Mathematics – Logic
Scientific paper
Apr 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009eguga..11.1618b&link_type=abstract
"EGU General Assembly 2009, held 19-24 April, 2009 in Vienna, Austria http://meetings.copernicus.org/egu2009, p.1618"
Mathematics
Logic
Scientific paper
Secular drift of a pole of an axis of rotation of the Earth is studied more than 100 years. On the modern data the pole of an axis of rotation of the Earth is displaced along a meridian 7209 W with angular velocity of 0"331 ± 0"003 1/cy[1]. Ratios of equatorial components of angular acceleration á¹- and Ë™q to angular velocity of the Earth ? make: Ë™p/? = 395×10-111/yr, Ë™q/? = - 1548×10-111/yr (on the appropriate axes of the Greenwich system of coordinates). A mechanical interpretation to this fundamental geodynamic phenomenon was given by author on the basis of geodynamic model of the forced interactions, oscillations and wanderings of the changeable and deformed of the core and the mantle of the Earth [2]. It was shown, that observably drift of a pole is there is not a result of postglacial rebound as sometimes it is accepted, but it is a consequence of much more fundamental phenomenon - of a secular drift of the liquid core relatively to the mantle. The gravitational attraction of displaced (superfluous) mass of the core results in the directed planetary reorganization of fluid masses - to slow inversion redistribution of these masses from a southern hemisphere in northern. Last process supposes a simple modeling by two points with variable masses [2], [3]. It is possible to show, that the similar model of the directed reorganization of mass of a planet (and about even big basis) can be applied to the Mars [4]. On my geodynamic model [5] the observably constant displacement of the centre of mass of Mars relatively to its geometrical centre (on huge distance of 2.85 km in the direction of a geographical point 570 N, 820 E) there is a result of dynamic evolution of system the core - the mantle of this planet which can to proceed with the certain intensity and in present geological epoch. I.e. by analogy to terrestrial processes we ascertain (we put forward a hypothesis), that on Mars is observed slow secular redistribution of fluid masses from a southern hemisphere in northern. As well as in the case of the Earth this process carries asymmetric, but strictly directed character. Such asymmetric slow redistribution of masses inevitably will result in secular variations of coefficients of gravitational potential of Mars, in particular in its coefficients of second and third zonal harmonics. The data available for today on variations of these coefficients basically already now allow to analyze these secular trends (more confidently for coefficient of the third harmonicJ3, and rather uncertainly for coefficient J2). In the given work they are estimated by the following figures: JË™2= - 57.0 × 10-11 1/yr and JË™3 = -4.94 × 10-11 1/yr. On base of these values the secular variations of masses of modeling points located on a surface of Mars at poles of axis OP (with coordinates 570N, 820 E and 570S, 2620 E) have been determined: á¹2 = 0.402 × 1015kg/yr and á¹1 = 0.257 × 1015kg/yr. It is possible, that value of velocity JË™2= - 57.0 × 10-11 1/yr is overestimated. Longer series of observations are necessary for its specification. Therefore the estimations executed in the given work for parameters of drift of a pole and angular acceleration of axial rotation of Mars (in other my report on the given EGU GA), are especially preliminary and can be considered as numerical evaluations or examples. These estimations turn out on the basis of known formulas for a components of pole drift of a deformable planet [6]: ( • • ) ( • • ) Ë™p = (1+ ?•Î© ) CË™21 I - Ë™P G ?, Ë™q = (1+ ? •Î© ) SË™21 I - Ë™Q G ?. Here ÄŠ21 and á¹ 21 are velocities of secular changes of coefficients of gravitational potetial C21 and S21. á¹- and Ë™ Q are velocities of secular changes of components of angular momentum of relative motion of the fluids of a planet. Ω is a Chandler frequency, taking into account rotational deformations of elastic planet, and ? is an angular velocity of diurnal rottaion of planet. G = ?C0 is an anperturbed value of angular momentum of rotation of Mars, C0 is a polar moment of inertia. Components á¹- and Ë™q determine drift of a pole relatively to the main equatorial axes of inertia of a body in its non-deformed (or initial) state CX and CY . The appropriate components of the relative angular momentum á¹- and also Ë™ Q are referred to the specified axes. We have no any reliable data on secular variations a component of the angular momentum of all fluids of Mars. Therefore in the given work we shall be limited to estimations of influence only variations of geometry of mass:
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