In 1665 Newton was doing his light experiments and discovering that light had "successive motion," that it had a speed and was not instantaneous. Also in 1665 the Jesuit mathematician Athanasius Kircher published his theory of "polar vortices." In 1667 Louis XIV established the Paris Observatory and the Paris meridian. In 1671 Richer determined the distance between Earth and Mars based on the parallax between the Paris meridian and the French Guiana meridian. The difference in the Mars observation was only 23 seconds of arc: but enough to make a very good estimate of 32,625,000 miles.
Nineteenth century European mathematics may have led impressionable minds to postulate that Mars can be reached by a land-route through the Earth’s South Pole "hole," if indeed such a thing exists. Mathematically, a group-theoretic topology of embedded spheres is not altogether inconsistent with the idea of a physical land connection; arguments can be made for and against. One can temper the radicalism of a land connection by considering only the magnetic fields of the planets. The big picture is a sharing of a single universal geometry.
|Figure 1: Antarctica with various meridians. The GREEN axis is the geomagnetic meridian of maximum dip, 69 degrees West in the northern hemisphere, and 111 degrees East in the south. It turns out that this geomagnetic orientation matches the remnant geomagnetic field of Mars, shown by the black sinusoidal line in Figure 2. The RED meridians in Figure 1 correspond to the Earth meridians that go through New Mexico, Germany, and Japan in the North. The BLUE meridians nearly bisect the RED and align with the Antarctic inlets, showing a triaxial structure.|
|Figure 2: The Hellas basin nestled snugly within one of the magnetic field maxima of Mars. Hellas corresponds to a southern locus. Likewise, the northern locus would be the area of the Alba Patera. The Martian geomagnetic equator corresponds to the present-day geomagnetic equator of Earth. Magnetic readings of core samples on Earth seem to indicate that the Earth’s equator 200 million years ago was canted about 30 degrees from today’s equator. In short, it followed the line of today’s geomagnetic equator.|
Thinking concentrically, at some point in the past the orientation of the equator of Mars matched the orientation of the equator of the Moon. Like the Moon, the spin axis of Mars was perpendicular to the solar ecliptic. Then, like the Earth, Mars "turned up its nose" at the Sun and tilted away from the solar ecliptic. The original South Pole of Mars tilted into the southern hemisphere and is now recognized as the Hellas basin. Surrounding the basin are the southern highlands of Mars, which can be thought of as a supercontinent that never broke up. Plate tectonics never got started on Mars, or if so, came to halt more than half a billion years ago.
Meanwhile, the original North Pole of Mars tilted downwards, and is now the Mons Olympus / Alba Patera area in the northern hemisphere. The original equator of Mars, as the planet tilted, followed the equator of the Earth, which was also tilting during the period of the breakup of Pangaea, some 400 million years ago.
As the continents began their slow drift northwards from Antarctica, the Earth compensated to achieve an equilibrium. The original equator now follows the line of the geomagnetic equator, which is aligned with the equator of the Moon; which is to say, with the solar ecliptic. Thus, all three planets – Earth, Mars, and the Moon – were once aligned with the solar ecliptic: that is, with the spin axis of the Sun.
One can draw a rough correlation between the geomagnetic northern maximum on Mars, being open northern lowlands or once a great sea; and the Eurasian continent on Earth. The southern maximum on Mars crosses through South America on Earth, with the Olympus Mons / Alba Patera area in the north finding a correlation with the Rockies heading north to the Alaskan peninsula. At the common zero meridian of Earth and Mars, Egypt is almost exactly aligned with Aeria, which not coincidentally is an old name for Egypt (see Figure 3 below). In short, everything above and below the geographic equator of Mars can be matched with everything above and below the geographic equator of Earth, given the remarkable fact that the zero-meridian of Mars and the geomagnetic dips match those of Earth.
