed in a new tab by clicking on the following button.
The 'key' from the Great Pyramid's lower northern shaft is essential to the design of the Dendera Zodiac because it provides an exact time and date from which the analysis of the sculpture can be commenced, that being the moment of the geometric winter solstice (when the Earth's axis and north pole is pointing directly away from The Sun) which occurred on January 14th 2729 BCE 17:29:25.6958 TDB at Julian Day 724669.228769627. Using NASA's DE441 ephemeris via the online portal, five numerical values can be extracted from the data at this moment in time which are required at the outset to start to solve the sculpture's design, and are shown in table 1 below.
Table 1 - The basic NASA DE441 data for the Earth-Moon system at the geometric winter solstice in the year 2729 BCE
THE CELESTIAL AXES AND THE KEY
The main illustration on the right shows the Dendera Zodiac with no rotations applied to the stone circles, with the horizontal line that runs through the right side of the stone split line
and its perpendicular both pinned to the outer hieroglyph ring.
The Moon carving in the central section of the Dendera Zodiac, which was identified by scholars in the past, is marked with the white circle with the standing God inside.
The smaller white ellipse, positioned below the circle, represents the Moon's orbit (hence its elliptical shape) and has the God seated inside it.
This symbol has not previously been identified by scholars.
The first step in fully decrypting the sculpture is to rotate the night sky and hieroglyph circle by 33+1/3 degrees clockwise to place the stonework into it's initial position as explained in the hieroglyphs, and as performed on the previous pages, so that the two black lines rotate and form the X axis and Y axis of the sculpture..
To keep track of the logic system in use in the Dendera Zodiac, the three sets of falcon Gods that have been solved during the initial rotation can be highlighted. The knees of the pair of falcon Gods on the left of the illustration give the alignment of the X axis line, the pair at the bottom give the Y axis line's position and those at the top contain the damaged section of stone that needs to be removed at the outset. Each of the three pairs of Gods serves a different purpose and they can be highlighted by clicking the next button, leaving just the falcon God on the right unsolved.
Notice that after the initial rotation the white ellipse representing The Moon's orbit is now located exactly on the X axis of the sculpture. This is a vital piece of information. It shows that the black axis lines are defined as being directly related the Moon's orbit.
The angle of the longitude of the ascending node of The Moon's orbit at the moment of the 2729 BCE geometric winter solstice can now be plotted onto the illustration using the intersection of the two rotated stone split lines as being the location of the center of The Earth through which the line needs to pass. The angle is plotted anti-clockwise relative to the Y axis.
As can be seen on the illustration, the yellow line showing the angle of the longitude of the ascending node of The Moon's orbit forms a near perfect tangent to The Moon circle carving. Because the black axis lines are already known to be directly related to The Moon's orbit it can be correctly deduced that the yellow tangent line to The Moon carving must represent celestial north and the black Y axis line must represent the ascending node line of The Moon.
The illustration can be refined further by applying technically correct astronomy principals to the drawing, working on the theory that the sculpture is a representation of The Moon's orbit in plan view and the solar system's reference plane must therefore be set at the angle of the orbit's inclination to the sculpture's plane. By applying the orbit inclination of The Moon to the longitude of the ascending node angle, thereby projecting it onto the plane of The Moon's orbit, the yellow line moves slightly to the left, which can be shown by clicking the following button.
The longitude of the ascending node line now forms a perfect tangent to The Moon circle carving, and there is sufficient detail in the carving of The Moon circle to be able to distinguish between the two possible positions of the longitude line, the difference in position being just less than 3mm at the tangent point. If you alternate between the two positions of the line, by clicking the above two buttons repetitively, you can see that accuracy with which the carving was created.
The illustration can now have the ICRF celestial N-S axis plotted onto it, with the north axis plotted as a solid white line. After this north line has been drawn an E-W axis line can be added perpendicular to it, plotted with dashed lines, meaning that the plane of reference for these axes lines is the Earth's equator allowing the equinox and solstice labels to be moved into their correct positions.
These celestial axis lines define The Earth's equinox and solstice points, and the winter solstice on the right side of the illustration is the classically defined solstice that was determined from looking it up on the NASA DE441 ephemeris on the previous page as falling on January 11th 2729 BCE at 10:36:47 TDB, and has a geocentric right ascension of The Sun of 270° by definition.
