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Efficient computation of the quadrupole light deflection

Efficient computation of the quadrupole light deflection for quasars/quasars and solar system objects within the framework of the baseline Gaia relativity model (GREM) is discussed. Two refinements have been achieved with the goal to improve the performance of the model: First, the quadrupole deflection formulas for both cases are simplified as much as possible considering the Gaia nominal orbit (only approximate minimal distances between Gaia and the giant planets were used here), physical parameters of the giant planets and the envisaged accuracy of 1 microarcsecond for individual systematic effects. The recommended formulas are given by Eq.(40) for stars/quasars and by Eq.(81) for solar system objects. Second, simple expressions for the upper estimate of the quadrupole light deflection have been found allowing, with a few additional arithmetical operations, to judge a priori if the quadrupole light deflection should be computed or not for a given source and for a given requested accuracy. The recommended criteria are given by Eq.(45) for stars/quasars and by Eq.(92) for solar system objects. Additionally, the quadrupole Shapiro effect for solar system objects is reconsidered. A strict upper bound of quadrupole Shapiro effect for solar system objects is given in Eq.(109).