Today, both the Earth South Pole and Mars South Pole are aligned with the SPA region on the lunar farside; and the North Poles with the KREEP terrain of Imbrium on the lunar near side. But the old South Pole of Mars (being Hellas) is aligned with today’s Indian Ocean on Earth, and with the nearside arc of the Moon’s southern quadrupolar axis (close to the Moon’s South Pole). Likewise, the old North Pole of Mars (Alba Patera) is aligned with the farside arc of the Moon’s northern quadrupolar axis, and with the Canadian auroral zone on Earth, where, incidentally, the oldest rocks on Earth are found. These rocks come from a vast area of the North American tectonic plate called the Canadian Shield which may have preceded Pangaea. Pangaea wasn’t an original configuration but merely the result of an even older crashing together of subcontinents. Rocks that are more than three billion years old are also found in nearby Greenland, which is also part of the ancient North American tectonic plate.
It may or may not be a coincidence that the zero-meridian of Mars is exactly aligned with the zero-meridian of Earth in the concentric scheme. A little digging reveals that the Mars zero-meridian was first defined by the German astronomers W. Beer and J.H. Madler in 1830-32. But they knew nothing of geomagnetic field lines or geocentric correlations. Through the telescope they pinpointed a small circular feature on Mars, which they called "a", and used it as a reference point to determine the axial rotation period of the planet – which, like Earth, is 24 hours. It may be that they chose "feature a" because, through the telescope at least, objects on the surface of Mars, when viewed from a certain meridian on Earth, will be sharpest if they lie on that same meridian on Mars. (The Germans of course would have known nothing of this theory.)
The story continues with Sir George Airy, who was the director of the Greenwich Observatory in England from 1835 to 1881. Airy installed a "circular transit" at Greenwich, probably at the end of his tenure, because it wasn’t until 1884 that it was used to define the Earth’s zero-meridian at Greenwich. Meanwhile, in 1877 the Italian astronomer Giovanni Schiaparelli (1835 - 1910) seemed to know all about the German "a" feature, since he carried on the tradition the Germans started and used it as the zero-point of longitude in his famous map of Mars published that year. As we will see, the Mars zero-meridian was probably based on the Paris meridian that preceded Greenwich.
The story continues with the return of images from the Mariner 9 orbiter in 1972. NASA scientists were keen to formalize the Mars zero-meridian, and they chose a crater five degrees south of the Martian equator, on the zero-meridian as they knew it, and named it "Airy" after George Airy. The Mariner 9 images revealed a tiny crater within the larger Airy crater, which scientists used as a new reference for the prime meridian, and which they called "Airy-0". NASA scientists were simply honoring the architect of the Greenwich meridian by naming a zero-meridian feature on Mars after him.
Historically, the zero-meridian of Earth dates back to the Paris Observatory and the Paris meridian of 1667. Whether Paris or Greenwich, if there were 360 choices for a zero-meridian on Mars, corresponding to 360 degrees in a circle, then the chances of picking a Mars zero-meridian that aligned with that of Earth, knowing what we do about the fixed concentric natures of Mars and Earth, were one in 360. Did Beer and Madler have special information which led to their choice of "feature a" on Mars? And why did NASA scientists name their own zero-meridian feature after Airy, and not the Germans? We can answer this last question by assuming that the Germans matched their "feature a" to the Paris meridian. NASA finally updated the old Paris meridian on Mars to Greenwich – they actually moved the "zero-point of longitude" a couple of degrees – and so honored Airy. And upon closer inspection, there are two craters near the meridian named after the Germans, as shown below. Probably the Madler crater was the original Mars meridian, which, like Paris, is about 2.5 degrees East of Greenwich.
Switching gears and looking at concentric theory, there’s another piece of data that seems to confirm the idea that the Hellas basin and Antarctica once respectively marked the South Poles of either planet. Mars is smaller than Earth, but thinking concentrically, the Hellas basin should cover the same percentage of Mars’ surface as does the Antarctic continent on Earth. And this is precisely the case. For Mars, a diameter of 4220 miles times pi gives a circumference of 13,082 miles. The Hellas basin covers roughly 40 degrees of a 360 degree circle, or one-ninth the circumference, giving an extent of 1435 miles across. (Actually, both Hellas and Antarctica are slightly ovoid, but we’ll ignore this for now.) For Earth, the circumference is 21615 miles, and one-ninth the circumference is 2400 miles. That’s precisely the diameter of Antarctica.
