The Dendera Zodiac's dimensions
The precise dimensions of the Dendera Zodiac sculpture are required in various parts of the solution to the puzzle, but can only be understood once the stonework rotations have been
decrypted and the angular position of the apsis line of the Moon has been determined. To explain how the dimensions of the Dendera Zodiac were created by the architects the
natural unencrypted Dendera Zodiac is shown on the illustration.
The dimensions of the Dendera Zodiac carving are derived from the ephemeris data of the Moon and are logical values, so long as the unit of measurement used by the stonemasons is known. During the work to understand the Great Pyramid of Giza already referenced previously (here) it was determined that the principal unit of measurement used in that building was the 'perfect meter' which is defined in the same manner that the modern meter was defined, by dividing the Earth's circumference arc from the pole to the equator into 10 million parts. The 'perfect meter' therefore has a value of 1.000196573 meters, the discrepancy being due to the errors that were made when our metric system was first designed. Throughout this work the stonemasons unit of measurement will therefore be referred to using metric notation (km,m and cm) in order to make the work easier to read, because the small difference between centimeters and the actual unit of measure 'perfect centimeters' is indistinguishable on the sculpture.
To convert distances given in Astronomical Units in the NASA tables into stonemason's units on the sculpture, the conversion factor is 2 AU = 1 km. The semi major axis of The Moon's orbit at the time of the geometric winter solstice in 2729 BCE in the DE441 ephemeris is 0.0025440959 AU, which therefore scales down to give the length of the major axis of the Moon's orbit on the sculpture as 254.440959 cm. Using the value of the orbit's eccentricity from DE441 at the same moment in time, the minor axis of the orbit ellipse can be calculated as being 253.93467 cm, and this ellipse can be drawn onto the sculpture with the major axis aligned to the Moon's apsis line that was determined in the previous section.
The bounding box which contains the ellipse has also been drawn onto the illustration in yellow, the dimensions of which can be calculated from the length of the ellipse's radii and its rotation angle. The box gives the combined outer dimensions of the two stones onto which the Dendera Zodiac is carved as being 254.27065 cm in the direction of the stone split line from left to right on the illustration and 254.00332 cm perpendicular to the stone split line from top to bottom on the illustration. (The missing part of the sculpture photograph on the left side of the image is where the mechanical holding brackets in the Louvre museum overlap the edge of the sculpture.)
If the orbit inclination of The Moon from the DE441 data in table 1 on the previous page is now applied to the orbit ellipse as a rotation around the Y axis, so that that the orbit becomes angled to the plane of the Dendera Zodiac, then the right side of the projected ellipse aligns perfectly with the outer circumference of the hieroglyph stone ring, which can be seen by clicking the next button.
The mathematics that dictates the radius of the hieroglyph ring gives the ring's radius as being 119.953205728 cm, and this outer circle can be drawn onto the illustration by clicking the next button.
The reason that the outer hieroglyph ring's radius is defined in this manner by the architects is to show that its shape is a circle and not an ellipse, due to the fact that there is only one point being used to specify the radius.
The inner circumference of the hieroglyph ring is also dictated by the ephemeris table values and can be best seen by removing the inclined outer ellipse and drawing the Moon orbit's apsis line that was determined on the previous page onto the illustration, again with the focal points of the orbit marked.
The positions of the two focal points are calculated from using the radius of the outer hieroglyph circle just defined as being representative of the Moon orbit's semi major axis giving the focal length as 7.326010460637037 cm and the distance between the focal points as 14.652020921274074 cm. Inspection of the illustration shows that the distance between the two focal points is identical to the width of the outer hieroglyph ring, so the inner radius of that ring of stone can be calculated mathematically as being 105.30118480754125 cm and this circle can now be drawn onto the illustration by clicking the next button.
Because the hieroglyph ring's inner and outer radii can be determined with such precision the photograph of the Dendera Zodiac that is being used in the analysis, and which is shown on the main illustration, can now be used to accurately determine the radii of the Decan ring by way of measurement. The inner circle of the Decan ring that separates it from the inner night sky has a circumference of exactly 360 cm allowing rotational values in degrees and linear measurements in cm to be interchanged.