Having defined this point, it is now possible to mark onto the illustration the geometric winter solstice, at the moment the Earth's north pole was pointing away from The Sun, which is known from DE441 and from the Great Pyramid's lower northern shaft's hook to have fallen on January 14th 2729 BCE at 17:29:26 TDB. The line will be drawn in green and, prior to rotating it into place, needs to start off aligned with the celestial north axis.
Because the celestial axes angular unit of measurement is right ascension then it is the value of the right ascension of The Sun at the geometric winter solstice on January 14th 2729 BCE shown in table 1 that needs to be used when animating this line, a value which is given as being 273.59355°. The geometric solstice line can be animated into position on the illustration by applying this angle in an anticlockwise direction to the green line by clicking the next button.
As can be seen on the illustration, the green geometric solstice line falls exactly in the center of the hook between the God's knees, which is exactly where you would expect it to align. Because the hook can only be positioned visually with the Dendera Zodiac's carving of the God's knees and therefore has an undetermined small error in its location, it is this green line that now precisely defines the position of the center of the hook relative to the north celestial axis. Since the north celestial axis' position is dictated by the projected longitude of the ascending node of The Moon's orbit, which is measured relative to the Y axis of the sculpture, the absolute angular position of the hook on the sculpture is now known.
The positions of all four pairs of falcon Gods has now been established and the puzzle's designers are showing by this that the next parts of the puzzle can now be solved.
The first step in fully decrypting the sculpture is to rotate the night sky and hieroglyph circle by 33+1/3 degrees clockwise to place the stonework into it's initial position as explained in the hieroglyphs, and as performed on the previous pages, so that the two black lines rotate and form the X axis and Y axis of the sculpture..
To keep track of the logic system in use in the Dendera Zodiac, the three sets of falcon Gods that have been solved during the initial rotation can be highlighted. The knees of the pair of falcon Gods on the left of the illustration give the alignment of the X axis line, the pair at the bottom give the Y axis line's position and those at the top contain the damaged section of stone that needs to be removed at the outset. Each of the three pairs of Gods serves a different purpose and they can be highlighted by clicking the next button, leaving just the falcon God on the right unsolved.
Notice that after the initial rotation the white ellipse representing The Moon's orbit is now located exactly on the X axis of the sculpture. This is a vital piece of information. It shows that the black axis lines are defined as being directly related the Moon's orbit.
The angle of the longitude of the ascending node of The Moon's orbit at the moment of the 2729 BCE geometric winter solstice can now be plotted onto the illustration using the intersection of the two rotated stone split lines as being the location of the center of The Earth through which the line needs to pass. The angle is plotted anti-clockwise relative to the Y axis.
As can be seen on the illustration, the yellow line showing the angle of the longitude of the ascending node of The Moon's orbit forms a near perfect tangent to The Moon circle carving. Because the black axis lines are already known to be directly related to The Moon's orbit it can be correctly deduced that the yellow tangent line to The Moon carving must represent celestial north and the black Y axis line must represent the ascending node line of The Moon.
The illustration can be refined further by applying technically correct astronomy principals to the drawing, working on the theory that the sculpture is a representation of The Moon's orbit in plan view and the solar system's reference plane must therefore be set at the angle of the orbit's inclination to the sculpture's plane. By applying the orbit inclination of The Moon to the longitude of the ascending node angle, thereby projecting it onto the plane of The Moon's orbit, the yellow line moves slightly to the left, which can be shown by clicking the following button.
The longitude of the ascending node line now forms a perfect tangent to The Moon circle carving, and there is sufficient detail in the carving of The Moon circle to be able to distinguish between the two possible positions of the longitude line, the difference in position being just less than 3mm at the tangent point. If you alternate between the two positions of the line, by clicking the above two buttons repetitively, you can see that accuracy with which the carving was created.
The illustration can now have the ICRF celestial N-S axis plotted onto it, with the north axis plotted as a solid white line. After this north line has been drawn an E-W axis line can be added perpendicular to it, plotted with dashed lines, meaning that the plane of reference for these axes lines is the Earth's equator allowing the equinox and solstice labels to be moved into their correct positions.
