435 may outweigh the inconsistency in the efficiency of the TASC cells. The primary components of the trade  study are included in Table 2 for average Low Earth Orbit (LEO) conditions.   All specific values for the BTJ and TASC cell properti es were collected from references [10] and [11] at  max power (V mp × I mp) conditions. With solar arrays on each side of the deployed array, power can be  collected throughout the entire sunlit orbit. However, bec ause of the nadir orientation of the array, its solar  incidence and therefore cell efficiency constantly ch ange according to the cosine of the incidence angle.  As a result, the primary power loss to the array is  estimated by the average incidence angle over the  sunlit orbit, or 43° at a 1000-km orbit. Based on thes e results it is obvious the BTJ cells, with an average  power of 23.1 W (nearly 5 times traditional CubeSat solar arrays), are the better choice.   Table 2. Beginning of Life Solar Cell Trade Study for 1000-km LEO Orbit 

 BTJ  TASC    Parameter  Value Value Units  Layout Solar Cell Area 32.86  2.28   cm2  Solar Cells Per String  2  6   Parallel Strings (Facet) 1  4      Number of Panels  16  16   Power Cell Efficiency at Referenc e Temperature 28.5 27.0 %  Reference Temperature 28.0  25.0  °C   Maximum Power 32.8  23.6  W   Temperature Loss Coefficient   -0.006 -0.021  %/°C  Temperature Power Loss at 67°C† -2.5  -12.7 %  Incidence Angle Power Loss at 43 Deg ‡ -26.8  -26.8 %  Net Max Power 32.0 20.6 W   Net Average Power  23.1  14.3  W    Attitude Control System

Beyond its obvious capabilities as a power generat ion tool, the XSAS system can provide enhancements  to the CubeSat attitude control syst em by its very nature. By elongating the CubeSat along a single axis,  the CubeSat will naturally begin to orient itself with its long axis perpendicular to the instantaneous tangent plane to the Earth underneath it. We can ex plore the relationship between length and this  orientation tendency through equation 1:   ሬ ሬԦൌ3 ቀఓ ோయቁଶ ݎԦݎڄܫԦ஻ሻ , (1) 

where ሬሬԦ is gravity gradient torque, ߤis the Earth’s gravitational parameter, ܴis the orbital radius, Ԧ ஻ is the  zenith vector in body coordinates, and ܫis the diagonal inertial matrix in the body frame. This restoring  torque causes the vehicle to return to a nadir point ing position should any disturbances occur (such as  orbital motion, radiation pressure or magnetic torquing ). It can easily be seen from the equations that no  torque exists if the body is oriented na dir. If the body is tilted, however, and ௭ then the nadir position  will be a stable equilibrium, and the vehicle will return to a nadir pointing position passively.   A complete design of XSAS must ensure that this restoring torque is greater than any of the lesser  disturbances to assure pointing accuracy and mission succ ess. Specifically in the case of the large flat  shape of the solar array on XSAS, the torque caused  by aerodynamic and solar radiation drag in LEO  must be examined with the following equations:                                                                † Temperature of a  typical flat solar panel in LEO [9]   ‡ Cosine (average array solar incidence angle)  NASA/CP-2010-216272