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The Graz kHz Satellite Laser Ranging (SLR) system is the first system operating with a 2-kHz-repetition-rate laser. Using Graz 2-kHz SLR data only, we applied a new analytical approach to determine the spin period of the passive satellite AJISAI. This method analyzes the range measurements to the single corner-cube-reflector panels of AJISAI, allowing accurate determination of an actual attitude of this satellite during day and night. Using Graz kHz SLR data of more than five years, we processed 877 passes of AJISAI (October 9, 2003-December 22, 2008) and calculated its spin period ( ~ 2 s) with an accuracy of 0.0042% (84 ??s). This spin period (T) is increasing, following an exponential trend:T =1.9028 ??Exp (0.014859 . (Year - 2003.0)) s. This slow down is mainly caused by the gravitational and magnetic fields of the Earth. The high accuracy allows, for the first time, the detection of small perturbations of the spin period caused by nongravitational effects related to the solar energy flux to which the satellite is exposed.