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Aims. The barycentric dynamics of the Sun has increasingly been attracting the attention of researchers from several fields, due to the idea that interactions between the Sun’s orbital motion and solar internal functioning could be possible. Existing high-precision ephemerides that have been used for that purpose do not include the effects of trans-Neptunian bodies, which cause a significant offset in the definition of the solar system’s barycentre. In addition, the majority of the dynamical parameters of the solar barycentric orbit are not routinely calculated according to these ephemerides or are not publicly available. Methods. We developed a special version of the IAA RAS lunar–solar–planetary ephemerides, EPM2017H, to cover the whole Holocene and 1 kyr into the future. We studied the basic and derived (e.g., orbital torque) barycentric dynamical quantities of the Sun for that time span. A harmonic analysis (which involves an application of VSOP2013 and TOP2013 planetary theories) was performed on these parameters to obtain a physics-based interpretation of the main periodicities present in the solar barycentric movement. Results. We present a high-precision solar barycentric orbit and derived dynamical parameters (using the solar system’s invariable plane as the reference plane), widely accessible for the whole Holocene and 1 kyr in the future. Several particularities and barycentric phenomena are presented and explained on dynamical bases. A comparison with the Jet Propulsion Laboratory DE431 ephemeris, whose main differences arise from the modelling of trans-Neptunian bodies, shows significant discrepancies in several parameters (i.e., not only limited to angular elements) related to the solar barycentric dynamics. In addition, we identify the main periodicities of the Sun’s barycentric movement and the main giant planets perturbations related to them. [ABSTRACT FROM AUTHOR]