THE DIURNAL TEMPERATURE REGIME OF THE SURFICIAL REGOLITH OF PHOBOS IN THE LANDING SITE REGION OF THE FOBOS-GRUNT LANDER FOR DIFFERENT SEASONS: THE MODEL PREDICTION. R.O. Kuzmin 1,2, E.V. Zabalueva 1 1 Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, 2 Space Research Institute, Russian Academy of Sciences. IKI RAS, Moscow October, 2011

The main factors determining the peculiarities of the thermal regime of the surface regolith on the Phobos: An atmosphereless body; Short duration of the Phobos’s day (7.7 hours); Short duration of the Phobos’s day (7.7 hours); Highly porous and low-density surface regolith of the Highly porous and low-density surface regolith of the impact origin with low thermal inertia ( 25–84 J m -2 s -1/2 K -1 ); impact origin with low thermal inertia ( 25–84 J m -2 s -1/2 K -1 ); Low surface albedo (average 0.05); Low surface albedo (average 0.05); Repeated eclipses of the Phobos by Mars; Repeated eclipses of the Phobos by Mars; Reflected and thermal radiation of Mars; Reflected and thermal radiation of Mars; The ellipsoidal shape of the Phobos figure; The ellipsoidal shape of the Phobos figure; The absence of internal heat sources. The absence of internal heat sources.

Location of the former (1) and new (2) potential landing sites for FOBOS-GRUNT mission Topography of Phobos based on HRSC stereo images 1 2

I II Suggested new landing sites (option I and II) Viking-1 image VO1_246a °N, 230°W Phobos albedo map based on the Viking Orbiter observations (from Simonelli et al., 1998) Shklovsky Lagado Planitia

Thermal Model of Phobos’s surface In developing the computer code we used as a basis the thermal model of the surface layer of Phobos (Kuhrt and Giese, 1989), which take into account: Ellipsoidal shape of Phobos Eclipses of Phobos by Mars Eclipses of Phobos by Mars Reflected and thermal radiation of Mars Reflected and thermal radiation of Mars Variable thermal conductivity and specific heat of material Variable thermal conductivity and specific heat of material Absence of internal heat sources Absence of internal heat sources Phobos albedo: 0.07 Phobos albedo: 0.07 Surface regolith density: 1100 kg m-3 Surface regolith density: 1100 kg m-3 Thermal conductivity and specific heat are temperature dependent Thermal conductivity and specific heat are temperature dependent with values analogous to lunar regolith with values analogous to lunar regolith (Thermal conductivity range: 8x10 -5 –2.2 x10 -3 W m -1 K (Thermal conductivity range: 8x10 -5 –2.2 x10 -3 W m -1 K Specific heat range: J kg -1 K) Specific heat range: J kg -1 K) For complete model description, see Kuzmin and Zabalueva (2003) For complete model description, see Kuzmin and Zabalueva (2003) Solar System Research, 37, Solar System Research, 37,

The main characteristics of the computational procedure: (1) The consecutive orbital positions of Mars are taken with a step equal to 1/100 of its annual period (6.9 days); (2)For each Mars position, the computation is made for one spin of Phobos around Mars (the satellite begins its motion at local noon for (2) For each Mars position, the computation is made for one spin of Phobos around Mars (the satellite begins its motion at local noon for the given point on Phobos); (3)The step in the Phobos orbit is taken to be 7.5° away from the eclipse and 0.5° within the eclipse zone. (3) The step in the Phobos orbit is taken to be 7.5° away from the eclipse and 0.5° within the eclipse zone. (4)The results of the calculation of the temperature as a function of time and depth were considered only after 5.5 Martian years. (4) The results of the calculation of the temperature as a function of time and depth were considered only after 5.5 Martian years. The model deals with a 40-cm-thick regolith layer, which is divided into sublayers, the first being 0.08 mm thick. The thickness of the subsequent sublayers increases as the progression with a geometric ratio of The regolith layer is assumed isothermal at the initial time and its temperature is taken to be 200 K. The computations start at the perihelion of the Martian orbit.

General characteristics of Phobos and Mars employed in the computer cod in the computer code Parameters Phobos Mars Albedo Surface layer density, kg/m Spin period of Phobos about Mars, s 2.76 ´ 10 4 Spin period of Mars about the Sun, s 5.94 ´ 10 7 Semimajor axis of Mars’ orbit, AU 1.52 Solar radiation on Mars’ orbit at 1.52 AU, W/m Inclination of equator plane to plane of ecliptic, deg 25.2 Eccentricity Angle (w ) between ascending node and perihelion of Mars’ orbit, deg 70 Ratio d of Mars’ radius (RM) to distance between Mars and Phobos (2.76 RM) Emissivity, 

Parameters obtained from the numericalmodeling: Parameters obtained from the numerical modeling: The diurnal course of the surface temperature for different seasons; The diurnal course of the surface temperature for different seasons; The diurnal variation of the temperature in the surface The diurnal variation of the temperature in the surface layer of the Phobos regolith; layer of the Phobos regolith; Max and min values of the diurnal surface temperature; Max and min values of the diurnal surface temperature; The diurnal temperature’s amplitude on the surface and in the depth; The diurnal temperature’s amplitude on the surface and in the depth; The thermal skin depth of the Phobos regolith; The thermal skin depth of the Phobos regolith; The depth with the temperature’s amplitude < 1°. The depth with the temperature’s amplitude < 1°.

The diurnal course of the temperature of the Phobos surface during the spring The diurnal variation of the temperature in the surface layer of the Phobos regolith during the spring layer of the Phobos regolith during the spring Spring, Ls=45.7°

The diurnal variation of the temperature in the surface layer of the Phobos regolith during the summer layer of the Phobos regolith during the summer The diurnal course of the temperature of the Phobos surface during the summer Summer, Ls=135.9°

The diurnal course of the temperature of the Phobos surface during the autumn The diurnal variation of the temperature in the surface layer of the Phobos regolith during the autumn Autumn, Ls=224.2°

The diurnal variation of the temperature in the surface layer of the Phobos regolith during the winter The diurnal course of the temperature of the Phobos surface during the winter Winter, Ls=316.8°

Spring Summer Autumn Winter

, Ls=263.07° late autumn The diurnal thermal regime in the surface layer of the Phobos regolith on the date of the landing.

Comparison of the diurnal course of the temperature on the opposite and sub-Martian hemispheres of the Phobos during the winter 15°N 230°W 15°N 310°W

Seasonal thermal parameters of the surface regolith layer in the potential landing site for Fobos–Grunt mission derived from the numerical modeling Seasons Seasons (northern hemisphere of Mars) Max T (K) Min T(K) Daily Dailyamplitude (deg.) (deg.) Thermal Thermal skin depth skin depth (cm) (cm) Depth, where amplitude <1 o (cm) (cm) Spring, L s =45.7 o Spring, L s =45.7 o ~0.33 ~0.33 ~1.7 ~1.7 Summer, L s =135.9 o Summer, L s =135.9 o ~0.33 ~0.33 ~1.8 ~1.8 Autumn, L s =224.2 o Autumn, Ls=265 o (Date of landing) ~0.32 ~0.32 ~0.31 ~0.31 ~1.7 ~1.7 ~1.8 ~1.8 Winter L s =316.8 o ~0.32 ~0.32 ~1.5 ~1.5 The results of conducted numerical modeling maybe useful at analysis of the measurements data from the instrument Thermophob (see Marov et al., 2010) which will work underneath of one of the Fobos-Grunt Lander’s legs.

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