**Abstract**

Daily ephemeris of Sun-Earth distances in two millennia (600–2600) showed significant decreases in February–June by up to 0.005 au in millennium M1 (600– 1600) and 0.011au in millennium M2 (1600–2600). The Earth's aphelion in M2 is shorter because shifted towards mid-July and perihelion longer because shifted to mid-January naturally explaining two-millennial variations (Hallstatt's cycle) of the baseline solar magnetic field measured from Earth. The S-E distance variations are shown imposed by shifts of Sun's position towards the spring equinox imposed by the gravitation of large planets, or solar inertial motion (SIM). Daily variations of total solar irradiance (TSI) calculated with these S-E distances revealed TSI increases in February–June by up to 10–12 *W=m*<sup>2</sup> in M1 and 14–18 *W=m*<sup>2</sup> in M2. There is also positive imbalance detected in the annual TSI magnitudes deposited to Earth in millennium M2 compared to millennium M1: up to 1.3 *W=m*2, for monthly, and up to 20–25 *W=m*<sup>2</sup> for daily TSI magnitudes. This imbalance confirms an ascending phase of the current TSI (Hallstatt's) cycle in M2. The consequences for terrestrial atmosphere of this additional solar forcing induced by the annual TSI imbalances are evaluated. The implications of extra solar forcing for two modern grand solar minima in M2 are also discussed.

**Keywords:** Sun: solar activity, Sun: magnetic field, gravitation, solar inertial motion, solar irradiance
