Date: 07-03Ä94 (19:21) F:UFO
Fr: DON ALLEN Read: NO
Subj: MESSAGE OF CYDONIA
The "Message of Cydonia"
First Communication from an Extraterrestrial Civilization?
By Richard C. Hoagland *
and Erol O. Torun @
Copyright (C) 1989
All Rights Reserved
For the past 13 years -- ever since an unmanned NASA Viking spacecraft
successfully photographed the surface of the planet Mars in 1976 -- a
mystery has loomed . . . a mile-long, 1500-ft high humanoid "face"
discovered in a northern Martian desert called "Cydonia." In its immediate
vicinity have been identified other "anthropomorphic objects": most
notable, several "pyramids" (see Fig. 1). Various investigators [Owen,
1976 -- see Hoagland (1987); DiPietro and Molenaar (1980); Hoagland (1986);
Pozos (1986); Hoagland (1987); and Carlotto (1988)] have examined this
collection of objects over the past 13 years, and have reached widely
varying conclusions. The essence of the controversey -- its potential
importance or non-importance as a "scientific" problem -- is perhaps summed
up best by Hoagland (1987):
"Either these features on Mars are
natural and this investigation is a complete
waste of time, or they are artificial and
this is one of the most important discoveries
of our entire existence on Earth. If they
are artificial it is imperative that we
figure them out, because they 'do not belong
there.' There presence may be trying very
hard to tell us something extraordinary."
Background to This Study
The initial purpose of this study was an examination of the "Cydonia
mathematics," which at first glance emphasize the importance of two
"dimensionless constants": "e" (the base of natural logarithms = 2.718282);
and "pi" [the ratio of the circumference of a circle (or sphere) to its
diameter = 3.14159]. These two constants appear, both separately (as "e"
and "pi"), and apparantly together (as "e/pi"), redundantly encoded in the
fundamental geometry of the layout of the "anomalous features" at Cydonia.
* The Mars Mission: Box 981, Wytheville, VA 24382; (703)-228-7822
The Significance of "e/pi"
Following these discoveries, the authors (this paper) began the
current systematic inquiry into whether there was indeed a "message" at
Cydonia: encoded geometrically in terms of specific placement of specific
objects, by means of redundant mathematical ratios derived by dividing the
observed angular relationships into one another. Over the last century or
so, several prominent proposals have been made for encoding "CETI" messages
by means of mathematical constants (Cocconi and Morrison, 1959; Sagan,
1973; Rubtsov and Ursal, 1984), and even physical geometric relationships
on planetary surfaces (Gauss, et al., -- see Crowe, 1986).
In particular, the authors were attempting to determine if e/pi =
0.865 [as opposed to the more fundamental ratio (sqrt 3)/2 = 0.866] was the
ratio specifically intended at Cydonia. Others (notably Davies) had
already raised key questions regarding this potential ambiguity.
Other constants demonstrated at Cydonia by Hoagland and Torun being
"sqrt 2," "3" and "sqrt 3" (1988), this confusion regarding which constant
was "really" represented by the observed, redundant angle ratios, trig
functions, and radian measure was considered an important question to resolve.
Since "3" and "sqrt 3" are numbers essential to calculating "areas" and
"volumes," Torun decided to explore their geometric implications first,
following on Gauss (op cit).
He began by investigating geometrical relationships among several
fundamental "Platonic solids": the tetrahedron, cube, octahedron,
icosohedron, and dodecahedron. In pursuing these explorations, Torun
examined the mathematical properties of "circumscribed polyhedra" -- the
Platonic solids embedded in a sphere.
Almost immediately, he discovered something quite astonishing (to a
non-specialist): the surface area of a tetrahedron (the "lowest order,"
simplest Platonic form), inscribed inside a "higher-order" form -- a sphere
-- results in a surface ratio (sphere/tetrahedron) almost precisely
equivalent to "e," the base of natural logarithms:
e = 2.718282
surface of sphere
------------------------------------ = 2.720699
surface of circumscribed tetrahedron
Difference = 0.002417
The derivation of the above is as follows:
(expressions are written in FORTRAN notation)
Let A(t) = surface area of tetrahedron
A(s) = surface area of circumscribing sphere
R = radius of circumscribing sphere
For a regular tetrahedron of edge a:
A(t) = a**2 * sqrt(3) and R = a * sqrt(6)/4
For the circumscribing sphere:
A(s) = 4*pi*R**2 = 4*pi * (a*sqrt(6)/4)**2 = (3/2)*pi*a**2
Area of sphere/area of circumscribed tetrahedron
A(s)/A(t) = (3/2)*pi*a**2/(a**2 * sqrt(3)) = 3*pi/(2*sqrt (3))
A(s)/A(t) = 2.720699 - an approximation of e = 2.718282
When Torun substituted this "close approximation of e", termed e', in
the equation most approximated at Cydonia:
e/pi = 0.865
He discovered that:
e'/pi = 2.720699/3.141593 = 0.866025 = (sqrt 3)/2
Or . . . precisely the observed "e/pi" ratio discovered at Cydonia!
The fact that e'/pi equals (sqrt 3)/2 can be demonstrated
Since e' was defined as 3*pi/(2*sqrt (3)),
e'/pi = 3*pi/(2*sqrt (3)) / pi = 3/(2*sqrt (3)) = sqrt(3)/2
To place the above math in simple terms:
The values of e/pi and (sqrt 3)/2 are
precisely equal when e/pi is evaluated using
the approximation of e that is generated by
the geometry of a circumscribed tetrahedron.
This simple fact completely resolves the ambiguity regarding which
ratio -- e/pi or (sqrt 3)/2 -- was intended at Cydonia (see Fig. 4):
Apparently, both were!
Since the most redundantly observed Cydonia ratio is 0.866 and not
0.865 (the true ratio of the base of natural logarithms, divided by Pi --
to three significant-figures), it must now be clear, however, that the
*primary* meaning of the "geometry of Cydonia" was in all likelihood
intended to memoralize the (sphere)/(circumscribed tetrahedron) ratio
[which is also (sqrt 3/2)], and not "e/pi".
Further examples of "e/pi" at Cydonia -- appearing in connection with
the ArcTan of 50.6 degrees (present at least twice in association with the
Face) -- when examined by Hoagland, confirm that Torun's "circumscribed
tetrahedral ratio" -- e' = 2.72069 -- and NOT the base of natural
logarithms (e = 2.718282) provides a closer fit to the observed number--
Thus strongly implying that "tetrahedral geometry" (and NOT the usual
association of "e" with "growth equations") is the predominent meaning of
"e/(sqrt 5)" and "(sqrt 5)/e" -- two other specific ratios found
redundantly throughout the complex:
e/(sqrt 5) = 1.215652
e'/(sqrt 5) = 1.216734
Cydonia ratio = 1.217 = ArcTan 50.6 degrees
(The detailed implications of this association -- e' and (sqrt 5) --
will be examined in a subsequent paper.)
