1. ON DETERMINATION OF THE MOMENT INERTIA AND THE RADIUS OF THE MARTIAN CORE Schmidt Institute of Physics of the Earth Russian Academy of Sciences zharkov@ifz.ru N.Zharkov and T.V.Gudkova V.N.Zharkov and T.V.Gudkova

2. For a rigid weakly three-axial ellipsoid of revolution σ E = ω (αβ) 1/2, where ω is the angular velocity of rotation of Mars, α=(C-A)/A, β=(C-A)/B, A  B  C – the principal moments of inertia of Mars where A c is the moment of inertia of the liquid core, k is the Love number, k 0 is the segular Love number, G and R are the gravitational constant and the mean radius of Mars. The Eulerian angular frequency and Chandler wobble a b c

3. Periodogram off the arc-by-arc seasonal solutions for С 21 and S 21 with the annual terms removed. The mars annual, semi-annual, tri-annual and ¼ annual are given by periods 1.881, 0.940, 0.627 and 0.470 yr and the Chandler wobble of 210 days by 0.575 yr (Konoplive et.al., 2006) The signature at the Chandler frequency is mixed with the nearly 1/3 Mars year mass redistribution term (229 days), and may cause the polar motion signal to shift to longer periods. The predicted value of T W ~ (200-210) days

4. If a Chandler period T W and corresponding Love number k 2 were determined from observations, the moment of inertia of liquid Martian core ( A c B c ) 1/2 ~ A c could be defined from the formular where T E is the Eulerian period., is the period of the rotation of Mars; A, B, and C are the principal moments of inertia of the planet The inferred elastic Love number (obtained from the gravity analysis of orbiting spacecrafts) k 2 =0.148±0.0.009 ( Konoplive et al., 2006) k 2 =0.156±0.0.009 ( Konoplive et al., 2011)

5. The set of interior structure models were constructed taking into account the experimental results of Bertka and Fei (1997,1998) with an analog of the Dreibus and Wänke (1985) composition. For 50-km thick crust its density is within for 100-km thick crust we have 3.0-3.2 g/cm 3 (Fe#20), 3.2 g/cm 3 (Fe#20), 2.8-3.1 g/cm 3 (Fe#22), 3.1-3.2 g/cm 3 (Fe#22), 2.7-2.8 g/cm 3 (Fe#25); 3.0-3.1 g/cm 3 (Fe#25) For all models the weight ratio Fe/Si is about 1.7. Fe#=25 (solid line) (B-F mantle profile) Fe#=18 (dot-dashed line) Fe#=28 (dashed line) Fe# - an iron atomic number of mantle silicates Fe 2+ /((Fe 2+ +Mg) multiplied by 100

6. The elastic Love number k 2 S as a function of the core radius (a) and the moment of inertia of the core C core /MR 0 2 for a set of Martian models used for the calculation of Chandler wobble periods (the filled circles (●) are for the 50 km crust and the open circles (○) are for the 100 km crust). The horizontal lines (dashed line – data from (Konopliv et al., 2006) and solid line –data from (Konopliv et al., 2011) show the upper and lower bound for k 2 S. The increased value of k 2 influences the choice of models. The model radius  1800 km.  there is no a perovkite layer, and the models have the ratio Fe/Si close to a chondritic one. The model value of a Chandler period is also increased, it is about 204 days. Thus, the range of Chandler period is narrowed and it is in the range of 204-209 days.

7. Conclusion The increase of Love number k 2 has led to the increase of a model value of Martian core (about 1800 km). The composition of Mars is close to a chondritic one. Taking into account observational data and interior structure modelling, the predicted value of a Chandler period is in the range of 204-209 days.