These celestial axis lines define The Earth's equinox and solstice points, and the winter solstice on the right side of the illustration is the classically defined solstice that was determined from looking it up on the NASA DE441 ephemeris on the previous page as falling on January 11th 2729 BCE at 10:36:47 TDB, and has a geocentric right ascension of The Sun of 270° by definition.
Having defined this point, it is now possible to mark onto the illustration the geometric winter solstice, at the moment the Earth's north pole was pointing away from The Sun, which is known from DE441 and from the Great Pyramid's lower northern shaft's hook to have fallen on January 14th 2729 BCE at 17:29:26 TDB. The line will be drawn in green and, prior to rotating it into place, needs to start off aligned with the celestial north axis.
Because the celestial axes angular unit of measurement is right ascension then it is the value of the right ascension of The Sun at the geometric winter solstice on January 14th 2729 BCE shown in table 1 that needs to be used when animating this line, a value which is given as being 273.59355°. The geometric solstice line can be animated into position on the illustration by applying this angle in an anticlockwise direction to the green line by clicking the next button.
As can be seen on the illustration, the green geometric solstice line falls exactly in the center of the hook between the God's knees, which is exactly where you would expect it to align. Because the hook can only be positioned visually with the Dendera Zodiac's carving of the God's knees and therefore has an undetermined small error in its location, it is this green line that now precisely defines the position of the center of the hook relative to the north celestial axis. Since the north celestial axis' position is dictated by the projected longitude of the ascending node of The Moon's orbit, which is measured relative to the Y axis of the sculpture, the absolute angular position of the hook on the sculpture is now known.
The positions of all four pairs of falcon Gods has now been established and the puzzle's designers are showing by this that the next parts of the puzzle can now be solved.
THE PRINCIPAL MOON ANGLES
If you consider the Dendera Temple to be a star observatory with a circular hole cut in the roof through which the night sky can be seen, then this observatory needs to be aligned to
the major axis of The Moon's orbit because the carving is a representation of The Moon's orbital ellipse. This alignment is done in much the same way as a modern circular observatory can be
mechanical rotated on its circular base.
To start the rotation of the building, a line can be drawn onto the illustration which represents the major axis of The Moon's orbit. At the outset this needs to be positioned in line with the celestial north axis which, by definition, is derived from The Earth's astronomy data and not The Moon's. Click the following button to add this line, along with a small circle at the end of it to represent The Moon and which will symbolise that the line is showing the position of a solar system object.
The whole of the Temple of Dendera can now be rotated on its base by the projected longitude of the ascending node of The Moon's orbit so that the the Moon line ends up positioned on the orbit's ascending node line, which is already known to be the black Y axis line. Rather than rotate the square carving and leave the night sky, Decan ring and Moon line in fixed positions it is visually much better to keep the square frame in a fixed position and rotate the line and the night sky and Decan ring in the opposite direction, which can be performed by clicking the next button.
The argument of periapsis of The Moon's orbit from table 1 can now be applied to the illustration, and once again the night sky and Decan ring need to rotate along with the line to The Moon because the Dendera temple is being rotated to align with the Moon's orbit major axis.
The temple is now aligned with the Moon's orbit major axis and the apsis line of the orbit can now be added to the illustration along with the focal points of the orbit's ellipse, which helps with visualising the orbit. The position of the focal points is calculated by taking the radius of the outer hieroglyph ring as representing the semi major axis of the orbit.
Once the apsis line of The Moon has been determined the final part of the stone rotation encryption can be performed which involves rotating the intermediate circle of stone, located between the Decan ring and the outer hieroglyph ring, by 90° clockwise which serves to align the periapsis marker on this stone ring with the apsis line. Click on the following button to highlight the carved objects on this ring of stone and then rotate it.
The true anomaly of The Moon can now be animated onto the illustration by rotating the Moon line by the true anomaly value taken from the table 1. Because the temple is already fully aligned with the Moon's orbit major axis, the night sky does not need to rotate during this animation, only the Moon line.