These results, combined with other examples in the Complex (D&M
Pyramid angles 60 degrees/ 69.4 degrees = 0.865 ) are what lead us to the
conclusion that in fact *both* constants -- e and e' -- are deliberately
encoded at Cydonia. In particular:
D&M Pyramid apex = 40.868 deg N
= ArcTan 0.865256 = e/pi
But another feature on the D&M -- the wedge-shaped projection on the
front -- defines the Pyramid's bilateral symmetry and orientation directly
toward the Face. This feature also now seems to mark an equally important
D&M "wedge" = 40.893 deg N
= ArcTan 0.866025 = e'/pi = (sqrt 3)2
Torun identifies a conspicuous "knob," lying at the end of this wedge,
as the "benchmark" designed to mark precisely the correct "e'/pi" latitude
-- 40.893 degrees, approx. 1/40th degree North of the true apex of the
Pyramid. The terminus of this wedge, together with the NW corner of the
pyramid, are the only two points on the pyramid that, when connected,
denote a line of latitude (see Fig. 5).
Again, putting this in simple terms:
The geometry of a circumscribed tetrahedron
is not only suggested by the alignments in
Cydonia, but also by the siting latitude,
size, shape, and orientation of the D&M
This discovery only underscores the importance apparently attached to
"circumscribed tetrahedral geometry" in the construction of Cydonia --
raising the important question:
The "Message of Cydonia"
Verification of a highly-specific and redundant communication of
"circumscribed tetrahedral geometry" -- including its obviously *deliberate*
extension to the siting of the Cydonia Complex on the planet -- would be
deemed a phenomenonal discovery. If this is indeed "the message of
Cydonia," crafted by what Mars' hostile environment strongly implies was a
visiting interstellar culture (Hoagland, 1987), then what could have been
To communicate the "importance" of tetrahedral geometry itself!
If this is the successful "decoding of the Message" -- its existence
(if not the sheer effort expended in its communication) must in turn raise
obvious questions regarding "hitherto unrecognized properties" of
Understanding the Meaning of "the Message": Verification
in Hitherto Unrecognized Geophysical Phenomena
Since the latitude of the entire Cydonia Complex seems to have been
carefully chosen to reflect the ArcTANGENT of this circumscribed
tetrahedral "message, it occurred to the authors that "something important
might lie at the LATITUDE represented by the vertices of a circumscribed
tetrahedron -- placed 'inside a planet'." This would represent the most
elegent expression of the ArcTANGENT trignometric function emphasized
repeatedly within the Complex -- especially the choice (out of more than
18,000 possible other choices, to equal numerical precision) of the
specific Martian latitude: 40.87 N.
In working out the several possible implications of such geometry,
Torun promptly discovered the following: if a circumscribed tetrahedron is
placed inside a globe representing a gridded planetary surface, with one
vertex located either on the geographical "North" or "South" polar axis,
the resulting latitude TANGENT to the other three vertices will lie at 19.5
degrees N. or S. -- 120 degrees of longitude apart.
Torun (1989) immediately noted on Earth the existence of several
significant Meso-American ceremonial complexes at this specific northern
latitude -- raising intriguing cultural and scientific possibilities for
lost or forgotten "ancient knowledge of the significance of circumscribed
tetrahedral geometry" (Becker and Hagen, 1987). Unfortunately, these
implications are too extensive for inclusion here.
Hoagland noted something more physically significant: the largest
shield volcanic complex on Earth -- the Hawaiian Caldera -- is located very
close to 19.5 North! He then realized that a similar latitude marks the
location of the largest shield volcano currently known in the entire solar
system: Olympus Mons, at 19 N. -- on Mars.
Subsequent survey of solar system geodetic maps -- made from
spacecraft photography of the past thirty years, encompassing planetary
surfaces from Lunar Orbiter images of the Farside of the Moon, to Voyager 2
close-ups of Uranus, its satellites, and now (at this writing) the planet
Neptune -- revealed a remarkable (and currently inexplicable) geophysical
phenomenon (see Table 1):
The majority of "active centers" on these objects -- from the greatest
shield volcanos on the "terrestrial planets" (including equivalent features
on their most anomalously active satellites!), to the enormous atmospheric
disturbances seen on some "gas giants" ("The Great Red Spots" of Jupiter
and, now, of Neptune) seem preferentially to occur very close to 19.5
degrees N. or S., irrespective of other planetary factors -- mass, rotation
rate, obliquity to their respective orbits, etc. (see Fig. 6)!
There was some indication, however, that the polarity of the dipole
magnetic field, offset from the spin-axis, determined in *which hemisphere*
the phenomenon appeared; Jupiter's GRS, at approximately 20 degrees S., is
consistent (in this model) with its opposite (from terrestrial convention)
dipole field polarity. [This raises the interesting possibility of a
"magnetic field prediction" vis a vis Neptune, before the up-coming Voyager
Encounter (Aug 25, 1989) -- based on observation that its "Great Red Spot"
is at the same latitude, and in the same hemisphere, as Jupiter's . . .]
"Embedded Tetrahedral Latitude" Discovered At Cydonia
Following this striking, system-wide geophysical confirmation of a
predictive (if baffling) "embedded tetrahedral model," the authors made
another significant geometrical discovery at Cydonia itself:
The critical 19.5-degree tangential latitude of the "embedded
tetrahedron" is specifically associated with a massive, *tetrahedral
pyramid* located TANGENTIALLY, on the circular rim, of a 2-mile impact
crater; in turn, this "pyramid" is connected TANGENTIALLY (via a line
denoting the exact North/South meridian) to a circular (planet-like?)
feature termed "the Tholus"; which, in turn, is connected to a third,
linear feature ("the Cliff") positioned TANGENTIAL to the same crater
(see Fig. 3b).
This highly-specific geometric "statement" -- a 19.5-degree angle
offset to the local meridian, connecting three objects (one of them a
tetrahedron!) in a way that reinforces the TANGENTIAL importance of that
relationship -- seems to explicitly establish a "geometric connection"
between "a tetrahedron" (the pyramid), a circular, "planet-like"
construction (the Tholus), and the linear "Cliff' (the 19.5-degree offset
reference), a relationship also known to be coded elsewhere in the Complex,
in terms of derived mathematical constants: specifically, "e'/pi."
This explicit geometric statement also uniquely establishes an
*identical* 19.5-degree angle offset between the D&M (at the other end of
the Complex) and the resulting "map grid" -- further underscoring the
significance of the D&M's unique latitude relationships (see Fig. 5).
These interlocking, extremely meaningful, and
highly predictive relationships -- coded now in both
the mathematical and blatant geometric aspects of the
Complex -- can only be interpretated with extraordinary
effort as anything other than the result of a deliber-
ate and systematic plan -- designed to underscore the
importance of "tetrahedral geometry."
