On models of Mars’ interior and amplitudes of forced nutations: 2. The effects of liquid core and mantle elasticity

Abstract

The numerical modeling of Mars’ forced nutation of the real Mars’ model with a radially heterogeneous, compressible, self-gravitating liquid core and elastic mantle is performed. Effects of three-axiality of Mars’ figure are taken into account to compute values for the periods of free core nutation (FCN) and the amplitudes of forced nutations. The effects of the liquid core for different models are of the order of few percents for the prograde semi-annual component and of the order of 10–15% for the semi-annual retrograde component. The absolute values of these effects are of the order of 5–20 ms of arc (mas) and 1–3 mas, respectively. Taking into account, that the modern accuracy of VLBI measurements for the case of the Earth is of the order of 0.02 mas, we see, that important results about Mars’ internal structure may be obtained even if the accuracy of Mars’ nutational measurements 1–2 order of magnitude less than accuracy for the Earth. The effects of the shear stress relaxation during long time intervals are studied: the corrections to the nutational amplitudes for prograde semi-annual component are between 8.93 and 9.8, for retrograde semi-annual component are between −4.81 and −8.2 ms of arc, and the period of free core nutation is varied in the limits between 257.2 and 295.8 Earth's solar days. The differences exceed significantly the errors of Mars’ nutational components measurements, and, consequently, these measurements can give new important information about Martian mantle rheology. The possibilities of inferring properties of the interior structure of Mars based on the measurements of its rotation are discussed.