Observing and modelling the LAGEOS spin axis behaviour

Mathematics

Scientific paper

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Scientific paper

The acceleration experienced by the LAGEOS satellites has been among the most intriguing issues of space geodetic research. These accelerations can be explained by the combined effect of a wide variety of non-gravitational forces. The attitude behaviour of the spacecraft is a crucial element here. The fact that LAGEOS-I, the oldest satellite, has almost come to a standstill complicates the problem even further. For the purpose of better understanding and describing the dynamical behaviour of the passive satellites, LOSSAM-II has been developed, which models both spin axis orientation and spin rate evolution. LOSSAM-II combines mathematical theory and independent observations. Observations of the spin rate and spin axis orientation are taken at a number of institutes and/or observatories: University of Maryland (USA), Matera Observatory (Italy) and Herstmonceux Observatory (UK). The measurements taken by the latter are based on sunlight, which is reflected by the front faces of cube corner reflectors, observed as a 'glint'. At Herstmonceux, each glint is detected by a photomultiplier attached to the telescope, and the epoch is measured by an 1-ms-resolution event counter. With nearly three years of observations, the evolution of the spin rate and spin axis orientation of LAGEOS-II has been estimated through analysis of the pattern of glint intervals and the geometry at a occurrence of every glint. Several perturbation torques are considered in the Euler equation for the rotational motion of the satellites. They account for (i) the geomagnetic field, (ii) the Earth's gravity field, (iii) the offset between satellite center-of-mass and center-of-pressure, and (iv) the difference in reflection properties of the northern and southern hemisphere of the satellites. The model provides initial orientation and spin rate values, magnetic polarization parameters, offset of the center-of-pressure w.r.t. the center-of-mass and offset between the axis of symmetry and the axis of rotation. The observations yield residuals of about 5 deg and 0.63 deg for the attitude, and 1 s and 0.66 s for the spin period for LAGEOS-I and LAGEOS-II respectively. In addition to providing a better description of the spin axis behaviour and input for the modelling of a number of non-conservative forces, LOSSAM-II also allows to make predictions of the future state of the satellite. This is important for observing the satellite under unfavorable conditions, i.e. when nearly non-rotating.

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