-Seasonal variations in D LOD are associated with the global atmospheric dynamics

1. THEORY The fundamental equation governing the rotation of a planet is the classical conservation equation for angular momentum valid in an inertial reference frame. Without external torques acting on it, it is expressed as: Length-of-Day variations (DLOD) represents the variations in the mean Length of Day (LOD) which is the time needed for the planet to make a complete rotation at constant angular velocity Ω. Liouville equations describe the change in angular momentum of the deformable planet due to internal and external excitations. In the case of atmospheric excitations, it is related to the atmospheric angular momentum (AAM) functions (Barnes et al. 1983) . AAM can be written explicitly as the sum of a matter (loading) term and a wind (motion) term. where, t is time, H is the spin angular momentum of the planet and L the external torque. The external torques (principally due to the gravitational attraction of other solar system bodies) can be neglected in seasonal time scales. Hence, the angular momentum variations of the fluid layers are balanced with the rotational changes of the solid planet. Axial angular rotation of the planet is expressed as function of a mean angular speed Ω0 and superimposed small amplitude variations m3: LENGTH OF DAY VARIATIONS OF MARSÖ. Karatekin, J. Wautier and T. Van Hoolst. Royal observatory of Belgium, 3, Avenue Circulaire 1180 Brussels, Belgium. Email: o.karatekin@oma.be Where, R is the mean equatorial radius of planet, φthe latitude, λ the longitude, g surface gravity, C mean polar moment of inertia, ps surface pressure, qice CO2 ice load, u zonal winds and k’ the loading Love number. The latter stands for the effect of surface deformation in response to the surface loading and depends on the structure and rheology of planetary interior. COMPARISON WITH OBSERVATIONS DLOD from MCD 4.2 We calculated DLOD from the output (u, ps, qice) of the recent Mars Climate Database (MCD) version 4.2. (Forget et al. 2007) using the angular momentum approach. Konopliv et al. (2006) determined amplitudes of DLOD using both lander and orbiter data. DLOD from the observations and MCD are in good agreement. Separate contributions from surface pressure, ice cap loading and winds on the rotation rate of Mars are calculated. The surface pressure variations have the largest contribution while the winds have the smallest effect in contrast with the Earth where the winds are the dominant source for seasonal length-of-day variations. The Martian atmosphere is highly variable. The MCD includes 4 different dust scenarios. The largest variations in DLOD occurs during 270<Ls<360 In comparison with the previous DLOD amplitudes from the older versions of the MCD, the present solution yields slightly smaller values. REFERENCES • Barnes R T H, Hide R,White H H, Wilson C A, Atmospheric angular momentum fluctuation, length-of-day changes and polar motion, Proc. R. Soc. London, Ser A, 387, 31-73, 1983. • Defraigne P, de Viron O, Dehant V, Van Hoolst T, Hourdin F, Mars rotation variations induced by atmosphere and ice cap, J. Geophys. Res. 105(E10), 24563-24570, 2000. • Forget et al. The new (version 4.2) Mars Climate Database, 7th Mars Conference, Pasadena, 2007. • Konopliv A S, Yoder C F, Standish E M, Yuan D N, Sjorgren W L, A global solution for the Mars static and seasonal gravity, Mars orientation,Phobos and Deimos masses, and Mars ephemeris, Icarus, 182(1), 23-50, 2006. • Sanchez B V, Rowlands D D, Haberele R M, Schaeffer J, Atmospheric rotanional effects on Mars based on the NASA Ames general circulation model, J. Geophys. Res. 108(E5), 5040, doi:10.1029/2004JE002254, 2003. • Van den Acker E, Van Hoolst T, de Viron O, Defraigne P, Forget F, Hourdin F, Dehant V, Influence of the winds and the CO2 mass exchange between the atmosphere and the polar ice cap on Mars’ orientation parameters, J. Geophys. Res. 107(E7), 2002. • Van Hoolst T, Treatise on Geophysics. VOL. 10: Planets and Moons. Elsevier, The rotation of terrestrial planets, p. in press, 2007. CONCLUSION: • -Seasonal variations in DLOD are associated with the global atmospheric dynamics • -DLOD from MCD v4.2 have amplitudes slightly lower than those calculated from its previous versions. • DLOD determined from MCD and tracking data are in good agreement. ACKOWNLEDGMENTS This work was financially supported by the Belgian PRODEX program managed by the European Space Agency in collaboration with the Belgian Federal Science Policy Office