One more correlation comes in the form of radioactive thorium. The University of Kansas survey of Antarctica that took place for three years starting in 1976, revealed no large deposits of uranium, but substantial amounts of thorium. The survey was conducted with a sensitive device carried by helicopter over the Antarctic terrain. Since most of the terrain was covered by ice, and since Antarctica is so huge, the survey at the end of three years had only covered one-tenth of one percent of the entire continent. The investigators reported that they had discovered no big uranium deposits of commercial value, but that they had found deposits of thorium. This is important because the lunar SPA region, aligned with the Earth’s South Pole, has elevated Thorium counts; and the KREEP terrain on the near side that aligns with the Earth’s North Pole follows the same pattern. (See the web page A Very Strange Operation for details.) An important subject for future study will be the investigation of thorium counts in the Hellas basin.
A word of caution about geomagnetism on Mars and Earth: today the Martian magnetic field is nearly extinct, which makes both identification of a geomagnetic equator and correlation with Earth sketchy. The Earth has evolved along a fifth order harmonic, surpassing the order-3 harmonic on Mars that came to an end aeons ago. All that can be said with confidence is that the two planets share a spin axis, and that the respective axial tilts and spin periods are nearly identical.
Is There Really a Physical Connection?
In curved space it is impossible to compare two far-distant vector spaces without some method of vector-space parallel transport. Parallel transport is described for a manifold in General Relativity by a set of 40 functions known as the "Levi-Civita connection."
Concentric tori – for example Mars inside of Earth – are separated by breaking horizons, which are transition spaces between event horizons. A transition space is a break between the internal symmetries of two vector spaces, so that two vector spaces can exist side-by-side and yet have different curvatures, which is what the case may be with Earth and Mars. Comparing two vector spaces asymmetrically instead of symmetrically requires something called absolute parallelism, which is a special case of parallel transport, and which is a way of ignoring the component curvatures of vector spaces.
A topology of interlocking worlds would involve a flat Minkowski background metric according to Feynman, and on top of that the field equations for General Relativity. When you do this you know the group structure associated with the topology, and when you do all the group calculations corresponding to the topology of the vector spaces, using absolute parallelism, a torsion gap may show up, which is a spin-gap between Lie groups. Since the Levi-Civita connection is hyperdimensional, the torsion between worlds is restricted to higher dimensions. At lower dimensions the torsion gap shows up as a singularity. A special case of Einstein-Hilbert gravity (called Einstein-Hilbert gravity with torsion) handles the torsion gap between worlds, and this explains how two different worlds like Earth and Mars can be topologically connected even though their gravities differ.
Since the gravities of Earth and Mars differ, then it’s a good bet that there is a torsion gap between these worlds and thus a singularity. Only gravity can move through a singularity, and so the idea of regular travel to Mars through the North or South Pole is incorrect. There is no continuous land surface between Earth and Mars.
Eniwetok and JFK
Most people know that Eniwetok was the location of the first hydrogen bomb test in 1952. This bomb was code-named MIKE and was so large that it required its own building. Different sources list its yield as anywhere from 3 megatons to 15 megatons, and it totally destroyed the island of Elugelab in the Eniwetok Atoll. When it exploded the fusion reaction was so powerful that it created two new elements: elements 99 and 100. These elements were detected in the explosion debris. These elements were not named until Glenn Seaborg and his group at U.C. Berkeley made small quantities in the lab in 1955, and then they became "einsteinium" and "fermium" respectively, named after Albert Einstein and Enrico Fermi, both of whom had died that same year.
In fact, 43 open-air and atmospheric tests were conducted at the Eniwetok Proving Ground between 1948 and 1958. After the close of the International Geophysical Year in 1958, the Eniwetok Atoll, like Antarctica, became a Trust Territory administered by the United Nations. The United States administered this Trust Territory for the United Nations. In early 1961 Glenn Seaborg became director of the AEC for the Kennedy administration, and by October the AEC was looking for a place to start up a new round of atmospheric testing. The State Department predicted that the UN would strenuously object to further testing in the Eniwetok Trust Territory.
