Finding Planet 9 by Telescope Aimed at Pyramid Faces

I was thinking of calling this article something more elaborate, like:

Aiming Telescopes at Pyramid Faces for the Purpose
of Using them as Space Microscopes 

Plus: Using Reflected Lasers to Rapidly Scan for Objects in Space

But that title was way too long.

I was reading about Planet 9 in the news recently.  It's pretty exciting to consider just how much stuff there is in space waiting to discover, and how impressive the science, and scientists, are with regards to the search for space-relating things.  Especially this new information and research into the possibility of finding Planet 9.  I've worked in science a little.  My dad worked on rockets and the Apollo projects, as well as a bunch of other things floating around in space.  I've seen first-hand how much discipline and diligence goes into proving and disproving and making sure it's all as tight and true as can be.

I was reading again this morning about the search for Planet 9, and how Caltech Brainiacs Mike Brown and Konstantin Batygin think it'll take 5-15 years to find it and snap a picture of it.  I lack that kind of patience and admire their discipline, but what if there was a way to search space faster, so we could find Planet 9... and maybe more fun stuff like it?

That got me thinking about massive telescopes, geometry and finding a spec of dust a gazillion miles away from our little blue dot as it's spinning and wobbling and screaming through space and I was pretty impressed that anybody could find anything with any degree of reliability, especially with telescopes.  Just stabilizing all that glass stuffed in tubes against gravity is hard enough.  But trying to get a stable picture out of it?  That's nothing short of genius, sweat, and miraculous.  That's what makes math and physics so awesome.  I'm pretty sure astrophysicists have overdrive or extra brains (or they make it up... hah!)  That stuff is out-there.

The Pyramid Faces and Turning Telescopes Into Microscopes

But, being simple, I was thinking of the geometry of looking with telescopes, because I can still kind of ruminate over math problems a little and it had me wondering if it might be significantly easier and more reliable to find Planet 9 by Pyramid.   What if somebody were able to point a Hubble-like telescope at the face of a giant first-surface mirror perfectly calibrated and oriented on the surface of the earth?  Wouldn't that make said telescope more of a microscope pointed into the giant petri dish of outer space?

The Pyramids are pretty perfectly calibrated and oriented.  When they were built, their surfaces were also constructed with optical precision.  The advantage a ground-based search, with telescope(s) pointed at the face of a Pyramid is that they're ground-based and can be instrumented.  Like a microscope, various focal length lenses can be outfitted and used to view into various regions of space.  Rather than a single telescope pointing into space, a telescope, or family of telescopes, could be outfitted to be oriented around the base, configured to view into regions of space.  The fact that the focal plane is so close provides an advantage with regards to stability and, would therefore, affect the quality of data collected.

Pointing a telescope at the face of the pyramids, which are effectively first-surface mirrors, would allow for faster scanning of the skies by virtue of the stability of the system and the ability to move and locate objects with high precision as the focal plane could be so close to the surface being observed.  Looking for something 50 gazillion miles away is hard when you're trying to aim straight at it.  It's significantly more stable to view a reflected image some 5 inches or 500 feet away while using progressively longer focal lengths to zoom in.  So long as the surface reflection honors the incoming light, both the direct telescope and the telescope looking at the reflected image are viewing the same light.  An array of lenses, from the wide angle to high magnification could be aligned with the reflection of a stellar body for simultaneous imaging because each reflected image is created by the same light source.

On top of being easier to stabilize and track in the reflection due to proximity of the reflection, a variety of focal length lenses and instrumentation could be installed and configured without affecting any previously installed data collection system, thereby allowing a variety of experiments to operate asynchronously and continuously, while also providing the ability to adjust a possible range of optics upon a target simultaneously.  In essence, the pyramids, by virtue of their size, stability and optically true surfaces, provide the opportunity to view into space, at myriad stellar bodies, for a variety of purposes, simultaneously, with a high-degree of precision and data quality.

Any telescope trained directly into space requires increasing degrees of stabilization with increased magnification and weight.  There appear to be advantages to having a ground-based system that can view reflected images up-close.  Along with the stability, looking at objects close-up provides greater opportunities for instrumentation, viewing with a variety of focal lengths, filtering, simultaneous experimentation of time-based systems (e.g. different telescopes/optics/filters on various faces trained on an object), and more.  It's possible to look at the same object through devices positioned feet away from each other, or on opposite faces.