That the anomalies predicted by this "geometry" encompass a range of
demonstrable solar system phenomena -- from deeply-buried planetary mantle
"hot spots," to associated shield volcanoes, to atmospheric thermal
"upwellings," etc. -- is also now readily apparent--
Even if the reason for their specific "latitude-dependence" is not!
The Significance of the "Cydonia Message"
Lest there be any confusion, the authors are NOT claiming there is "a
tetrahedron buried inside each planet!" Rather, it is suggested that the
"tetrahedral geometry" explicitly designated by "Cydonia" is revealing an
equivalent higher-order mathematical topology: i.e., a vorticular "two-
torus" energy flow and internal fluid dynamics, equivalent to tetrahedral
mathematics. That such an internal "vorticular pattern" could be
explicitly modeled by an "embedded tetrahedral topology" is mathematically
well-known (Porteous, I. R., 1981). That such a "geometric short-hand" --
directing us specifically to some underlying physical manifestation of
tetrahedral mathematics -- was left specifically for us at Cydonia, seems
now almost inescapable . . . if not inescapably significant.
A quantitative treatment of the physics underlying this phenomenon
would appear likely to advance our understanding of energy transfer inside
planets considerably -- a not unexpected outcome, if this indeed is
"Mankind's first successfully-decoded extraterrestrial message."
Additional observations suggest, however, that the significance of these
predictions could extend far beyond "the simple siting of active volcanic
centers on the surfaces of near-by worlds . . ."
"Cydonia Tetrahedral Model" Extended to the Giant Planets
We have already alluded to the surprising conformance of the planet
Neptune to this mysterious "embedded tetrahedral model." Its newly-
discovered "Great Red Spot" (as imaged by the Voyager 2 spacecraft) now
strikingly coincides with the "19.5-degree latitude predictions"
communicated by Cydonia. It is the growing suspicion of the authors,
however, that the imminent Voyager studies of Neptune, coupled with a re-
analysis of those studies it conducted of Uranus, may provide vital
evidence that the "Cydonia equations" are trying to tell us about more than
just energy transfer . . .
Based on the evidence detailed below, it is our suggestion that these
observations may relate to actual energy generation.
For many years there have been observed "energy excesses" in the
overall energy balances exhibited by the four major planets of the outer
solar system: Jupiter, Saturn, Uranus and Neptune. These planets,
inexplicably, all radiate significantly more energy into space than they
receive from the Sun at their respective distances (Hubbard, 1980).
Jupiter's positive energy balance (1.67 -- compared to solar input)
apparently derives mainly from primordial heat retained during it's
"collapse phase" from the original solar nebula, 4.5 billion years ago. A
secondary contribution is calculated as created by the internal separation
of helium from hydrogen ("helium drip"), with the resulting release of
additional gravitational potential energy (Smoluchowski, 1967; Graboske et
Saturn, far less massive than Jupiter, is considered too small to have
retained significant primordial heat. Thus, it's observed "excess" (1.78
solar input) is wholly ascribed to the gravitational separation of helium
from hydrogen, tentatively verified by the 1980 and 1981 Voyager infrared
observations of Saturn (Hanel, et al., 1983).
Ground-based data prior to Voyager's 1986 Uranus Encounter indicated
that Uranus and Neptune, similar telescopically from Earth, differ
dramatically in their observed "energy excesses" (Pollack, et al., 1986).
Uranus from ground-based studies seemed to possess only a marginal (if any)
heat source, compared to Jupiter and Saturn; Voyager's January, 1986 fly-by
enabled investigators to lower even this minimal estimate (Pearl, et al.,
1989). The new upper-limit on the ratio of internal Uranian heat to solar
input is 1.14 -- almost non-existent compared to Jupiter and Saturn, and
dramatically lower (by comparison) than current ground-based measurements
of Neptune's radiated excess (2.7) over solar input.
Conventional sources for explaining Uranus' internal energy, as slight
as it is, encounter difficulties. Based on Voyager data interpreted as
evidence of a non-depleted helium/hydrogen ratio in the Uranian atmosphere,
the "helium drip" model (so successful for Saturn) is not thought
applicable (Conrath, et al., 1987). And, for assumed early solar system
nebula compositions, resulting in a "rocky core" for Uranus equal to
between one and three earth masses, only 15-50% of the formal excess can be
accounted for in terms of "radiogenic heating" (decay of radioactive
elements -- Williams and von Herzen, 1974). This leaves "exotic elemental
compositions" (more than 6 earth masses of "rocky materials") and novel
energy transport mechanisms ("suppressed deep-atmosphere convection") as
remaining "conventional" possibilities (Stevenson, 1987). These
difficulties in accounting for the source of Uranus' internal heat are only
made more difficult when the planet is compared to Neptune -- it's supposed
"twin" in terms of size and (presumably) composition.
Because of these potential compositional problems, and the great
disparity in internal energy-generation between these two otherwise so-
similar planets, the authors are led to propose another possibility:
That the "Cydonia equations" may really be attempting to describe, not
merely internal energy transport, but internal energy generation -- most
evident (because of sheer distance from the Sun) in the overall energy
balances of Uranus and Neptune.
Further, the authors believe study of the detailed Voyager infrared
Uranus observations support this possibility:
Uranus, because of its extreme obliquity (98 degrees) relative to its
orbit, alternates each pole toward and away from the Sun for a quarter of
its 84-year revolution. Despite this unique geometric shadowing effect (
the Uranian south pole not having "seen" sunlight for over 20 years, at the
time of the Voyager Encounter)--
THERE WAS NO GLOBAL TEMPERATURE DIFFERENCE OBSERVED BETWEEN THE DAY AND
Because of the problems cited above with any internal Uranian heat
source, and the distinct possibility that (within the error's of Voyager's
measurements) Uranus actually possesses zero internal energy, discussion in
the literature has attempted to explain this global temperature uniformity
as "redistribution of intercepted solar input," via "shallow atmospheric
advection" (Friedson and Ingersoll, 1987); if the solar energy is being
transported around to the nightside of the planet by a shallow, upper
atmospheric mechanism, this would radically decrease (because of the non-
necessity for warming the entire nightside atmosphere) the amount of heat
(energy) required for transport to the nightside -- otherwise needed to
account for Voyager's global-temperature distribution measurements.
A major problem for this model, however, was the Voyager observation
that the winds (clocked by observing several discrete clouds) blow in the
same direction as the rotation of the planet (Smith, et al., 1986); pre-
Encounter theoretical predictions had firmly anticipated a four-day
retrograde rotation of the upper atmosphere, driven by external solar
radiation. [The planet Venus, where such opposite winds (to the rotation
of the planet) are observed, has its atmosphere dynamically-determined by
intense external solar radiation.] Further, the fact that the observed
Uranian clouds were seen circling the pole in a series of concentric
circles (parallel to decreasing latitude) as Voyager approached, leads to
difficulties in modeling heat transport to the nightside, pole to pole --
across the latitudinal windflow.