In 1962 Kennedy and Seaborg were probably told by AEC scientists that Eniwetok was a radioactive "hot-spot," and that it was better to leave it alone than to use it for more nuclear testing. The alternative to Eniwetok was Johnston Island in the Pacific, which was the launch site for the HARDTACK test in 1958 and for some unpublicized tests in 1960. Johnston Island is 30 degrees over from Eniwetok, at 169 degrees longitude W, and is a better fit for the Chryse Acidalia meridian than the Ross meridian of 175 degrees W as shown in the diagram above. As the DOMINIC series got underway in April 1962, the AEC chose the British protectorate of Christmas Island at 157 degrees W for the staging area. Air drops of 29 nuclear devices were made in the region between Christmas Island and Johnston Island. This series also included the controversial high-atmospheric detonations launched by rocket from Johnston Island, including STARFISH.
After the ARGUS tests over the Atlantic in 1958, White House advisor Captain Howard T. Orville stated that the Department of Defense was studying "ways to manipulate the charges of the Earth and sky and so affect the weather by ionizing or de-ionizing the atmosphere over a given area." Three ARGUS shots took place in 1958, in August and September, and each required a three-stage rocket (the Lockheed X-17) to boost it into the ionosphere. The X-17 lifted the last and highest ARGUS shot some 260 nautical miles. Since charged particles from a nuclear explosion (and also from a solar flare) are injected into the atmosphere along longitudinal lines of force, and since shockwaves travel along geomagnetic meridians, weather changes would occur at the blast meridians. And this is just so: after the Johnston Island HARDTACK test in 1958, an unusual magnetic storm was observed at Apia, at longitude 171 degrees W, latitude 13.5 degrees S.
Atomic sodium forms a spectroscopic "band" in the Earth’s atmosphere, and during the 1950s rockets carrying spectroscopes measured sodium lines most strongly at a height of 55 miles. On November 11 1958 Russian scientists observing the twilight sky discovered a new line in the sodium band (the sodium D-band at 5890 angstroms). The new reading was of lithium, at 6708 angstroms, and was a confirmation of a French reading from that same year. These lines were a result of the airglow left behind by British atmospheric nuclear tests (code-named Grapple) in 1958 near Christmas Island in the Pacific. The lithium resonance was measured as far south as New Zealand and Antarctica. The British tests took place at the same time as the American Argus tests.
Like sodium, lithium is one of the alkali metals. Alkali metals are very reactive because their atoms contain one s-orbital electron in their outermost shell, which is easily lost, giving rise to an ion or positively charged atomic particle with the structure of an inert gas. An exotic form of lithium is produced when uranium is bombarded with energetic protons. This exotic form of lithium is incredibly radioactive because of the energies involved to create it – energies on par with those of the Sun.
The lithium left behind in the airglow in 1958 was caused by the acceleration of ions by atmospheric nuclear tests. Scientists may have been trying to simulate with nuclear explosions the chemical reactions that occur in the corona of the Sun. The bombs were boosted with solid lithium-6 deuteride, but lithium left over from the detonations decayed to tritium gas over time. Lithium-6 is a slightly less energetic version of the kind of lithium produced by cosmic rays, lithium-7. Oxygen and nitrogen are bombarded with cosmic ray protons, which produces beryllium-7, and this decays to lithium-7. Part of this process involves the Earth’s magnetic field, which slows and bends the cosmic rays. Cosmic rays also produce lithium-6. Like cosmic ray intensities, the intensities of a bomb blast are measured by various factors: initial energy, rate of energy loss, particle velocity, and the rigidity of the surrounding magnetic field. Immediately after the August 22 detonation the intensity of lithium was equal to the sodium D-line intensity, but by early September the lithium intensity was one-tenth of what it had been. The lithium intensity also decreased the farther south the measurements were made along the line of longitude of the explosion.
The Spherical Harmonics of Mars
Another angle on the magnetic meridians of Mars comes from an early paper on spherical harmonics. In a classic bit of scientific reasoning, Miyamoto (see reference below) hypothesized that Mars conforms to third-order spherical harmonics. Miyamoto makes the assumption that mantle convection exists for both the Moon and Mars, just as with Earth. What’s more, mantle convection is responsible for how the surfaces of the planets have developed over time. The craters are assumed to have formed not by impact, but by mantle convection.