It'd all be fun if it could improve our ability to peer into space with less issues related to dampening, vibration, and reduced accuracy with distance, though there's always the concern about atmospheric interference.  Still, since it's all the same light, it seems to make good sense to increase the precision by viewing the light in the most stable way.  Looking at the reflected image of a far-distant object appears to be an optimal viewing solution, especially since the reflection affords multiple instances of the same image from different viewing perspectives.

The Pyramids As Deep Space Scanners With Lasers

What if, in combination with giant telescopes as microscopes looking for the equivalent of far-far-distant specks of dust, the pyramids could use powerful lasers in tandem with telescope-microscopes - like point-scanners, flashlights or distance sensors?

If the orbit can be calculated for Planet 9, to within a certain region of space, sets of lasers could be oriented such that they reflect off of points on the pyramid faces and converge upon a point inside the orbital envelope of Planet 9.  Where they converge would be a bright spot of known, calibrated intensity.  It wouldn't have to be a point, it could be a smiley face, it just has to be discover-able and track-able.  To calibrate such an array, the spot would be located in a scanner capable of measuring light intensity over a set of calculated locations and values, all of which could be located by telescope peering into the reflection of the pyramids from the region of space being scanned.

Sighting a device at the face of the pyramids, such as a telescope, equipped with light sensor, to track the signal of the spot of convergence, while moving the spot through space means that as the beams move through the orbital envelope, the system would be capable of monitoring the spots through space.  Any object the beams encounter would interrupt the signal, and trigger an alarm that would provide the exact location and time.  Finer resolution scans could be used to find the bounds of any body discovered by the absence of a visible signal within the body, bordered by signals to either side.
In essence, the pyramids could likely be used as giant scanners and microscopes, scanning space until a body is found, then finding the size of the object, distance and velocity by the same technique, using higher resolution intervals.

Given the projected distance to Planet 9, the time for light to travel to the orbital envelope would be about 55-110 hours (estimated at 10-20 times the distance to Pluto - it takes 5.5 hours for light to travel to Pluto.)  I have to calculate the light intensity requirement in order to determine the number of lasers and the intensity required, but they'd pretty much be aligned around the base(s) at some elevation which would allow them to be positioned such that they could target a range of positions on the faces of either or both pyramids to escape at any angle throughout the visible hemisphere, from rising horizon, to meridian, to setting horizon, in order to converge at points in space within a set of search parameters.

By an estimate of the size of the proposed planet and the orbit, it would be possible to calculate the number of scan points required to find it.  Scanning every 1/2 of the best guess of the diameter of the considered object should be sufficient to map space, though there's likely an optimal search step that would prevent any large object from hiding within the search results.

It would seem plausible to turn the search for Planet 9 into a scan plot that searches depth or breadth first through regions of space.  A series of pulses could be sent out to locations at regular intervals, based on the pulse duration of the laser units, time to aim the units, and any needed sequenced firing to avoid heating the atmosphere.

I'm sure there are potentially a million issues, but if this idea isn't hair-brained and it actually got built and it actually worked, it'd be likely we'd go full-tilt and fire constantly every fraction of a second to cover the huge expanse of space the planet is considered to inhabit.  I'm going to see if I can calculate the number of data points required to scan a region and the time it would take to process them.  It's probably a long time.  It's been forever since I calculated AU and converted it to small steps.  Did I say forever?  I meant never.  I've calculated a lot of stuff, but never AU for any reason.  After looking at the orbit and distances, it really seems like looking for a planet - or anything, for that matter - with a telescope would be excruciatingly painful and s-l-o-w.

The sequence for a sample might be 1) aiming the lasers, 2) firing the lasers*, 3) scanning for the response at the expected time of arrival, 4) detecting the signal and recording the response.  From there, it would require mapping the successful soundings, while doubling back over any reading that resulted in a lost signal to see if it was caused by interference or having bonked a planet.  Once the initial delay for the first signal to travel to destination is discovered, it'd be possible to collect data every few minutes, seconds, or fractions of a second, depending on ability to sequence, aim, fire, and detect.

Looking for reflected light far, far away is hard.  Putting a bright spot into space and waving it around until it hits something is fast and easy.  Ask any kid with a flashlight.  Scanning empty space with telescopes that shake, vibrate, and need massive data correction is so 1923.  It's time for telescope-microscopes with laser finders.  If the idea has merit, of course.

In Conclusion

By pointing a telescope onto an optically precise, reflective surface, they become, in essence, a microscope, capable of viewing into space consistently, by virtue of short focal distance to the object being reflected.  Combining surface stability with the ability to accurately aim and move the telescope (as microscope) slowly, and with equal or better precision relative to the orientation of the observing platform (accurately aligned pyramids), large areas of space could conceivably be scanned quickly, methodically, and with great accuracy and precision.

