Astra
Giza
Satellites



...before i can do anything... i need to start with...
exact, established, accepted measurements of the
pyramids and other various structures themselves
(such as the satellite pyramids, and the sphinx, etc)
...for the 3 main pyramids... i started with Legon
who seems comprehensive, and cites Petrie's data
...but the measurements for "the Queens"
or "satellite" pyramids are not easy to find
and there seems to be a discrepancy
in the conversion of a cubit to the
more familiar (modern) measurements
...which i haven't needed until now
what Legon calls a Royal Egyptian Cubit
equal to 20.62 inches or 0.52375 meters
is apparently a different kind of cubit
than what the common folk are using....
from: Tour Egypt, (Khufu), (Menkaure)
Queens Pyramid G1a
Base length 49.5 meters square
Original height: 30.25 meters
Angle of inclination 52

Queens Pyramid G1b
Base length 49 meters square
Original height: 30 meters.
Angle of inclination 52

Queens Pyramid G1c
Base length: 46.25 meters square
Original height: 29.62 meters.
Queens Pyramid G3a
Base length: 44 meters
Original height: 28.4 meters
Angle of inclination: 52 15'

Queens Pyramid G3b
Base length: 31.24 meters

Queens Pyramid G3c
Base length: 31.24 meters
i can find no correlation to those particular ratios
every conversion website says a cubit = 18 inches
...and while there are a few other types of cubits
none of them chime in at that magic 20.62 inches
...the closest is long cubit (biblical) 0.5334 m, 21"
...so, it's... been a... little bit o... frustrating...
i want to keep it as simple and basic as possible
while maintaining a responsible level of accuracy
...and i definitely want to use Legon's cubits...
...that's where the numbers seem to match best...
(maybe i can convert everything to modern meters)
....... Mean Sides of the Giza Pyramids ....
...... Petrie .................. Legon .....
..... Inches .. Azimuth  .. Cubits .. Design
G1 .. 9068.8 ..  -3' 43" .. 439.81 .. 439.82
G2 .. 8474.9 ..  -5' 26" .. 411.00 .. 411 
G3 .. 4153.6 .. +14' 03" .. 201.44 .. 201.5 
so... this is what i have to start with...
which leaves me alot of blanks to fill in
39.3701 inches per meter
0.0254 meters per inch
20.620 inches per cubit
0.0484 cubits per inch
0.524 meters per cubit
1.909 cubits per meter
 ..... inches ... meters .. cubits .. Design .. model
G1a .. ------ ... 49.50 ... ------ .. ------ .. -----
G1b .. ------ ... 49.00 ... ------ .. ------ .. -----
G1c .. ------ ... 46.25 ... ------ .. ------ .. -----

G1 ... 9068.8 ... ------ .. 439.81 .. 439.82 .. 440
G2 ... 8474.9 ... ------ .. 411.00 .. 411.00 .. 411
G3 ... 4153.6 ... ------ .. 201.44 .. 201.50 .. 201.5 

G3a .. ------ ... 44.00  .. ------ .. ------ .. -----
G3b .. ------ ... 31.24  .. ------ .. ------ .. -----
G3c .. ------ ... 31.24  .. ------ .. ------ .. -----
 ... meters / 0.0254 = inches
G1a = 49.50 >> 1948.8188976377952755905511811024
G1b = 49.00 >> 1929.1338582677165354330708661417
G1c = 46.25 >> 1820.8661417322834645669291338583
inches / 20.620 = Royal Egyptian Cubits
G1a >> 94.511100758379984267243025271678
G1b >> 93.55644317496200462817996441033
G1c >> 88.305826466163116613333129673036
G3a = 44.00 >> 1732.2834645669291338582677165354
G3b = 31.24 >> 1229.9212598425196850393700787402
G3c = 31.24 >> 1229.9212598425196850393700787402
G3a >> 84.009867340782208237549355797042
G3b >> 59.647005811955367848660042615907
G3c >> 59.647005811955367848660042615907
...or... using Legon's...
conversion factor, direct
0.52375 meters per cubit
1.90931 cubits per meter
slightly off... (1000ths)
 ... meters / 0.52375 = cubits
G1a >> 94.510739856801909307875894988067
G1b >> 93.556085918854415274463007159905
G1c >> 88.305489260143198090692124105012
G3a >> 84.009546539379474940334128878282
G3b >> 59.64677804295942720763723150358
G3c >> 59.64677804295942720763723150358
 ..... inches ... meters .. cubits .. Design .. model
G1a .. 1948.82 .. 49.50 .... 94.51 .. ------ .. -----
G1b .. 1929.13 .. 49.00 .... 93.56 .. ------ .. -----
G1c .. 1820.87 .. 46.25 .... 88.31 .. ------ .. -----

