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Description: Cometary activity affects the orbital motion and rotation state due to sublimation induced forces. The availability of precise rotation-axis orientation and position data from the Rosetta mission allows one to accurately determine the outgassing of comet Churyumov-Gerasimenko/67P (67P). We derive the observed non-gravitational acceleration of 67P directly from the Rosetta spacecraft trajectory. From the non-gravitational acceleration we recover the diurnal outgassing variations and study a possible delay of the sublimation response with respect to the peak solar illumination. This allows us to compare the non-gravitational acceleration of 67P with expectations based on empirical models and common assumptions about the sublimation process. We use an iterative orbit refinement and Fourier decomposition of the diurnal activity to derive the outgassing induced non-gravitational acceleration. The uncertainties of the data reduction are established by a sensitivity analysis of an ensemble of best-fit orbits for comet 67P. We find that the Marsden non-gravitational acceleration parameters reproduce part of the non-gravitational acceleration but need to be augmented by an analysis of the nucleus geometry and surface illumination to draw conclusions about the sublimation process on the surface. The non-gravitational acceleration follows closely the subsolar latitude (seasonal illumination), with a small lag angle with respect to local noon around perihelion. The observed minor changes of the rotation axis do not favor forced precession models for the non-gravitational acceleration. In contrast to the sublimation induced torques, the non-gravitational acceleration does not put strong constraints on localized active areas on the nucleus. We find a close agreement of the orbit deduced non-gravitational acceleration and the water production independently derived from Rosetta in-situ measurement.