Further, a collection of lasers aimed onto the surface of the pyramids, such that they converge on a distant point in space, and with controlled intensity, could possibly (maybe?) make it possible to use them as a scanning and detection system for distant bodies, especially those hard to observe because they're so far distant from light sources.  The advantage of multiple lasers converging on a point means that the work of the lasers can be distributed, lower cost, lower energy, emitting lower heat.

The array of lasers would be constructed to ensure that the intensity of the spot created by their union was detectable in the region of space being observed and/or scanned.  Such a targeting system would likely and significantly improve our ability to locate objects in space.

Measuring Redshift in the Faces of the Red Pyramid of Giza

In the previous paper I'd posted on the pyramids of Giza, I did my best to show that they were constructed as astronomical observatories by virtue of the precise nature of their construction.  I tried to show how, by virtue of highly uniform, reflective surfaces of optician's quality, a group of individuals could monitor and survey the heavens and measure the precise location of an object in the space above the pyramids with a high-degree of precision.

In this paper, I'll attempt to show how the red pyramid of Giza, in concert with the two larger pyramids of Giza, both finished with white limestone, could have been used to measure the red shift in bodies in the reflection on the faces.

The math to survey objects reflected in the face of the red pyramid would be identical to the math to find an object in the face of the two larger pyramids.  What would differ is the color that would be allowed to pass through the specular reflection of the face.

Because the surface of the red pyramid is red, it would enhance the visibility of red in the objects reflected (by enhancing saturation), while reducing colors in the green/blue/violet end of the spectrum.

I'm no astronomer, but I'm pretty sure filtering on the characteristics of the redness of objects would make it possible to give some thought to redshift of the objects.  If some determination of redshift (or red spectral data) were possible, then by combining positional detail from the main pyramids, with redshift data from the red pyramid, a complete picture of the location of an object can be determined, along with the speed at which the object is moving away from the point of observation.  That kind of sounds like astronomy to me.

I've been really busy of late and haven't had time to write the stack of papers in my head regarding the pyramids.  I'm hoping that after I finish something else I've been working on, I can devote more time to the pyramids and start putting the science into the overview.  It'd be fun to bring in some mathematicians and scientists to work out some of the modes and methods of operation the pyramids provided to the study of astronomy, space, and physics.

The Pyramids of the Giza Plateau: Astronomical Observatories Based on a Mathematical Model of Vision

[Note: This article was originally posted on the blog 'Luck-e Jake']

December 6, 2015
Michael J. Ajemian

The Pyramids of the Giza Plateau:

Astronomical Observatories Based on a Mathematical Model of Vision

[updated intro 12/21/15; added background description and fixed a typo.]  This concept was an accidental discovery on 6/18/95.  I'd read a book about the Great Pyramid, kept wondering why all the precision construction, then noticed something in the reflection of a marble table as I moved my head - I realized I could see things using reflection that I couldn't see directly as I looked at the view out the window in the table.  The math wasn't difficult to understand.  But for a head injury I briefly died in just prior to learning how it worked, this would have been written years ago.  I hope you enjoy it, because to me, it's really exciting!

The pyramids of the Giza plateau represent perhaps the most recognizable architecture in the world.  The Great Pyramid is an engineering marvel and enigma.  The entire structure inspires a sense of awe for it's dimension, sringent specifications, and the incredible problems in engineering that had to be solved just to build the hulking structure.

At the time of construction, the pyramids were covered in highly polished limestone.  Evidence of the limestone casing is seen around the base of the pyramid of Cheops.  Sir Flanders Petrie noted the precision of the casing stones as being "equal to opticians' work of the present day, but on a scale of acres" and "to place such stones in exact contact would be careful work; but to do so with cement in
the joints seems almost impossible". (Romer, 2007, p. 41) Pretty cool stuff to look at.  From an engineering perspective?  It's mind-blowing.

While most people think the pyramids are monstrous tombs, the unbelievably surreal precision of the faces suggests a purpose to the structure beyond simply shining like a jewel in the sun.  In fact, it seems to me they were built for astronomy by some people who understood the mathematics of vision.

The faces of the pyramids were optically true and highly reflective.  Both a true surface and high reflectivity are requirements of a mirror.  Since each face is angled skyward, they'd allow a viewer looking at a face to see reflections of objects in the sky with superior clarity.

The courses of highly-polished limestone of optical precision were of a small range of sizes, but their courses varied at somewhat regular intervals.  Interestingly, in the dark, the 1/100th gap between casing stones would have provided a grid within which to assist in precisely locating object position relative to an observer surveying the surface.

