Mathematics – Logic
Scientific paper
Sep 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008epsc.conf...32k&link_type=abstract
European Planetary Science Congress 2008, Proceedings of the conference held 21-25 September, 2008 in Münster, Germany. Online a
Mathematics
Logic
Scientific paper
The first fundamental statement of the wave planetology [1-6 & others] is about ubiquity of tectonic dichotomy. All celestial bodies move, as it was established by I. Kepler, in non-round but elliptical orbits. This means that they all notwithstanding their sizes, masses, physical states and chemical compositions have alternating increasing and decreasing accelerations producing forces (Newton: F = m·a) warping celestial bodies. This wave warping rotating bodies (but all bodies rotate!) is decomposed into four orthogonal and diagonal directions of standing waves. An interference of these directions gives tectonic blocks of three kinds: uplifting (+), subsiding (-) and neutral (0). The block sizes depend on warping wavelengths. The fundamental wave long 2πR (R - a body radius) is present in all bodies thus making one hemisphere rising and the opposite one falling (more precise relation is 1/3 to 2/3 or 2/3 to 1/3). A geometrical proof of this relation is given in [6] where two famous tectonic dichotomies of Earth and Mars were explained by one wave reason. This ubiquitous phenomenon was described as the first theorem of the wave planetology: "Celestial bodies are dichotomous". There are many examples proving it among planets, satellites and asteroids, even Sun is dichotomous. But up to recent time the studied partially Mercury's surface was not a good example of this phenomenon as not fully visible Caloris basin didn't show its real dimension. Now, after the Messenger flyby we know that it is about 1500 km in diameter, that is about 1/3 of the Mercury's diameter and the rule is not violated. The third theorem of the wave planetary tectonics states: "Celestial bodies are granular". This means that celestial bodies are warped by individual waves lengths of which are inversely proportional to their orbital frequencies: higher frequency - finer granules, lower frequency - larger granules (Fig. 1). Observations fully support it not only in sense of granules diameters but also in granules amplitudes reflected in planetary relief range. It increases with the solar distances: Venus ~14, Earth ~20, Mars ~28-30 km. Without good topography on Mercury we theoretically assumed that this planet's relief range must be significantly lower (3-6 km) just to not violate the observed sequence (Fig. 2). The Messenger's measurements show that the real range does not exceed ~5 km. (small vertical relief differentiation is accompanied by small petrological differentiation expressed by a low albedo range, Fig. 2). One of Mercury's surprises is Caloris basin. Basins on planetary surfaces are normally lowlands filled with denser material (basalts for the terrestrial planets). Subsiding tectonic blocks - depressions - basins - occupying narrower and narrower space must be contracted, squeezed, wrinkled, rippled. This is confirmed in many occasions. But in the case of Caloris there is an extension confirmed by concentric and radial cracks. Uplifting and extending basin is a consequence of the wave tectonics. Waves have two phases (up and down) and a period after which the phases change. That is why initially subsided block - basin now (it started maybe a few milliards or hundreds millions years ago: the larger block - the longer wave phase period) experiences uplifting with extension. Is it the only case in the Solar system? Quite not. And Earth is a good example. Its southern mainly oceanic (thus subsided) hemisphere is filled with basalts, what is normal for planetary depressions. But precise geodynamic measurements show that the southern hemisphere increases lengths of its parallels that is expending. This dynamics is confirmed by widening modern planetary rifts in Atlantic, Indian ocean, Pacific in the southern direction and around Antarctic ("Southern" ocean) - a kind of the radial-concentric structure. A geochemical anomaly in oceanic basalts of this region ("DUPAL" anomaly after S.R. Hart, 1984) is characterized by relatively high Rb/Sr, Th/Pb, Th/U - a continental (uplifting) trend related to potassium enrichment. P. Castillo (1988) correlates this the largest mantle geochemical anomaly with a zone of decreased seismic velocities in the lower mantle - again decreased densities are tied to uplifting. The majority of hotspots are above the low velocity regions. Mesozoic continental flood basalts of the southern hemisphere (the Ferrar magmatic province) are low-Ti and high in Si, Rb/Sr, 87Sr/86Sr (initial 0. 707 - 0. 713)[7]. So, the shrunk planet due to cooling and important loss of volatiles [8] is no exception from the regular row of planets structurized by wave warping according to their solar distances.
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