Uncontrolled attitude motion of a gravitationally-aerodynamically stabilized LEO nanosatellite is considered. The analytical cumulative distribution functions of the maximum angle of attack for Rayleigh and uniform distributions of the nanosatellite's initial transverse angular velocity value were obtained. The formulas for choosing the design parameters of the gravitationally-aerodynamically stabilized CubeSat standard nanosatellite which has the deviation value of the longitudinal axis from the local vertical less than acceptable value with a given probability for fixing altitude and known initial angular velocity errors were acquired. The nomograms, which allow simply and clearly to choose the main design parameters of the gravitationally-aerodynamically stabilized CubeSat standard nanosatellite were constructed.