Having a structure that is stable, oriented to true north, and is highly reflective, except for the thin lines of the gaps between stones comprising the shadowed grid, would appear to provide the means to view the reflections of objects in the sky and their position in the faces with superior precision.

Should an intrepid viewer have positioned themselves at the center of the base of the south face and simply looked up the apothem, the center line of the face, it would have been possible for them to have observed the passing of stars in the reflection of the face, simply by observing along the apothem:

Figure a. The Apothem

If our observer were to find themselves in possession of a pencil, papyrus roll, and time keeping device, they could not only have observed the location of the (primarily northern) stars passing
through the line marking the center of the face, but transferred that position detail to their papyrus.  The papyrus could conveniently roll along with the passing of time and be a collection of pencil dots
where bodies were recorded at the time they transited the meridian (the apothem is aligned with the meridian).  By collecting data in such a manner, it would seem possible that way back in the olden, olden, olden days, they could have made star maps with the help of the pyramid tombs.

Having one observer on one face represents an opportunity to collect good data, but it's limited.   Were a set of four observers positioned, each before a face of the pyramid, such that they were each observing the same celestial bodies in the reflections at the precise time the object reached the meridian it would appear to be possible to calculate the celestial longitude, latitude, and distance to bodies in the sky.

Figure b & c, show two views of the same observation in a somewhat iconic way.  Each observer would see in the reflection in their respective faces as S transits the meridian of the pyramid.  Both observers 2 and 4 note the time as S transits the meridian.  The time will be used to calculate the hour angle of S from a reference meridian.  All observers record position detail with the intention of calculating a set of angles to derive declination of the star relative to the celestial equator.

Figure b. Top view of a star to four observers on their respective faces.

Figure c. Side view of a star to three observers on their respective faces.

Declination is derived by:

1. Finding the position of the star by intersection of the vectors at a point S.
2. Projecting a vector from the center of the earth through the point S
3. Calculating the angle formed between the vector projecting from the center of the earth through the equator at hour angle T.

Because the structure was so stable, it would appear to have been possible to measure bodies in the sky with a great deal of precision over time.

Once it becomes possible to calculate distance to a point, it becomes possible to calculate distance to a myriad of points.  It would also be possible to record colors, though that's not the focus of this paper.

This paper will attempt to highlight how the pyramids of the Giza plateau were constructed such that they operated as a mathematical model of vision, complete with color mapping, and depth perception.

Constants and Structural Notes

The concept is initially explored using one pyramid.  First, some facts about the Great Pyramid:

1. At time of construction, the surfaces of both pyramids were complete and uniform.
2. The surfaces of both pyramids have "optical precision on a scale of acres." (Romer, 2007, p. 41)
3. The surfaces of both pyramids are highly reflective.
4. The faces are slightly concave, with a noticeable depression running down the center of each face.  The center of the four sides are indented with precision, thus forming an 8-sided pyramid.
5. The pyramid is oriented to true north.
6. The angle of the faces of the pyramid are each 51.8 degrees.

The math of a single pyramid as it relates to vision

In order to highlight the function of the pyramid as observatory, a series of experiments will be presented, from the basic to the complex.

Experiment 1 - Reflection of a vector on the face

An observer is positioned at the center of a face, orthogonal to the base, sighting the apothem on the horizontal.

Using Reflection

Having established the observer's position, attitude, and distance from the base, a point is marked on the viewers horizontal, coincident with the apothem.  By establishing a stable viewing position along the horizontal, it becomes possible to calculate the angle of reflection.  This is an essential starting point.  Because the angles of the face (A and B) are known, and the observation vector is horizontal, the angle of reflection is the special case, found by subtracting the angles:

R = 90.0 - 51.8 = 38.2

Figure 2. Finding the angle of reflection for degenerate case (horizontal observation.)

This case is meant to highlight how to begin using the system.  The ray from the observer's eye is projected to the surface and the incident angle is discovered.  In this base case, the incident angle of the reflected ray is calculated by virtue of the stable angles of the face (angle B is 38.2 degrees.)

Experiment 2 - The Intersection of Reflected Vectors

Before finding the intersection of a vector, the reflection vector needs to be calculated.  The following graphic highlights the sequence to solve for reflection vector P.

Figure 3.1. Sequence of calculations to find the projection vector P.

The sequence to solve for the projection vector P, as displayed in Figure 3.1, are repeated for clarity:

1. Measure distance CF, from point of observation to base.
2. Calculate triangle ABC
3. Calculate triangle BDE
4. Calculate triangle BEF
5. Calculate reflection angle R
6. Project vector P
7. Calculate the intersection of P with other vectors (not shown.)