As can be seen on the illustration the green line that passes through the center of the hook, which shows the reference position of the geometric winter solstice event, and the yellow line that shows the position of the Moon at this moment in time are not aligned, and the puzzle that is encoded into the Dendera Zodiac becomes clear. These two lines should be in exactly the same angular position and the reason that they are not is because of the errors that are inherent in our modern ephemeris data in table 1.
The puzzle's required solution is therefore defined as follows: correct the values of the ephemeris data so that the green and yellow line's angular positions are equal. Expressing this in terms of the astronomy data and mathematics, when modulated by 360° the sum of the three clockwise angles of the projected longitude of the ascending node of the Moon's orbit + argument of periapsis of the Moon's orbit + true anomaly of the Moon's orbit + the anticlockwise angle of the right ascension of The Sun at the moment of the geometric winter solstice = 360°.
Because the longitude of the ascending node angle needs to be projected onto the plane of the Dendera Zodiac, the orbital tilt of the Moon is the first piece of numerical data that is required to start to solve equation one, and this value is cleverly concealed and precisely specified within the dimensions of the sculpture which are explained on the next page.
To start the rotation of the building, a line can be drawn onto the illustration which represents the major axis of The Moon's orbit. At the outset this needs to be positioned in line with the celestial north axis which, by definition, is derived from The Earth's astronomy data and not The Moon's. Click the following button to add this line, along with a small circle at the end of it to represent The Moon and which will symbolise that the line is showing the position of a solar system object.
The whole of the Temple of Dendera can now be rotated on its base by the projected longitude of the ascending node of The Moon's orbit so that the the Moon line ends up positioned on the orbit's ascending node line, which is already known to be the black Y axis line. Rather than rotate the square carving and leave the night sky, Decan ring and Moon line in fixed positions it is visually much better to keep the square frame in a fixed position and rotate the line and the night sky and Decan ring in the opposite direction, which can be performed by clicking the next button.
The argument of periapsis of The Moon's orbit from table 1 can now be applied to the illustration, and once again the night sky and Decan ring need to rotate along with the line to The Moon because the Dendera temple is being rotated to align with the Moon's orbit major axis.
The temple is now aligned with the Moon's orbit major axis and the apsis line of the orbit can now be added to the illustration along with the focal points of the orbit's ellipse, which helps with visualising the orbit. The position of the focal points is calculated by taking the radius of the outer hieroglyph ring as representing the semi major axis of the orbit.
Once the apsis line of The Moon has been determined the final part of the stone rotation encryption can be performed which involves rotating the intermediate circle of stone, located between the Decan ring and the outer hieroglyph ring, by 90° clockwise which serves to align the periapsis marker on this stone ring with the apsis line. Click on the following button to highlight the carved objects on this ring of stone and then rotate it.
The true anomaly of The Moon can now be animated onto the illustration by rotating the Moon line by the true anomaly value taken from the table 1. Because the temple is already fully aligned with the Moon's orbit major axis, the night sky does not need to rotate during this animation, only the Moon line.
As can be seen on the illustration the green line that passes through the center of the hook, which shows the reference position of the geometric winter solstice event, and the yellow line that shows the position of the Moon at this moment in time are not aligned, and the puzzle that is encoded into the Dendera Zodiac becomes clear. These two lines should be in exactly the same angular position and the reason that they are not is because of the errors that are inherent in our modern ephemeris data in table 1.
The puzzle's required solution is therefore defined as follows: correct the values of the ephemeris data so that the green and yellow line's angular positions are equal. Expressing this in terms of the astronomy data and mathematics, when modulated by 360° the sum of the three clockwise angles of the projected longitude of the ascending node of the Moon's orbit + argument of periapsis of the Moon's orbit + true anomaly of the Moon's orbit + the anticlockwise angle of the right ascension of The Sun at the moment of the geometric winter solstice = 360°.
(OM'm + Wm + TAm) mod 360 + RAs=360
Equation 1
Because the longitude of the ascending node angle needs to be projected onto the plane of the Dendera Zodiac, the orbital tilt of the Moon is the first piece of numerical data that is required to start to solve equation one, and this value is cleverly concealed and precisely specified within the dimensions of the sculpture which are explained on the next page.
NEXT PAGE - DIMENSIONS