The annotated MOLA map below shows longitudinal variations corresponding to third-order spherical harmonics. This is the same tri-axial arrangement, indicated with yellow arrows in the map, as the magnetic meridian scheme discussed above.
Figure 3. Annotated MOLA Map
There is also a latitudinal regime for such harmonics. Some researchers prefer to align the northern and southern hemispheres of Mars with the geomagnetic equator rather than the geographic one. Thus the black sinusoidal line shown in the map above divides the Martian surface into roughly two hemispheres. To the south of this line the altitudes are on average higher than to the north. Because the dividing line is inclined with respect to the equator, the hemispheres can be referred to as "northerly" and "southerly" in contrast to "northern" and "southern". However, Miyamoto doesn’t resort to this device and considers the Mars hemispheres directly.
Miyamoto wrote his paper in 1966 when the only space-based data that existed for Mars was from the Mariner IV orbiter, which reached Mars in 1965. (Mariner III had failed during launch, and Mariner II was sent to Venus.) Thus the physical data was fuzzy at best, but much better than visual observations from Earth. This fuzziness gave Miyamoto a measure of freedom to interpret results that may not have been possible with later, more accurate and distracting topographic data. This scientific freedom resulted in a superb interpretation of the Martian surface.
Miyamoto assumed that magmatic differentiation had taken place on Mars, and that the crust was composed of two layers, the basic maria and the more acidic continental deserts. He assumed the same thing for the lunar surface, and of course by 1966 the theory of continental drift on Earth had become established. Thus, mantle convection on all three planets was assumed to be responsible for the distribution of maria and continental or highland areas. Continental blocks tend to shift towards descending currents of convection, and the maria spread over the ascending currents.
The most basic spherical harmonic is of order 1. One can picture a descending current on the Moon’s far side that passes through the center of the planet and returns to the upper layer on the near side, and then passes below the crust along the full circumference of the sphere before subsiding again at the far side or antipode, towards the center. This type of mantle convection is characterized by a continental hemisphere and an oceanic hemisphere. The ur-continent of the Earth, before the drift of its continental fragments, corresponds to this initial, order 1, stage. In general, the topography of Mars also has this quality, with its north polar ocean and its south polar highlands. The Moon’s near side can be interpreted as a pole facing the Earth, of ascending currents in general; and its far side as the opposite pole characterized by highlands and descending currents.
All three planets went on to develop higher-order harmonics. The Earth evolved into a fourth-order system, and then was characterized by fifth order harmonics starting about 200 million years ago. The Moon seems to have frozen in "state" early in its evolution, but did develop along half lines with second order harmonics, with descending currents at the libration points on either side of the Moon’s face, and an ascending axis towards the Earth. (See the web page He3 and Stellar Evolution for more on the Moon’s evolution and its relationship to Earth.)
Mars evolved into a system with third-order spherical harmonics. Miyamoto came to this conclusion from albedo observations. The snow line around the south pole appears more irregular than that of the northern cap, and isolated mountains (Novus Mons and Mons Argenteus) appear to be covered with snow after the snow line has retreated polewards. Thus the south pole appeared to Miyamoto to be highlands – and he was right.
On the other hand, the north pole was observed as three conspicuous maria – Mare Acidalium, Mare Utopia, and Propontis (Mare Amazonis) – all between northern latitudes of 30 to 45 degrees. (See the map above.) North of these maria, the snow line of the polar cap is more circular than that of the southern cap, and Miyamoto concluded, rightly, that the north polar region is flatter and distributed with maria.
This then describes, so far, the classic distribution of an order-1 spherical harmonic. An order-3 surface has an additional belt of maria in the southern hemisphere, and continental features in the north. Thus, Miyamoto singled out Hellas, Noachis, Argyre, Phaetontis, Electris, Eridania, and Ausonia (some of these are classically named albedo features, and some are now known to be craters or maria) in the southern latitudes between 30 and 55 degrees. In the north, continental features singled out by Miyamoto, between northern latitudes 0 and 30 degrees, are the Tharsis-Tempe region (to the west of Acidalium); Aeria (an old name for "Egypt" and now consolidated with Arabia Terra, to the west of Utopia); and Elysium (to the west of Propontis/Amazonis). Thus, an order-3 surface is characterized by four latitudinal bands of alternating continent and maria rather than two for an order-1 surface.