These observations make it at least plausible to the authors that
internal energy, not "shallow advection of absorbed solar radiation"
constitute the primary driver for the Uranian atmosphere; a final, detailed
Voyager infrared observation, would seem to add significant support to this
In scanning both hemispheres -- the dayside South pole and the
nightside North -- the Voyager IR instrument detected a small but
significant 1-2 K temperature drop in both hemispheres -- at approx. 20
degrees N. and S. latitude (Pearl, et al, op cit). Interpretated as the
spacecraft viewing small-scale emissive and reflected temperature profiles
of colder, higher clouds (consistent with similar observations made at
Jupiter and Saturn -- including measured temperatures of Jupiter's Great
Red Spot, which is also colder because it is higher than the surrounding
Jovian atmosphere), the Uranus' observations could be interpreted as "some
kind of massive 'upwelling' within the Uranian atmosphere," creating
condensation products -- clouds -- as the atmosphere rises to higher
Narrowly straddling the "plus and minus 19.5-degree latitude" where
the "embedded tetrahedral model" of the Cydonia equations would predict --
for an internal, energy-driven "upwelling" on the planet!
The difficulties involved in modeling a process, driven by external
solar radiation, which could create such upwellings and then "know" where
to create them -- at the "magic 19.5-degree latitude" predicted by Cydonia
-- are formidable. In the opinion of the authors, it is much easier to
ascribe these symmetrical upwellings to an internal energy source --
released according to the now-familiar Cydonia pattern observed elsewhere
in the solar system of "internally-driven energy emission."
The fact that these upwellings appear symmetrically in Voyager IR
scans of both hemispheres presents, however, an interesting contradiction
to other "planetary upwellings" -- which seem to be restricted to one
hemisphere, and to one localized latitude region. Those on Uranus (if the
model is applicable) are not.
The apparent enigma is resolved, we think, by the fact that the
Uranian magnetic field is radically different from any other planet:
aligned at approximately 55 degrees to the inertial spin axis (Ness, et
al., 1986). It is at least interesting to propose that somehow this almost
right-angles magnetic orientation with respect to the geographic poles
"allows" the internal energy processes predicted by the "embedded
tetrahedral model" to manifest symmetrically in both hemispheres. If true,
this in turn allows some insight into the role of planetary magnetic fields
in the "Cydonia phenomenon": in some geometries, that of selective
hemispheric suppression of an internal energy-transport mechanism.
Based on all of the above, it is the considered opinion of the authors
that at Uranus, the Cydonia "embedded tetrahedral model" reveals itself as
not only a mechanism for energy tranport within planets -- but, quite
likely, as a process of internal energy generation as well. The implications
of verifying this hypothesis -- for all planets where these phenomenon are
observed to follow the "Cydonia predictions," including Earth -- the authors
think are obvious . . . if not highly significant in terms of other astro-
physical environments, where involving a potential "new source" of energy
might lead to wholly different fundamental models.
Extension of the Cydonia "Tetrahedral Model" Beyond Planets
Heartened by the apparent success of this "embedded tetrahedral model"
in empirically predicting surface manifestatons of internal planetary
dynamics, the authors decided to extend the model to the Sun. This is the
With no solid lithosphere, the solar plasma "photospheric surface" is
of course far more like the banded, turbulant atmospheres of the giant
outer planets (though much hotter!), than the dense, solid crusts of the
"terrestrial" planets. And like the atmospheres of the giant planets,
there is a recurring "surface phenomenon" which is measurable -- in terms
of a coordinate system referenced with relation to the rotational axis:
Though appearing dark against the surrounding photospheric background,
sunspots are still measured at approximately 3500 K, and radiate enormous
energy per unit area. More significant for our discussion here, though
convection within the spot "umbra" (the darkest, central part) is
suppressed by intense, local magnetic field strengths (Hale, 1913), there
is evidence of enhanced energy emission around the spot itself -- perhaps
as much as one or two percent over the normal photospheric background.
When flare activity is considered (which occurs in the intense, tangled
magnetic fields between sunspot groups), spots -- as opposed to being
"regions of lower solar output" -- are in fact localized areas of "enhanced
energy emission" (Brandt, 1966)
The recurring 22-year solar sunspot cycle is made up on average of two
back-to-back 11-year components. Sunspots at the beginning of each cycle
usually appear in pairs, with opposite magnetic polarity -- N. and S.
(though, entire localized "sunspot regions" -- see above -- can also form),
at high solar latitudes (-- 40 degrees). The appearance of new additional
"spot pairs" (and the dying of "old" ones), as the cycle progresses,
subsequently drift North and South (depending on the hemisphere) --
eventually converging late in the cycle in the solar equatorial regions.
11 years later, on average, a new cycle begins, with sunspot pairs of
now opposite polarity (compared to the initial cycle) "breaking out" once
again at high solar latitudes -- with subsequent spots appearing at
decreasing latitudes as the new cycle moves toward its 11-year completion.
To our amazement, when the mean latitude of the majority of sunspot
and associated flare activity was examined, the mean in both hemispheres --
from beginning to end of each cycle -- was found to be remarkably close to
20 degrees (Fig. 7)!
The apparent appearance in the Sun of the same phenomenon so
successfully predicted by Cydonia for planets -- including the possibility
that the effect is somehow related to a new source of energy generation and
not "merely" energy transport -- opens up extraordinary possibilities.
These must include consideration that solar luminosity could be a mixture
of two energy sources: the "traditional" fusion of hydrogen within the
solar core; and another, still inexplicable process, somehow modulated by
the general wax and wane of solar magnetic activity! [R. C. Wilson, after
many years of careful observations at Mt. Wilson, has demonstrated direct
variation of the solar constant in synchronization with the solar sunspot
cycle (Wilson, et al., 1980). Newer Solar Max satellite data from above
the atmosphere confirm the findings.]
A detailed discussion of these observations is beyond the scope of
this inquiry. However, the authors feel they would be remiss if they did
not conclude by at least mentioning two additional areas where future
observations could greatly increase our confidence in the reality of this
phenomenon -- if not our understanding of its nature.
In view of apparent solar conformance with "circumscribed tetrahedral
geometry," one area for further research seems immediately apparent:
In addition to "flare stars" and other highly-variable stellar objects
with surface phenomenon thought to be similar to solar processes, we feel
that, if the Cydonia mathematics are attempting to describe not only energy
"flow" but somehow "energy generation" -- then the ability to test these
ideas via radio astronomy should be the highest in terms of one class of
exotic objects in particular: pulsars.
The common link connecting all the objects for which the Cydonia
"embedded tetrahedral model" seems to work -- from the planets to the Sun--
seems at this stage to be based on one significant association: angular
momentum and magnetic fields. Before the adoption of the present, complex
"self-excited dynamo theory" (with internal, circulating, conducting
"fluids" as the mechanism for general planetary and stellar magnetism),
another -- strictly empirical -- hypothesis was proposed: a strikingly
simple relationship between the observed total angular momentum of the
object, and a resulting dipole.
