Ground-based broadband photometric observations of four inactive geosynchronous satellites of "box-wing" design were frequently performed between March 2012 and December 2013 to commence a long-term study of their attitude dynamics. The brightness of the satellites was observed to vary in a periodic fashion, which was interpreted to mean that reflected sunlight was being modulated due to satellite spin. The average observed spin periods inferred from the light curves ranged from 158 to 1548 s. The variation of each satellite's inferred spin period was observed to be small or negligible over hourly timescales but varied significantly (from 15 to 25% of the average) and smoothly (possibly cyclically) over monthly to yearly timescales. The characteristics of the observed spin-period variations, including the amplitudes, timescales, and shapes, differed greatly between satellites and suggest a relationship between the average observed spin period and the variation amplitude. The observed spin-period variations were interpreted as being due to one or more external disturbance torques acting on the spacecraft. The most significant torque was found to be solar radiation pressure acting on the large-area solar panels. The magnitude of this torque produced sufficient angular accelerations to explain the observed spin-period variations. A first-order phenomenological model is proposed to explain the high-level aspects of the observed phenomena. Nomenclature A = amplitude of spin-period variation, s A panel = area of a single solar panel, m 2 a = length of satellite central box (cube) side, m D = residual dipole moment, A · m 2 I = moment of inertia, kg · m 2 l panel = length of a single, fully deployed solar panel, m l tot = total length of a satellite (wingspan), m M = total mass of satellite, kg M Earth = magnetic moment of the Earth, T · m 3 m box = mass of the central satellite box (cube), kg m panel = mass of a single solar panel, kg P rad = average solar radiation pressure at one astronomical unit from the sun, Pa q 1 = reflectivity of a solar panel side q 2= reflectivity of the opposite solar panel side to q 1 R = distance from the center of the Earth, m T = satellite spin period, s T Earth = orbit period of the Earth, days T 1 = observed satellite spin period at one specific epoch, s T 2 = observed satellite spin period at an epoch later than T 1 , s T = average satellite spin period, s t = day of year, days t 0 = reference time that determines the phase parameter, days t 1 = reference time 1, s t 2 = reference time 2 (later than t 1 ), s t 3 = reference time 3 (later than t 2 ), s w panel = width of a single solar panel, m α = equatorial right ascension coordinate, deg of arc α HGS max = maximum observed angular acceleration of HGS-1, μrad · s −1 · day −1 α SRP = angular acceleration due to solar radiation pressure torque, μrad · s −1 · day −1 α SRP max = maximum angular acceleration due to solar radiation pressure torque, μrad · s −1 · day −1 α spin = net spin angular acceleration, μrad · s −1 · day −1 α = angula...

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