Because the inner Decan circle is defined from a logical centimeter integer value circumference it can be correctly deduced that the outer circumference of this stone ring also has a logical integer centimeter value which can be determined as being 500 cm.
If you now look carefully at the small God carvings that are all the way around the Decan ring of stone you will notice that their feet do not touch the circle that defines the outside of the Decan ring. This observation shows that the Decan ring needs to have two inset circles drawn onto it so that it ends up with a border just like the hieroglyph ring has, and the architects are deliberately posing the question of how the circle that dictates the position of the feet of the Gods on the Decan ring is defined.
The answer is that it is done with pinpoint mathematical precision. Before explaining the solution to how this ring is formed, you can click the following button to see a graphical representation of the solution on the illustration showing the circle upon which the Decan ring Gods are walking.
Analysis of the system that is used to determine the radius of this circle shows that it is defined using the stone split line, which can be added to the illustration by clicking the following button.
The inner circle and Decan ring need to be rotated in the same manner that was performed on the previous page by applying the projected longitude of the ascending node and the argument of periapsis angles to the inner night sky stone circle, which can be animated on the illustration by clicking the following button.
If you look at the top of the inner Decan ring circle you can see that the intersection of the rotated stone split line with the Y axis of the sculpture is the determining factor in producing the Decan circle's radius. Therefore to find the radius' numerical value the stone split line needs to be mathematically defined, and this is where the mathematical precision appears along with a very accurate method for calculating the orbital tilt of The Moon.
The yellow bounding box of the Dendera Zodiac provides the frame of reference for the coordinates of the stone split line. The Y coordinate of the right side of the stone split line can be determined by measuring from the bottom right corner of the sculpture's bounding box to the point where the stone split line meets the bounding box on the right. The logic of how this distance was created in the sculpture can be worked out because it is related to the ephemeris data that has already been used. The distance in centimeters is ten times the orbit inclination of The Moon in degrees, with the units swapped over. A constant value of 1/100th of a cubit is then added to the distance to get the full definition of the Y coordinate on the right side of the stone split line. The precise value of the cubit is known to great precision from work previously carried out in the Great Pyramid and has a value of 52.3223744607554 cm.
The X coordinate of the split line end on the right must be half the bounding box's width.
Analysis of the stone split line shows that it is not parallel to the X axis of the carving but is angled at exactly 1/3 of a degree, the left side being higher than the right. Because the point on the right side of the stone split line is fully defined and the line's angle is also known, the line equation of the stone split line can be determined and the rotation of the stone split line that was just performed can be done with mathematical precision. The equation of the rotated split line gives its intersection point on the Y axis as 77.86181288083884 cm, which is the point that dictates the radius of the inset circle on the Decan ring.
The two inset ridges of stone on the hieroglyph ring have the same width as that on the Decan ring that was just calculated, and can be added to the illustration along with an inner ring of the Decan circle by clicking on the next button.
The reason that the definition of the inner Decan circle is so complex is that it provides the decimal precision for the inclination of the Moon's orbit at the moment of the geometric winter solstice in the year 2729 BCE. The Y coordinate of the rotated stone line's intersection with the Y axis, the constant in the line equation, of 77.86181288083884 cm provides the digits to correct the DE441 value of the Moon orbit's inclination, which is given by NASA as 19.200778933263°. The portion of the inclination that is shown in bold characters can be replaced by the line constant digits, ignoring the decimal point.
The system is beautifully designed because the stone split line's right side end point is defined using The Moon orbit inclination, as is the first of the two rotation angles, so the corrected value of the orbit's tilt can be fed back into the mathematics and the calculation run again to further refine the numerical digits in the orbital tilt value, and this procedure can be repeated until the value stabilises.
The mathematics is a converging iterative process which will always give the correct value of The Moon's orbit inclination regardless of the starting value. In the software that is running this website a starting value of 19.2° is used for the Moon's orbital tilt value, and the corrected value of 19.20077861812881° emerges from the mathematics.
