| Secular motion of the Earth pole and non-tidal acceleration of its diurnal rotation have
obtained rather precise explanation with the help of simple one-point model of the directed
transport of fluid masses from a southern hemisphere in northern hemisphere with the general
direction, given by geocentric axis OP directed to pole P with coordinates 700N,
10403 E[1]. The another generalized model represents a system of two material points with
masses m2 and m1, located on surface of the Earth at poles of geocentric axis OP. Masses
are linearly changed in the time with velocities [2]: á¹2 = 0.179 -
1015kg/yrand
á¹1 = 0.043 -
1015kg/yr.
A reduction of fluid masses of the appropriate thin spherical layer of the Earth correspond
to secular increasing of masses of model points. The specified model has allowed to explain
values of fundamental geodynamic parameters observably and determined during decades: a
direction and velocity of drift of a pole of the Earth; value of non-tidal acceleration of
axial rotation; to explain a secular variations of coefficients of the second, third,
fourth, sixth and eighth zonal harmonics of a geopotential; coefficients of secular
changes of a surface of ocean for the last approximately 150 years; a direction of
secular drift of a geocenter and other planetary phenomena [3]. The role of the
angular momentum of redistributed masses of the Earth in rotation of the Earth
appeared not essential at the given stage of researches. On the essence the offered
model has semi-empirical character as it bases on values of velocities of change of
masses of points and the given position of axis OP. For their determination and
estimations the part of the observant data was used, and other parameters were
designed under analytical formulas. The obtained results have precisely confirmed
competency and affectivity of geodynamic model [4] about existence of secular drift of a
liquid core along radial direction OP with velocity about 2.6 cm/yr in the northern
direction to Taimyr peninsula. Thus the gravitational attraction of superfluous mass of
the core (19 % from the Earth mass) causes secular asymmetric inversion tide [2]
of fluids which effectively manages to be modeled by two points with variable
masses.
In the given work the attempt to construct a similar model of the directed secular
redistribution of fluid masses of Mars from a southern hemisphere in northern is undertaken
with the purpose of an explanation of observably tendencies in redistribution of masses
between hemispheres and with the purpose of a prediction of the new phenomena in its rotary
motion. The hypothetical assumption is made, that secular redistribution of fluid masses from
a southern hemisphere in northern hemisphere of Mars mainly is determined by areocentric
axis OP directed to the pole P with coordinates 570N, 820 E (as is known in this direction
the centre of mass of Mars relatively the centre of a figure on 2.8 km is displaced).
Material points with masses m2 and m1 settle down at poles of geocentric axis OP
on a surface of Mars, and their masses change linearly in the time with velocities
[5]:
á¹2 = 0.402 -
1015kg/yr and á¹1 = 0.257 -
1015kg/yr.
The given modeling characteristics correspond to prospective secular variations of
coefficients of the second and third zonal harmonics of gravitational potential of
Mars: JË2= - 57.0 -
10-11 1/yr and ËJ3 = -4.94 -
10-11 1/yr, more less agreed
for today with the data of observations (Dehant, private communication, 2008)
[6].
Let’s emphasize, that the discussed phenomena of asymmetry of hemispheres, intensity of
inversion processes, and bipolarity and inversion of all structures of Mars much more
expressive, than at the Earth. Therefore we in the right to expect the greater efficiency in
application of geodynamic model and more significant secular effects in rotation of Mars in
comparison with the Earth.
The constructed model has allowed to estimate non-tidal acceleration of axial rotation
which as it would be possible to expect, essentially surpasses the similar characteristic of
rotation of the Earth.
The obtained result means, that angular velocity of Mars in present period increases on
the law r = (0.708821808000+ 0.000000001038-
t) -
10-4 1/s, here t - in years. It is
possible assume that the estimation of acceleration can be obtained directly on the basis of
the data of observations in the nearest years. Velocity of secular change of duration of day for
Mars (LOD) thus can make significant value about -0.0903 ms/yr, that considerably
surpasses similar value for non-tidal acceleration of the Earth (-0.006 ms/yr). The
ratio of positive acceleration of the Earth rotation á¹ to its angular velocity Ï makes
á¹-Ï = (6.9± 1.7) -
10-11 1/yr[7]. In case of Mars the estimation of acceleration was carried
out under the formula [8]: á¹/ Ï = -Ä- C -á¹- G --Ä- C = 103.8 -
10-11 1/yr.
We here have neglected by an influence of secular change of the axial angular momentum
of fluid masses (atmospheric and underground) of Marsá¹.
As shown in other my report on EGU GA 2009 in case of the Earth the total angular
momentum of fluids really is small and within the limits of mistakes can be accepted equal to
zero. In the case of Mars we the same as and in case of the Earth, expect of secular change of
the angular momentum of Mars and change of global superrotation of its atmosphere
which, at least, in part, will be compensated by the angular momentum of fluids.
Thus, expected non-tidal acceleration of axial rotation of Mars can be at 10-15
times more those, but observably by astronomical methods, for the Earth. Certainly,
the estimations obtained here are preliminary and the phenomena discussed here
require more detailed studying with using of new data of precision observations.
First of all it is important to obtain the specified values of secular variations Ë
J2 and
Ë
J3.
In case of the Earth the tidal deceleration of daily rotation of the Earth essentially
surpasses non-tidal acceleration (35 %) which as shown the author is caused by the directed
redistribution of fluid masses of the Earth, in turn caused by polar drift of the centre of mass
of the liquid core of the Earth to the north [1]. In case of Mars the opposite picture is
expected. It is quite possible, as show the executed estimations, that tidal deceleration of axial
rotation of Mars much less than its positive acceleration caused by global dynamics of shells
(the core and mantle). And it means, that as against the Earth in axial rotation of Mars in
the present epoch an acceleration, instead of deceleration of rotation should be
observed.
References
[1] Barkin Yu.V. (2001) Explanation and prediction of the secular variations of the
Earth rotation, geopotential, force of gravity and geocenter drift. Proceedings of
International Conference «AstroKazan-2001». Astronomy and geodesy in new
millennium (24-29 September 2001), Kazan State University: Publisher «DAS», pp.
73-79.
[2] Barkin Yu.V. (2007) To an explanation of non-tidal acceleration of the Earth diurnal
rotation and secular trend of its pole. Proceedings of IUGG XXIV General Assembly,
Perugia, Italy 2007: Earth: Our Changing Planet (Perugia, Italy, July 2-13, 2007), (G) – IAG,
GS003, p. 3799. www. iugg2007perugia.it.
[3] Barkin Yu.V. (2007) Celestial geodynamics and solution of the fundamental problems
of geodesy, gravimetry and geophysics. Proceedings of IUGG XXIV General Assembly,
Perugia, Italy 2007: Earth: Our Changing Planet (Perugia, Italy, July 2-13, 2007), (S) –
IASPEI, JSS011, p. 2149. www. iugg2007perugia.it.
[4] Barkin Yu.V. (2002) Explanation of endogenous activity of planets and satellites and
its cyclicity. Izvestia cekzii nauk o Zemle. Rus. Acad. of Nat. Sciences, Issue 9, December
2002, M.: VINITI, pp. 45-97. In Russian. |