G1 ... 9068.8 ... 230.5 ... 439.81 .. 439.82 .. 440
G2 ... 8474.9 ... 215.25 .. 411.00 .. 411.00 .. 411
G3 ... 4153.6 ... 105.5 ... 201.44 .. 201.50 .. 201.5 

G3a .. 1732.28 .. 44.00 .... 84.01 .. ------ .. -----
G3b .. 1229.92 .. 31.24 .... 59.65 .. ------ .. -----
G3c .. 1229.92 .. 31.24 .... 59.65 .. ------ .. -----
so... already accepting
the commonly established
440 cubits per side for G1
that rounded off conversion
comes out to: 230.56 meters
...rounding off, there...
...there's a discrepancy:
440 x 1.909 = 230.4871...
440 / 230.56 = 1.90839...
of almost 7.3 centimeters
230.56 - 230.4871 = .0729
seventy-three millimeters
over just a quarter km...
...or inches to meters...
it's off (about the same)
in the other direction...
...i couldn't find any...
meter measurements online
(for the main 3 pyramids)
at that level of accuracy
to verify my calculations
...so that's close enough
for the non professionals
so, i'll just use these numbers
...(and be happy i have any)...
 ..... model
G1a ..  95
G1b ..  94
G1c ..  88

G1 ... 440
G2 ... 411
G3 ... 201.5 

G3a ..  84
G3b ..  60
G3c ..  60
if anything turns out off a little bit
i can always come back here n check...
now for heights
...in cubits...
 ..... meters . cubits
G1a .. 30.25 .. 57.756563245823389021479713603819
G1b .. 30.00 .. 57.279236276849642004773269689737
G1c .. 29.62 .. 56.553699284009546539379474940334

G3a .. 28.40 .. 54.224343675417661097852028639618
G3b .. .....
G3c .. .....
 ..... base . height
G1a ..  95 ... 57.76
G1b ..  94 ... 57.28
G1c ..  88 ... 56.55