Termed "Schuster's Hypothesis" (Schuster, 1912), it has been
successful in predicting magnetic field strengths (Blackett, 1947; Warwick,
1971) ranging from the earth's, to the sun's, to Jupiter's vast field
(20,000 times the terrestrial dipole moment) -- a prediction made over sixty
years prior to the 1973-74 Pioneers' 10 and 11 close-up confirmations
(It should be pointed out, ground-based radio astronomy had
successfully deduced Jupiter's magnetic field strength -- thus its
conformance with "Schuster's Hypothesis" -- some twenty years before the
Pioneer magnetometer observations confirmed the radio data and Schuster --
who's very name and empirical discovery is, inexplicably, completely
missing from all NASA literature on planetary magnetism.)
Commented Warwick on the remarkably predictive power of "Schuster's
Hypothesis," even in 1971:
"Dynamo theory has not yet successfully predicted any cosmical fields.
It's use today rests on the ASSUMPTION that no alternative theory
corresponds more closely to observations [original emphasis]."
Taking Schuster's 1912 proposal, the authors have plotted contemporary
parameters for angular momentum versus observed the magnetic dipole moment
(for all planetary objects now visited by spacecraft with magnetometers),
and find Schuster's Hypothesis amazingly confirmed (see Fig. 8) -- with the
exception of Mars (for which we have extremely poor data -- no American
spacecraft since Mariner 4, including Viking, has carried a magnetometer to
Mars!), and Uranus (discussed below).
It is tempting to propose that what we have observed in terms of the
"Cydonia equations" -- a remarkable correlation between external, localized
energy emission and a planetary spin-axis, somehow modulated by the
orientation (if not the intrinsic value) of the magnetic field -- may be
trying to tell us about the physical process underlying "Schuster's
Hypothesis": how magnetic fields in spinning bodies form . . . if not how
their formation may be associated with internal energy generation.
In terms of an observable, visible connection between these two
parameters -- planetary magnetism and planetary surface features -- it is
interesting that Warwick in 1976 already had observed:
"It seems likely that, corresponding to atmospheric belts and zones as
seen in Jupiter's cloud top level, there is a belt-like structure in the
magnetic field not strong enough to alter the dipole structure radically
[thus not mappable by spacecraft' instruments -- unless in very close-in
orbits] but still sufficient to play a role in magnetospheric diffusion as
Neil Brice suggested some years ago. This magnetic fine structure also
must play a role in decametric [radio emission] phenomenonology . . .
[which], especially [as exhibited in] longitude patterns throughout the
Jupiter year, is strictly reproducible over the two decades of radio
observations. The conclusion I draw from this fact is that the magnetic
fine structure near the [cloud top] surface of Jupiter has remained constant
over the same time interval. In support of this conclusion is the more or
less constant belt and zone structure of Jupiter since 1950 . . . Such a
correlation, which is ultimately [in this theory, associated] with magnetic
fine structure, would tend to confirm the existence of magnetohydro-
dynamic turbulance near the surface of Jupiter."
Warwick's inferences regarding the role of magnetism and fluid
physics, in possibly generating the patterns long-observed in radio
astronomy's "decametric observations," would seem to lend support to our
own tentative proposals:
That the Cydonia "embedded tetrahedral model" (merely, if we're
correct, an equivalent geometrical expression of the far more complex
mathematics associated with a "vorticular fluid-flow") is in fact
predicting the latitudes and sizes of the Great Red Spots on Jupiter (and
now on Neptune!), and the largest volcanic centers of emission on
"terrestrial planets," through deep-seated, vorticular magnetohydrodynamic
processes -- operating in the highly conducting mantles of these bodies. A
similar mechanism probably underlies the Sun's conformance to "tetrahedral
geometry" as well.
That each "upwelling" (at least in the atmospheres of these two giant
planets), seems scaled strictly in terms of the respective size of each
respective body, provides further elegant support for an internally-
determined "fluid" model.
The fascinating, observed correlation between angular momentum and
magnetic dipole moment -- if not field polarity, evidenced by the selective
hemispheric appearance of energy emission at 19.5 N. or S. -- has made us
wonder, however, about more fundamental correlations . . . . We suspect
that the puzzling and periodic "field-reversals" of the terrestrial
geomagnetic field are another indication of the "Cydonia embedded
tetrahedral model" -- modulated by the constant gravitational "tidal
kneading" of the Moon. If this process is involved in periodically
"flipping" the entire magnetic field (and the resulting "hot spots"), then
the precise physical mechanism should raise provocative questions involving
electromagnetism, mass, inertia . . . and possibly gravity itself. Sirag,
in observing this same remarkable correlation between angular momentum and
electromagnetism (1979), raised similar considerations.
If the Cydonia mathematics are attempting to direct us to energy
generation and subsequent energy transfer inside astronomical objects,
involving a hitherto unknown relationship between two of the four basic
forces of the Universe -- gravity and electromagnetism: i.e. a "Unified
Field" -- this process in our opinion cannot help but manifest itself more
clearly in astrophysical environments where both parameters have reached
Which brings us once again to pulsars.
Even the "average" spinning neutron star (the favored "pulsar model")
possesses surface gravitational accelerations, angular momentum, and
magnetic field strengths billions of times more intense than similar
quantities in any solar system object. Moreover, since Schuster's
Hypothesis strikingly succeeds in its prediction of even these
extraordinary magnetic dipole moments (see Fig. 8), we cannot help but
wonder at what rich new confirmations of the "Cydonia mathematics" may lie
hidden in existing -- and currently mystifying -- pulsar observations . . .
If in the "Cydonia tetrahedral mathematics" we are truly seeing the
deliberate communication of demonstrable astrophysical effects of a long-
sought "Unified Field Theory," this in itself would be remarkable
confirmation of current efforts to discover such fundamental mathematical
connections between Nature's elemental forces. For, most provocative: one
leading mathematical approach to successfully modeling such connections is
essentially based on a tetrahedral model, and a resulting mathematical
expansion into "higher-dimensional, n-space relationships" (recently
discovered) between the five Platonic solids (Sirag, 1989). In
particlular, these studies relate tetrahedral geometry as being
topologically equivalent to three-toruses -- tori extending into "one more
dimension than our familiar three." [Many current efforts in pursuit of
"unified field models," such as the much-acclaimed "super-string theory,"
routinely involve up to ten mathematical dimensions. Some more recent
theories are exploring twenty-six (Sirag, ibid).]
Phrased in simple terms:
The routine mathematical representation of
vorticular flow in more than three dimensions --
a three-torus -- by means of three-dimensional
tetrahedral models, opens up the possibility
that the demonstrable geophysical effects of the
"Cydonia tetrahedral message" are attempting to
communicate the reality of additional dimensions
(as opposed to mere mathematical abstractions)
-- and the observable reality of vorticular
energy flow between adjoining "n-spaces."