The logic of this system is identical to the one used in the Great Pyramid to determine the axial tilt of the Earth and it can be concluded that the two systems were designed by the same architect, thereby fixing the association of the two structures.
The dimensions of the Dendera Zodiac carving are derived from the ephemeris data of the Moon and are logical values, so long as the unit of measurement used by the stonemasons is known. During the work to understand the Great Pyramid of Giza already referenced previously (here) it was determined that the principal unit of measurement used in that building was the 'perfect meter' which is defined in the same manner that the modern meter was defined, by dividing the Earth's circumference arc from the pole to the equator into 10 million parts. The 'perfect meter' therefore has a value of 1.000196573 meters, the discrepancy being due to the errors that were made when our metric system was first designed. Throughout this work the stonemasons unit of measurement will therefore be referred to using metric notation (km,m and cm) in order to make the work easier to read, because the small difference between centimeters and the actual unit of measure 'perfect centimeters' is indistinguishable on the sculpture.
To convert distances given in Astronomical Units in the NASA tables into stonemason's units on the sculpture, the conversion factor is 2 AU = 1 km. The semi major axis of The Moon's orbit at the time of the geometric winter solstice in 2729 BCE in the DE441 ephemeris is 0.0025440959 AU, which therefore scales down to give the length of the major axis of the Moon's orbit on the sculpture as 254.440959 cm. Using the value of the orbit's eccentricity from DE441 at the same moment in time, the minor axis of the orbit ellipse can be calculated as being 253.93467 cm, and this ellipse can be drawn onto the sculpture with the major axis aligned to the Moon's apsis line that was determined in the previous section.
The bounding box which contains the ellipse has also been drawn onto the illustration in yellow, the dimensions of which can be calculated from the length of the ellipse's radii and its rotation angle. The box gives the combined outer dimensions of the two stones onto which the Dendera Zodiac is carved as being 254.27065 cm in the direction of the stone split line from left to right on the illustration and 254.00332 cm perpendicular to the stone split line from top to bottom on the illustration. (The missing part of the sculpture photograph on the left side of the image is where the mechanical holding brackets in the Louvre museum overlap the edge of the sculpture.)
If the orbit inclination of The Moon from the DE441 data in table 1 on the previous page is now applied to the orbit ellipse as a rotation around the Y axis, so that that the orbit becomes angled to the plane of the Dendera Zodiac, then the right side of the projected ellipse aligns perfectly with the outer circumference of the hieroglyph stone ring, which can be seen by clicking the next button.
The mathematics that dictates the radius of the hieroglyph ring gives the ring's radius as being 119.953205728 cm, and this outer circle can be drawn onto the illustration by clicking the next button.
The reason that the outer hieroglyph ring's radius is defined in this manner by the architects is to show that its shape is a circle and not an ellipse, due to the fact that there is only one point being used to specify the radius.
The inner circumference of the hieroglyph ring is also dictated by the ephemeris table values and can be best seen by removing the inclined outer ellipse and drawing the Moon orbit's apsis line that was determined on the previous page onto the illustration, again with the focal points of the orbit marked.
The positions of the two focal points are calculated from using the radius of the outer hieroglyph circle just defined as being representative of the Moon orbit's semi major axis giving the focal length as 7.326010460637037 cm and the distance between the focal points as 14.652020921274074 cm. Inspection of the illustration shows that the distance between the two focal points is identical to the width of the outer hieroglyph ring, so the inner radius of that ring of stone can be calculated mathematically as being 105.30118480754125 cm and this circle can now be drawn onto the illustration by clicking the next button.
Because the hieroglyph ring's inner and outer radii can be determined with such precision the photograph of the Dendera Zodiac that is being used in the analysis, and which is shown on the main illustration, can now be used to accurately determine the radii of the Decan ring by way of measurement. The inner circle of the Decan ring that separates it from the inner night sky has a circumference of exactly 360 cm allowing rotational values in degrees and linear measurements in cm to be interchanged.
Because the inner Decan circle is defined from a logical centimeter integer value circumference it can be correctly deduced that the outer circumference of this stone ring also has a logical integer centimeter value which can be determined as being 500 cm.