G1 ... 440 ... 280
G2 ... 411 ... 274.5
G3 ... 201.5 . 125

G3a ..  84 ... 54.22
G3b ..  60 ... -----
G3c ..  60 ... -----

diagram of G1abc, showing erosion and passageways, (below)
from: http://www.touregypt.net/featurestories/greatpyramid6.htm
(click for hi-rez)
downward view of G1abc, from G1, facing ESE (above)
from: http://cheops-pyramide.ch/pyramid-building.html
side view of G3abc, from the south, facing north (below)
with G3, G2 and G1 in the background from: Wikipedia
just bearing in mind...
the satellites are fuzzy...
and that significant erosion...
over... (however many) millennia...
puts the satellites so much smaller...
relative to their original dimensions...
than their larger parental counterparts...
...now, the first question i asketh the gods
when presented with pictures like this... is
why don't they restore them, to the original
height and base squares, make it look nice ?
(or, being gods... kindly direct someone to)
...and then i'm given a map like this one...
so that i should stop asking silly questions
...as for positioning: this is supposedly...
...the best map available (to the public)...
high resolution (2000 pixels square) scan of
something somebody drew, basically... hooray
...but, this is what the cool kids are using
G1abc (above)
G3abc (below)
...shaded, from
the GPMP map
(as on Layout)
view full version:
small (500x500)
large (995x1000)
giant (1991x2000)
...and i don't have height data for G3b or G3c...
so, for now, they'll just be proportional to G3a
(i won't be lopping their tops off, yet, anyways)
maybe i can get a nice side view
and calculate from their slopes,
but they're step-pyramids, so...
and i'll do those
that's no trouble
(but by how much)
...anyways... positioning...
...deriving... coordinates...
the one thing... i really need
to be as accurate as possible:
(where they are on the ground)
zero data available... and the
official map everybody's using
...well... i've been to a mall...
...this is what they throw at you
when they want you to go away
...an exit, i can discern...
Giza has got to be... the most... meticulously measured...
cartographed, categorized... and studied set of structures
ever officially known to exist on this or any other planet
...and this is the best map available... to the public...
so now i have to go to Petrie... and derive, geometrically
(triangulation, coordinates, same Petrie data source link)
...or i could just... try my luck with the satellite image...
...which is the kinda thing... ya hafta admit failure with...
before you even begin, but there's proportions to be had
the very large nice one i have... Quickbird
is at 657 x 778 pixels for the pyramid area
...which translates to 1417.5 x 1732 cubits
resampling that image, to those dimensions:
means expanding it to 223 percent original
bringing it up to about 1 pixel per cubit
...and it's not aligned perfectly NSEW...
so, i have to rotate it... 0.2 degrees...
and a pixel isn't the same... X to Y axis
so, i have to stretch my overlay template
and that's when you begin to doubt it all
cubit per pixel scale template (above)
pyr-scales.gif (900x950) half scale size
pyr-scale.gif (1800x1900) pixel per cubit
template with stretched overlay (below)
pyr-scales.jpg (900x950) half scale size
pyr-scale.jpg (1800x1900) pixel per cubit
and the above is a work in progress...
every time i look at it, i think maybe
it's off a little... here and there...
from my Layout page, i know where G1, G2 and G3 are
and i know what their dimensions are supposed to be
(and i know the measure of the spaces between them)
G1 = 440
G2 = 411
G3 = 201.5
G1-G2 = 213 x 250
G2-G3 = 152 x 129.5
total = 1417.5 x 1732
the basic idea is: to just stretch the satellite image
until the 3 main pyramids match the pixel template
and then just line up the satellites the best i can
but, because the Quickbird satellite image
was captured from something other than
directly above the exact, precise location
which is evident from the off-center peaks
...it's not off by exactly the same amount
from one side of the image to the other...
it needs to be stretched in 3D perspective
by a very tiny amout... couple of degrees
either that, or the measurements are wrong
and while i haven't measured them, myself,
...i trust those as well established figures...
...and the lines are categorically unclear...
wherever any pyramid... meets the ground
...it's just impossible to be totally certain...
and i don't want to stretch the template
...though i could always stretch it back
...what i need is an algebraic formula...
...and then some software to plug it into
...but, what i really need is... just some proper measurements...
...what i guess i'm saying is... it's the 21st century already...
somebody's laid some lasers down... those're the digits i require
it's tricky... ya gotta watch the shadows,
ya gotta compare as many sources as ya can
...weighing them for what they're worth...
and ya don't always know,,, can't possibly
(there's an unknowable number of unknowns)
...but ya keep playin with it...
...adjusting... here n there...
and then you have to walk away
...clear your muddled mind of it
and come back again later, fresh
reckonings for centers (x)
G1a .. 156 N G1s, 153 E G1e 
G1b ... 40 N G1s, 150 E G1e 
G1c ... 60 S G1s, 144 E G1e
G3a ... 84 S G3s,  8 E G3x 
G3b ... 88 S G3s, 16 E G3w 
G3c ... 88 S G3s, 72 W G3w
perhaps with a better understanding of the geometry involved
we can get a better idea and possibly adjust more accurately
that's fancy talk
for... "whatever"
G1a = ... 220 + 153 = 373 ....... -220 + 156 =  -64
G1b = ... 220 + 150 = 370 ....... -220 +  40 = -180
G1c = ... 220 + 144 = 364 ....... -220 -  60 = -280
G1a ... ( 373 ,  -64 )
G1b ... ( 370 , -180 )
G1c ... ( 364 , -280 )
G3a = -1096.75 +  8 = -1088.75 .. -1512 - 84 = -1596
G3b = -1197.50 + 16 = -1181.5 ... -1512 - 88 = -1600
G3c = -1197.50 - 72 = -1269.5 ... -1512 - 88 = -1600
G3a ... ( -1088.75 , -1596 )
G3b ... ( -1181.50 , -1600 )
G3c ... ( -1269.50 , -1600 )






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