Such totally unexpected (to non-specialists) and remarkable
mathematical correlations -- between as yet unpublished theoretical work
into Unified Field Models, and the specific tetrahedral geometry apparently
intended at Cydonia -- gives added confidence that such a linkage was in
fact intended. If so, there may be an additional confirmation of a such a
radical "Cydonia Unified Field Model"--
In the continuing, puzzling departure of some celestial objects from
strict "Newtonian mechanics."
Careful observation of the outer planets over the last two centuries
has revealed that "the motions of Uranus and Neptune cannot be adequately
represented within the present gravitational model of the solar system"
(Harrington, 1988). While gravitational perturbations originally ascribed
to Pluto (Tombaugh and Moore, 1980) have now definitely been eliminated as
of adequate magnitude to explain these astrometric deviations (Harrington,
op cit), "the suspicion of the existence of a tenth planet" has resulted in
renewed efforts (Seidelmann and Harrington, 1988) to search for another
unseen object which could gravitationally account for the persistant
residuals of Uranus and Neptune.
However, other experts in celestial mechanics are open to the
possibility that (as opposed to a new planet) a fundamental modification to
gravitational theory itself may in fact be necessary, in order to
adequately model the puzzling outer planet motions (Anderson, 1989) --
which, curiously, are most "anomalous" for Uranus.
As a direct consequence of the apparently successful application of
the "Cydonia predictions" to Uranus and Neptune, and because of a probable
fundamental link this has revealed between angular momentum (rotating mass)
and electromagnetism, we suggest a third alternative should be considered:
A derivative "anomalous gravitational effect," somehow created by
Such an admittedly radical proposal must of course be subject to some
stringent observational tests; we believe that Voyager's own 1986 Encounter
has fortuitously supplied us with just such an opportunity--
In the form of "anomalous" Voyager 2 X-band range-rate residuals,
acquired during the fly-by of Uranus itself.
For over a month prior and subsequent to the January, 1986 Encounter,
calibrated ranging signals were transmitted to and from the Voyager 2
spacecraft. Examination of five days of ranging data, centered on the time
of Closest Approach, reveals a series of curious, systematic "range errors"
-- seen only around the time of periapsis of Voyager to Uranus (see Fig. 9);
at this time, the spacecraft exhibited a range error of up to 100 meters
(an order of magnitude larger than instrumentation-limited range uncertainties
of approx. 9 meters, introduced by the Voyager/DSN radio ranging system
itself.) These systematic errors were also inexplicably centered
symmetrically on periapsis (Anderson, et al., 1988).
Explanations which would attribute this effect to "group delay of the
ranging modulation by free electrons between Earth and Voyager 2" remain
unconvincing, when the data are compared to similar residuals (Fig. 9)
recorded during Voyager 2's Encounter of Saturn (Campbell, et al, 1989).
The latter, by comparison, are "flat" (as opposed to the systematic
increase and decrease observed at Uranus): reflecting no similar
"symmetrically-centered curve," mirrored around the moment of Closest
Approach to Saturn.
We believe therefore that these demonstrably unique, and highly
suggestive ranging observations are interpretable as potentially direct
evidence of the modification of the Uranian gravitational metric, by some
additional "space-time effect" associated with the Cydonia "embedded
tetrahedral model." We further suspect that the highly anomalous Uranian
magnetic field-geometry Voyager observed with respect to the planetary spin
axis (>60 degrees) -- if not the significant departure of the planet's
overall magnetic dipole moment from "Schuster's Hypothesis" (see Fig. 8) --
may somehow be involved.
One important reason for raising this possibility now is the imminent
Voyager 2 Encounter with Neptune.
Uranus and Neptune -- essentially "twins" in terms of mass, angular
momentum and (probably) composition -- provide important constraints on
several fundamental predictions of the Cydonia mathematics. The great
difference in internal energy balance between the two planets (1.14 for
Uranus; 2.7 for Neptune), coupled with the unique configuration of the
Uranian magnetic field, leads us to propose that the field orientation with
respect to the planetary spin axis is an important element in determining
in what form the internally-generated energy appears: in Uranus, with an
almost 90-degree field orientation, little energy appears as heat. In
consonance with conservation of energy, we suggest it may be "appearing" in
some other form -- possibly as a change in the local "space-time metric."
The authors, based on this energy discrepancy, and the conformance of
Neptune's "Great Red Spot" with the "embedded tetrahedral mathematics,"
feel a prediction of the Neptune field polarity (opposite the earth's), an
estimate of its specific orientation with respect to the planetary spin
axis (within 20 degrees), and its overall intensity (approximately one-
tenth Saturn's) is now possible--
Before the Voyager August 25, 1989 Encounter.
The relevance of these predictions to the question of "anomalous solar
system motions" of these respective planets is fundamental: in Uranus, the
energy not dissipated as internal heat (in comparison with Neptune) may be
appearing as an associated distortion of the "overall metric" connecting
the planet with the Sun, resulting in its anomalous motions with respect to
current gravitational model for the solar system.
If similar metric distortions are underlying Neptune's (smaller though
equally-puzzling) astrometric residuals, we predict that Voyager should
experience a smaller (when corrected for the difference in periapsis radii)
though significant set of "range residuals" -- when compared to its
Encounter at Uranus; in addition, its instruments should verify our
predictions of the magnetic field parameters.
In terms of those, one complicating factor is the orbit of Neptune's
largest natural satellite: Triton. The essentially circular (though
retrograde) orbit, indicates significant internal tidal dissipation of
Triton's kinetic energy within Neptune -- and thus a significant source of
internal heating, in addition to possible radiogenic and other ("embedded
tetrahedral?") sources; Triton's retrograde "drag" on Neptune's interior
must also have some (currently unknown) effect on any process that couples
overall planetary angular momentum with the creation of a magnetic dipole
Thus, predictions of internal heating, or "exotic gravitational/
electromagnetic interactions," indicated by the success of the "Cydonia
equations" on the other planets, are at this point somewhat ambiguous when
applied to Neptune; the only positive indication so far that this unknown
process is somehow effectively operating in the Neptune interior, is the
discovery of Neptune's "Great Red Spot" -- precisely where "embedded
tetrahedral mathematics" would predict.
Thus, whatever is discovered during Voyager's Encounter of Neptune, in
our opinion, cannot help but provide important additional constraints on
the nature and applicability of the "Cydonia equations."
[We also suggest that all the giant outer planets, by virture of their
vastly larger angular momenta and magnetic dipole moments -- compared to
the "terrestrial planets" -- exhibit to a greater or lesser degree these
effects exhibited by Uranus and Neptune -- including internal energy
release and small (but perhaps measureable) distortions of the "local"
gravitational metric; however, other mechanisms dominate at Jupiter and
Saturn, relegating these potential "tetrahedral model contributions" to a
minor role, if any, in comparison to other sources (primordial energy
release, and helium/hydrogen gravitational separation.
