Mathematics – Logic
Scientific paper
Sep 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008epsc.conf..783k&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 wave planetology [1, 2, 3 & others] declares in its first theorem that all celestial bodies are dichotomous. This is a result of a warping action of the fundamental wave (wave 1 long 2πR where R is a body radius) that appears in any body due to its movement in non-round (elliptical, parabolic) keplerian orbits with periodically changing accelerations. Having a standing character and four crossing directions in rotating bodies (but all bodies rotate!) these waves inevitably press in one hemisphere and bulge out the opposite one tending to impose on a body convexo-concave shape. This shape is leveled out in larger bodies due to enhanced gravity but is clearly observed in smaller ones with diminished gravity. Still, in the larger bodies as, for an example, in Earth the tectonic dichotomy is expressed as an opposition of the subsided western Pacific hemisphere and the uplifted eastern continental hemisphere. At Mars even sharper dichotomy is in the north-south direction. Small bodies (normally less than 400-500 km across) notwithstanding their type (asteroids, comets, satellites), size and composition (stones, metals, ices) are flattened and bended by the fundamental wave. That is why all asteroids in the main asteroid belt have an oblong shape what was established rather long ago but never was properly explained. Now a number of small satellites is observed by Cassini spacecraft in the saturnian system that makes together with jovian and martian small satellites a representative group for comparisons. In the figures below are shown asteroids, satellites and a comet arranged in a row of increasing sizes. They all are flattened except the largest in the row Enceladus (505 km) and bended tending to acquire a convexo-concave shape. Asteroids: Itokawa (0.5 km long), Eros (33 km, PIA03111). Satellites: Calypso (22 km, PIA07633), Atlas (32 km, PIA08233), Prometheus (102 km, PIA08192), Hyperion (350 km, PIA06645), Enceladus (505 km, PIA08258, comet-like behaviour). Comet: Borrelli (core 8 km long). Various body types, sizes, compositions, but there is the same style of deformation because of a warping action of the fundamental wave long 2πR. There is a tendency to extend and break the convex hemisphere with production of deep cracks ("saddles") and to squeeze (contract) an antipodean one expelling internal material (a scheme of this process is in the drawing -the upper right corner). In extreme cases a body can break down with production of binaries and satellites of small bodies what is not rare in cosmos. A satellite Calypso and an asteroid Eros have near sizes but different compositions (ice and stone) and occur in different zones of the solar system. But they are deformed similarly. A bending action leaves morphological traces on body surfaces. In this respect the 102 km long satellite Prometheus is very exemplary as it shows diverging ridges with closer spaced ends at the concave hemisphere (up in the image) and wider spaced ends at the convex one. This pattern witnesses an opposition of contracted and extended hemispheres. In volatile rich bodies - comets this process is marked by squeezing material under contraction from the concave hemisphere (dust-gaseous tale) and more quite degassing of cracked convex hemisphere (Borrelli). This dichotomy shows also icy satellite Enceladus. Its southern pole region under contraction (the tiger stripes structure) expels vapor-ice mixture; its northern pole region in contrast is quite but has many craters - traces of the past degassing. In this respect the tiny icy satellite could be treated as a large comet core still spitting material into space; this material is not wasted vainly but is needed to mighty Saturn for making one of its outer rings (E-ring). The largest irregular satellite in the solar system - Hyperion has various appearances in many acquired images. It is not so oblong as smaller bodies but its convexo-concave shape is very pronounced. Its polygonal outlines also can be seen betraying a tendency to acquire a tetrahedron shape. The simplest Plato's figure - tetrahedron is dichotomous in its nature because a section across any of its four axes produces from one side a vertex and from another a face. To a vertex three faces narrow - contraction, to a face three other faces diverge - extension. So, dichotomous structures of celestial bodies are an expression of their wave geometrization by interfering fundamental waves. In figures from the right row the tetrahedron features of satellites are seen more sharply: Hyperion- PIA08904, dimension 175 x 120 x 100 km, Thebe-PIA02531, 110 km, Telesto-PIA07546, 25 km across. References: 1. Kochemasov G.G. Concerted wave supergranulation of the solar system bodies // 16th Russian-American microsymposium on planetology, Abstracts, Moscow, Vernadsky Inst. (GEOKHI), 1992, 36-37. 2. Kochemasov G.G. Tectonic dichotomy, sectoring and granulation of Earth and other celestial bodies // Proceedings of the International Symposium on New Concepts in Global Tectonics, "NCGT-98 TSUKUBA", Geological Survey of Japan, Tsukuba, Nov 20-23, 1998, p. 144-147. 3. Kochemasov G.G. Theorems of wave planetary tectonics // Geophys. Res. Abstr.1999. V.1, #3, p.700.
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