As well, an order-3 surface has longitudinal variation, as characterized by the tri-axial arrangement of the Martian north pole (see Figure 3 above). There are three so-called "vapor courses" connecting the two hemispheres. Miyamoto gives their locations in a rough way as: Mare Acidalium-Nilokeras-Lunae Lacus-Sinus Aurorae (shown with a yellow arrow under "Acidalium" in Figure 3); Utopia-Nepenthes-Syrtis Major (shown with a yellow arrow under "Utopia"); and Propontis-Cerberus-Mare Cimmerium (all of these names have passed out of use except for Terra Cimmeria on the southernmost point: the area corresponds to Arcadia and Amazonis Planitia in the north, shown with a yellow arrow under "Amazonis").
Therefore the tri-axial arrangement of the north polar area is in fact an integral part of an order-3 spherical harmonic surface. The phrase "vapor course" can be explained by the old-fashioned idea that the darkening of canals or tectonic valleys from season to season was due to the melting of ice in the northern hemisphere, and the movement of water vapor or clouds from the northern hemisphere to low latitudes of the southern hemisphere. This idea in fact still has merit, given the scenario of ice clouds being one source of solar reflections.
Interestingly, the order of harmonics of a planet’s surface directly correlates to the size of its core. An order-1 surface has a minimal core or no core at all, allowing the mantle currents to pass virtually through the center of the planet. The core size favorable for order 3 convection on Mars is between 0.35 and 0.50 of its radius. Thus Mars is thought to have a small iron core. The Earth’s order-5 harmonics require a core larger still. The Earth’s mantle stops at about .62 of the Earth’s radius. Von Weiszacker proposed a concentric system of vortices, not dissimilar to currents of mantle convection, for the structure of the inner solar system. The concentric system might also describe piggy-backed concentric convection cells, with higher orders residing farther out from the order-1 core. Thus, the Moon would reside inside of Mars, which in turn would reside inside of the Earth. However, one would have to combine such a theory with many other assumptions which are hard if not impossible to prove.
Miyamoto calculated the temperature difference between ascending and descending mantle currents on Mars as 0.5 deg C. Ascending currents, trapped inside the hot rock of the mantle, and uncooled by continuous exposure to the crustal regions, is hotter than descending currents. For the Moon, and assuming an order-2 convection, Miyamoto came up with a temperature difference of 50 deg C. The Earth weighs in with a temperature difference of 0.3 deg C. The table below shows this sequence along with the mantle current-velocities and core sizes for the three planets.
|Planet||Temp diff||Mantle velocity||Core size|
|Moon||50 deg C||2 cm / year||< 0.3 radius|
|Mars||0.5 deg C||25 cm / year||0.3 - 0.5 radius|
|Earth||0.3 deg C||100 cm / year||0.62 radius|
It’s intriguing to note that starting with an Earth radius of 3440 miles, a core size of 62 percent gives the Mars radius, about 2133 miles. Likewise, given this Mars radius, a core size of 50 percent gives the Moon radius, about 1066 miles. The best way to interpret this is that the convection radii inside of the Sun somehow get translated into space as the radii of the planets.
Percival Lowell was part of the generation of Mars observers who believed in "canals." He wrote, "Now, in the special case of Mars, we have before us the spectacle of an old world, a world well on in years, a world much older relatively than the earth, halfway between it and the end we see so sadly typified by our moon, a body now practically past possibility of change. To so much about his age Mars bears evidence on his face. He shows unmistakable signs of being old. What we know [that] would follow advancing planetary years is legible there. His continents are all smoothed down; his oceans have all dried up."
Lowell’s informal remarks mirror Miyamoto’s numerically-backed conclusion that the velocity and temperature difference of Martian mantle convection are intermediate between those of the Moon and the Earth. (See table above.)
Throughout history mankind has explored "interiors." On a stellar level, from the departure point of Earth, the Moon and Mars would be interior destinations. But Mars is a protected domain. The smooth Martian horizon is very tenuous, very refined in its old age, and we must be careful not to disturb it. Mars is our Sun, as is the Moon, and so too the Earth itself.
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