[Beyond the Voyager Neptune Encounter, the imminent (mid-1990's)
insertion into Jovian orbit of the Galileo Orbiter may provide the only
solar system opportunity for some time to come for long-term tests of
certain subtle aspects of these suggestions.]
The true astronomical tests of these extraordinary possibilities --
apart from a manned landing at Cydonia, and discovery of additional records
specifically supporting these suggestions -- will come, in our opinion,
only with redundant astrophysical observations of objects far beyond the
solar system, and over a far longer span of time. In particular, we
suggest that radio astronomy observations of peculiar binary pulsar systems
(such as newly-discovered PSR 1957 + 20 -- Fruchter, et al., 1988) --
where, once again, conditions should be uniquely maximized for key
observational effects created by "non-relativistic, gravitational
distortions" -- could provide enlightening confirmation.
If these observations do lead to substantiation of this (admittedly,
most speculative) aspect of the "Cydonia equations" -- an inextricable link
between gravity and electromagnetism -- in our opinion this would certainly
represent the ultimate manifestation of a Unified Field Model, if not
verification of the true intent of the "Cydonia Message" itself.
In terms of the overall reality of such a "Message at Cydonia," the
authors feel the observable geophysical phenomena photographed all across
the solar system, and cited in this paper, now substantially demonstrate
the likelihood of such a "deliberate, technical communication." The full
extent of its predictions, beyond these initial observations however, is
currently unknown -- as must be the answer to the Ultimate Question: "What
was their intent?"
Common sense dictates that, whatever the origin and culture of the
"senders," their purpose clearly would have been to communicate something
"of fundamental significance." This has been a common theme in discussions
involving "radio messages" that someday might be successfully intercepted
and decoded, as part of "Communication with Extraterrestrial Intelligence"
[CETI - (Sagan, op cit)]. The existence of a "Unified Field" message --
potentially capable of demonstrating an intrinsic connection between
gravity and electromagnetism, and already yielding a range of other,
observable astrophysical effects -- would certainly in our opinion qualify
Particularly . . . if it leads to near-term technological control and
application (Holt, 1980).
It will be left to future studies to decide if this is indeed "the
Message of Cydonia."
A set of remarkable "anomalous objects" on Mars, when examined by two
investigators using a "geometric relationship model," has yielded specific,
mathematical predictions which have been subsequently verified across the
solar system. The discovery of a redundant "tetrahedral geometry," encoded
at the Martian site known as "Cydonia," has led the authors to the
discovery that every major energy center -- on the sun, and on most of the
planets and their active satellites -- emerges at the surface in
conformance with predictions of an "embedded tetrahedral model": primarily
at either 19.5 degrees north or south latitude.
The implications are significant: from identification of a potential
new source of energy and laws governing its transfer within stars and
planets, to possible discovery of a long-sought fundamental link between
gravity and electromagnetism itself. At the least -- besides confirmation
that there is a "message at Cydonia" -- these discoveries could hold out
the prospect for eventual human utilization of a new energy resource
(Smith, W. B., 1950). Learning to control the associated electromagnetic/
gravitational forces (if any), could however result in a near-term,
dramatic breakthrough in fundamental space propulsion technology (Holt,
ibid) -- with obvious implications for space exploration and eventual
In the opinion of the authors, these possible "breakthrough
applications," of a currently unexplained but demonstrable physical
phenomenon in operation throughout the solar system, are an urgent reason
for immediate verification of the "Message of Cydonia" -- not least,
through additional high-resolution imaging by Mars Observer in 1993, and
With a manned landing at Cydonia itself.
[Because of the inherent limitations of pictorial data viewed
via computer, the GRAPHICS and computer-enganced Viking photographic half-
tone figures for this paper are not included in this file -- but are
available through THE MARS MISSION (P.O. Box 981, Wytheville, VA. 24382),
or by downloading "RESOURCES" in THE MARS MISSION BBS (703) 228-7822 ]
The authors would like to acknowledge the following people for their
support of our continuing research into the reality and meaning of Cydonia,
as well others for their specific help in the preparation of this paper:
Dr. Mark Carlotto (The Analytic Science Corporation; Mars Mission Imaging
Consultant), for continued Cydonia imaging enhancements and three-
dimensional modeling of Viking data; Mr. Merton Davies (the RAND
Corporation), for up-dating his "1982 Mars Control Network" as applied
specifically to the problem of accurate Cydonia control points; Dr. John
Anderson (JPL; Voyager Celestial Mechanics), for providing detailed Voyager
Saturn and Uranus tracking data, and historical Uranus and Neptune
astrometric information; Dr. J. C. Pearl (Goddard Space Flight Center;
member, Voyager IR Experiment), for furnishing the latest Voyager IR Team
Uranus conclusions; Dr. James Warwick (University of Colorado, Boulder;
Principal Investigator, Voyager Planetary Radio Astronomy Experiment), for
introducing us to "Schuster's Hypothesis," and its potentially unique
application to this problem; Mr. Saul-Paul Sirag, for furnishing important
references linking tetrahedral mathematics with "two and three-torus
topologies," and for providing examples from his own research of not only
Schuster's Hypothesis as potentially applicable to a Unified Field Model --
but for specifically referencing tetrahedral mathematical topology and the
Platonic Solids as directly applicable; and finally, Mr. Stan Tenen (The
Meru Foundation), for introducing us to Saul-Paul Sirag, for furnishing
examples of his own research into the historical importance of the Platonic
Solids (tetrahedra, in particular), and for valued general discussion of
some of the more controversial aspects of our work.
All opinions and conclusions presented in this paper, however, are
strictly the responsibility of the authors.