If you now look carefully at the small God carvings that are all the way around the Decan ring of stone you will notice that their feet do not touch the circle that defines the outside of the Decan ring. This observation shows that the Decan ring needs to have two inset circles drawn onto it so that it ends up with a border just like the hieroglyph ring has, and the architects are deliberately posing the question of how the circle that dictates the position of the feet of the Gods on the Decan ring is defined.
The answer is that it is done with pinpoint mathematical precision. Before explaining the solution to how this ring is formed, you can click the following button to see a graphical representation of the solution on the illustration showing the circle upon which the Decan ring Gods are walking.
Analysis of the system that is used to determine the radius of this circle shows that it is defined using the stone split line, which can be added to the illustration by clicking the following button.
The inner circle and Decan ring need to be rotated in the same manner that was performed on the previous page by applying the projected longitude of the ascending node and the argument of periapsis angles to the inner night sky stone circle, which can be animated on the illustration by clicking the following button.
If you look at the top of the inner Decan ring circle you can see that the intersection of the rotated stone split line with the Y axis of the sculpture is the determining factor in producing the Decan circle's radius. Therefore to find the radius' numerical value the stone split line needs to be mathematically defined, and this is where the mathematical precision appears along with a very accurate method for calculating the orbital tilt of The Moon.
The yellow bounding box of the Dendera Zodiac provides the frame of reference for the coordinates of the stone split line. The Y coordinate of the right side of the stone split line can be determined by measuring from the bottom right corner of the sculpture's bounding box to the point where the stone split line meets the bounding box on the right. The logic of how this distance was created in the sculpture can be worked out because it is related to the ephemeris data that has already been used. The distance in centimeters is ten times the orbit inclination of The Moon in degrees, with the units swapped over. A constant value of 1/100th of a cubit is then added to the distance to get the full definition of the Y coordinate on the right side of the stone split line. The precise value of the cubit is known to great precision from work previously carried out in the Great Pyramid and has a value of 52.3223744607554 cm.
The X coordinate of the split line end on the right must be half the bounding box's width.
Analysis of the stone split line shows that it is not parallel to the X axis of the carving but is angled at exactly 1/3 of a degree, the left side being higher than the right. Because the point on the right side of the stone split line is fully defined and the line's angle is also known, the line equation of the stone split line can be determined and the rotation of the stone split line that was just performed can be done with mathematical precision. The equation of the rotated split line gives its intersection point on the Y axis as 77.86181288083884 cm, which is the point that dictates the radius of the inset circle on the Decan ring.
The two inset ridges of stone on the hieroglyph ring have the same width as that on the Decan ring that was just calculated, and can be added to the illustration along with an inner ring of the Decan circle by clicking on the next button.
Orbit inclination
The reason that the definition of the inner Decan circle is so complex is that it provides the decimal precision for the inclination of the Moon's orbit at the moment of the geometric winter solstice in the year 2729 BCE. The Y coordinate of the rotated stone line's intersection with the Y axis, the constant in the line equation, of 77.86181288083884 cm provides the digits to correct the DE441 value of the Moon orbit's inclination, which is given by NASA as 19.200778933263°. The portion of the inclination that is shown in bold characters can be replaced by the line constant digits, ignoring the decimal point.
The system is beautifully designed because the stone split line's right side end point is defined using The Moon orbit inclination, as is the first of the two rotation angles, so the corrected value of the orbit's tilt can be fed back into the mathematics and the calculation run again to further refine the numerical digits in the orbital tilt value, and this procedure can be repeated until the value stabilises.
The mathematics is a converging iterative process which will always give the correct value of The Moon's orbit inclination regardless of the starting value. In the software that is running this website a starting value of 19.2° is used for the Moon's orbital tilt value, and the corrected value of 19.20077861812881° emerges from the mathematics.
The logic of this system is identical to the one used in the Great Pyramid to determine the axial tilt of the Earth and it can be concluded that the two systems were designed by the same architect, thereby fixing the association of the two structures.
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