The sequence above is repeated in the next example to find the point of intersection (I) for two observers surveying points at equal height e and e-prime along the apothem:

Figure 4.  Calculating the point of intersection from point of observation (f).

Figure 4 shows two vectors reflected at an equal altitude, along the apothem of opposing faces.  By virtue of their being projected along the apothem, they'll intersect somewhere, but in this special case, their being surveyed at equal altitudes means they'll intersect directly over the cap of the pyramid.

In order to observe how resolution changes with height, the viewers agree to sample a more points along the apothem at equal altitude.  As the reflection angle increases, the altitude of the point of intersection decreases.  As the reflection angle decreases, the altitude of the point of intersection increases.  The change in altitude is akin to depth perception in the eyes.

Figure 5. Change in altitude of vectors calculated at equal, but progressively greater heights.  An increase in altitude of the point of reflection results in a decrease in altitude at the point of intersection.

The following graphic shows the field of view available to a single observer at the center of the base of a face of the pyramid.  By combining the field of view available to observers at the center of all four faces, a single pyramid can be used to observe, via reflection, points that lie most anywhere within the celestial hemisphere.

figure 5 - Celestial Hemisphere

It's Three Dimensional

Figure B (above) shows the position of a star, and its reflection on four faces.  It shows iconically the reflection of the star in each of the faces.  By having each observer measure position on the face (height, distance from apothem) the angular measures can be discovered and the reflection vectors calculated.  In this case, the calculations are a bit more complex, especially finding the point of intersection of the vectors.  But the sequence is stable and consistent.


Stereoscopic Vision & Meridians

The following graphic shows how the star S from Figure B might appear to 8 observers at the faces of two pyramids.

Figure 7.  Stereoscopic view of star S in the reflections of the faces of two pyramids at time T(0).

Figure 8.  Stereoscopic view of star S in the reflections of the faces of two pyramids at time T(1).

Figure 9.  Stereoscopic view of star S in the reflections of the faces of two pyramids at time T(2).

In the series of figures (7-9), a star S is shown at three positions in time.  One of the nice features of having two pyramids aligned to true north is that each provide an arc time and angle at the meridian for each.  The earth's rotation provides a constant background to measure the arc angle and arc time against.  The arc time between the pyramids is a constant.  If something moves faster or slower than the earth's rotation, it would seem to indicate the direction of travel of the object.  Plus, if the declination or distance changed, especially as measured over time, the direction and velocity of the object would appear to be possible to determine.

While star calculations are interesting, scanning applications are pretty interesting too.  Calculating the distance to a point in space using one pyramid appears to provide high utility in that a number of vectors can be calculated, with accuracy increasing with the number of viewing positions.  The introduction of a second pyramid would seem to improve precision.

But, the ability to measure depth in the angled faces in the pyramids, combined with a relatively large distance between pyramids, means that each face can be used to construct patches of an object by collecting a range of data points from each face.  The patches constructed from the survey of the reflected points of the object in each face represent distinct views of the surface of an object, with depth, which when assembled (using reference points to align patches) would create a projection of the object in three dimensions.

It would seem that any object which could be recorded, could also be projected to reconstruct the object or location in space above a projection mechanism.  It'd be fun to see if this would work to create holographic projections.

Construction of Surfaces

Creating a scanner using the pyramids would involve utilizing a large number of observational positions to an object.  The number of observational positions and their location would vary, but the more positions records as points in space, the more surface detail to an object are recorded as a point cloud.  The ability to construct surfaces from point clouds has a set of well-defined solutions and products which facilitate surface construction.

While one pyramid is enough to get a sense of the shape of an object, using the two pyramids would seem to facilitate constructing stereoscopic images from a collection of manifolds, each created by virtue of collecting a large cross-section of points, converted to a manifold.

Conclusion

In conclusion, the math appears to support the distinct possibility that the pyramids at Giza were used to reckon stars accurately, and that the reckoning would be by arc angle, declination, and distance.  By virtue of a stable structure and a series of well-defined steps, it would be possible to calculate vector projections through a point on the face, extending into space.  The vector projections, when combined from observational positions near the original observational position, provide a stable mathematical base to calculate distance to an object.

It would seem, if the system is as stable as it appears, that with a little creativity and insight, this mechanism can provide hours of fun and entertainment to creative individuals as a surveying instrument, holographic projection system, medical scanner, surgical knife, medical 3D scanner.  Seems like whatever we would use our eyes to do could be modeled, from the highly focused to the wide angle.