Anderson, J. D., personal communication
Anderson, J. D., et al., "Bounds on Dark Matter in Solar Orbit," DOE-
ER40200-143, The Center for Particle Theory, The University of Texas at
Austin, June 1988
Becker, W., and B. Hagens, "Planetary Grid System: Update on Research,"
(1987), Intercultural Studies in Global Mapping and Communications;
Governors State University, University Park, Il. 60466
Blackett, P. M. S., (1947), Nature 159, 658-666
Brandt, J. C., The Sun and the Stars, McGraw-Hill, Inc.; New York, 1966
Campbell, J. K., and J. D. Anderson, "Gravity Field of the Saturnian System
from Pioneer and Voyager Tracking Data," The Astronomical Journal, Vol. 97,
No. 5, May (1989)
Carlotto, M. J., "Digital Imagery Analysis of Unusual Martian Surface
Features," Applied Optics, Vol. 27, 1926-1933, (May 15, 1988)
Conrath, B. J., et al., "The Helium Abundance of Uranus from Voyager
Measurements," Journal of Geophysical Research, 92, 15003, 1987
Crowe, M. J., The Extraterrestrial Life Debate: 1750-1900, Cambridge
University Press, 1986
Davies, M. E., and F. Y. Katayama, "The 1982 Control Network of Mars,"
Journal of Geophysical Research, 88:7503, 1983
Davies, M. E., personal communication
DiPietro, V., and G. Molenaar, "Unusual Martian Surface Features," Private
Monograph, published by Mars Research, P.O. Box 284, Glenn Dale, MD 20769
Friedson, J., and A. P. Ingersoll, "Seasonal Meridianal Energy Balance and
Thermal Structure of Uranus: A Radiative-convective-dynamical Model,"
Icarus, 69, 135, 1987
Fruchter, A., et al., Nature, May 19, 1988
Gauss, C. F., J. J. von Littrow, A. Hall, J. N. Lockyer, S. Newcomb, et
al.. Reports of their discussions re creating significant engineering and
geometric figures on Earth "to signal basic mathematical theorems and
Earthly intelligence to prospective Martians," in The Extraterrestrial Life
Debate: 1750-1900, Crow, M. J., Cambridge University press, 202-207, 1986
Graboske, H. J., et al., "Thermodynamics of Dense Hydrogen-Helium Fluids,"
Astrophysical Journal, 199, 255, 1975
Hale, G. E., "The Earth and Sun as Magnets," Smithsonian Report for 1913 ,
Hanel, R. A., et al., "Albedo, Internal Heat Flux, and Energy Balance of
Saturn," Icarus, 53, 262, 1983
Harrington, R. S., "The Location of Planet X," Astronomical Journal,
96 (4), October 1988
Hoagland, R. C., "The Curious Case of the Humanoid Face . . . on Mars,"
Analog, Vol. CVI, No. 11, November, 1986
Hoagland, R. C., The Monuments of Mars: A City on the Edge of Forever,
North Atlantic, Berkeley (1987)
Hoagland, R. C., "Discovery of Specific Geometric Redundancies at Cydonia
Mensae: Support for the Relationship Model Indicating a 'Martian'
Intelligence," (1988) in press. Also available for downloading via THE MARS
MISSION Computer Bulletin Board (703) 228-7822
Holt, A. C., "Prospects for a Breakthrough in Field Dependent Propulsion,"
American Institute of Aeronautics and Astronautics Preprint AIAA-80-1230
Hubbard, W. B., "Intrinsic Luminosities of the Jovian Planets," Review of
Geophysics and Space Physics, 18, 1-9, (1980)
Moore, P., The New Atlas of the Universe, Crown Publishers, New York (1984)
Ness, N. F., et al., "The Uranian Magnetic Field," Science, 233, 1986
Owen, T., member Viking Imaging Team. Original discovery of "the face,"
page 4, The Monuments of Mars, Hoagland, R. C., North Atlantic,
Pearl, J. C., et al., "The Albedo, Effective Temperature, and Energy
Balance of Uranus as Determined from Voyager IRIS Data," Icarus (1989) in
Pollack, J. B., et al., "Estimates of the Bolometric Albedos and Radiation
Balance of Uranus and Neptune," Icarus, 65, 442, 1986
Porteous, I. R., Topological Geometry, Cambridge University Press, second
Pozos, R. R., The Face on Mars: Evidence for a Lost Civilization?, Chicago
Review Press (1986)
Rubtsov, V. V., and A. D. Ursal, The Problem of Extraterrestrial
Civilizations, Moldavian Academy of Sciences, USSR (1984)
Sagan, C., (Ed) Communication with Extraterrestrial Intelligence (CETI),
MIT Press; Cambridge, 1973
Schuster, A., (1912) Proceedings of the Physcial Society of London,
A 24, 121-137
Seidelmann, P. K., and R. S. Harrington, Celestial Mechanics, (1988)
Sirag, S., Nature, 1979
Sirag, S., (1989) personal communication
Smith, B. A., et al., "Voyager 2 in the Uranian System: Imaging Science
Results," Science, 233, 43-64, 1986
Smith, W. B., "Geo-magnetics," Department of Transport internal, Top Secret
Memorandum (now declassified) -- relating experimental development in the
early 50s of self-sufficient geomagnetic field motor technology -- Canadian
Government (November, 1950). Available: THE MARS MISSION Computer Bulletin
Board files [see "RELATED"] (703) 228-7822
Smoluchowski, R., "Internal Structure and Energy Emission of Jupiter,"
Nature, 215, 69, 1967
Stevenson, D. J., "Uranus," Bulletin of the American Astronomical Society,
19, 851, 1987
Tombaugh, C. W., and P. Moore, Out of the Darkness, (1980) Stackpole,
Harrisburg; Lutterworth, Guildford
Torun, E. O., "The Geometry of the D&M Pyramid," (1988) in press. Also
available for downloading via THE MARS MISSION Computer Bulletin Board
Torun, E. O., "The Geometry of the D&M Pyramid: Appendix B," (1988) in
press. Also available for downloading via THE MARS MISSION Computer Bulletin
Board (703) 228-7822
Warwick, J., "The Relation of Angular Momentum and Magnetic Fields:
Schuster's Hypothesis Revisited," in Phys. Earth Planet. Interiors 4, 229-
232, (1971), North-Holland, Amsterdam
Warwick, J., "Magnetic Fields in the Solar System," in Magnetospheric
Particles and Fields, 291-299, B. M. McCormac (Ed.), (1976), D. Reidel,
Wilson, R. C., et al., "Direct Measurements of Solar Luminosity Variation,"
Science, 207, 177, 1980
Williams, D. L., and R. P. von Herzen, "Heat Loss from the earth: New
Estimate," ^BGeology^B, 2, 327, 1974
Planetary Latitudes of Emergent Energy Phenomena
Object Feature Latitude Comment
Earth Hawaiian Caldera 19.6 N. Largest shield
Moon Tsiolkovskii 19.6 S. Unique Farside
Venus Alta Regio 19.5 N. Current volcanic
Beta Regio 25.0 S Current volcanic
Mars Olympus Mons 19.3 N. Largest shield
Jupiter Great Red Spot 22.0 S. Vast atmospheric
Io Loki (2) 19.0 N. (Voyager 1 & 2
Maui (6) 19.0 N. volcanic plumes)
Pele (1) 19.0 S. Presumably driven
Volund (4) 22.0 N. by intense Jovian
Saturn North Equatorial 20.0 N. Region of "storms"
Belt observed from
South Equatorial 20.0 S. Same as above
Uranus (Voyager 2 IR
Northern IR 1-2 K. 20.N Presumably, deep
Southern IR 1-2 K. 20.0 S. Same as above
Neptune (Voyager 2 Imagery)
"Neptune Great Red 20.0 S. Presumably same as
Spot" Jovian counterpart
Source: NASA and U.S. Geological Survey