**Acknowledgements**

The S-E distance shifts are found to lead to a migration of the Earth's aphelion and perihelion to their classic position on the major axis of the ellipse to occur on 21 June and 21 December, respectively, appropriate for the ideal elliptic Earth revolution. For example, the aphelion is shifted: in 1600 to 28 June, in 2020 to 5 July and in 2060 to 16 July, while and the perihelion migrates from 21 December to 28 December in 1600, 5 January in 2020 and to 16 January in 2600. The shifts of the S-E distances lead to the shifts of the Earth aphelion and perihelion from the major ellipse axis to the intermediate (shorter) axis, which passes through the SIM position of the Sun for the year and the ellipse orbit centre. Therefore, these shifts define the skewness of Sun-Earth distances along the Earth orbit towards the real position of the Sun, because it is moved outside the focus owing to the orbital perturbations of the Sun's motion about the barycentre caused by the gravitational

These shifts of Sun-Earth distances lead to the changes in the total solar irradiance reaching the Earth atmosphere and baseline magnetic field measured from the Earth. Because of this reduction of the S–E distances caused by SIM, the TSI at the Earth is shown to increase from 1700 to 2600 by about 11 *W=m*<sup>2</sup> (0.95%) in February–March (and decreased in August–September), by 15–18 *W=m*<sup>2</sup> (1.2%) in April–May (and decrease in October–November) and by 7–8 *W=m*<sup>2</sup> (0.5%) in June– July (and decrease in December–January). While the shift of the maximal distance (aphelion) from regular 21 June date in 1600 to mid-July in 2600 can naturally explain the skewness of the baseline magnetic field towards the Northern polarity in 2600 and the minimum of the baseline magnetic field in 1600, by its skewness

It is also shown that since 1600 to 2020 there was an increase of the annual TSI

However, in 2020 the Sun has entered the period of a reduced solar activity: the Grand Solar Minimum (2020–2053). The orbital variations of solar irradiance will be combined with the variations of solar activity, or solar magnetic field, imposed by the variations of solar dynamo [1, 10]. The decrease of solar irradiance during this GSM is expected to be about 3 *W=m*2, or 0.22%. Therefore, the reduction of solar irradiance caused by the GSM effect will work in opposition to the increase of solar irradiance caused by the orbital SIM effects in the current Hallstatt's cycle. The baseline temperature (not including any terrestrial effects) is shown

modern GSM1 the terrestrial temperature is expected to be lowered by 1.0<sup>∘</sup>

irradiance and the baseline terrestrial temperature is expected to return to the pre-GSM level. Then the irradiance and temperature will continue increasing because of the SIM effects combined with radiative transfer of solar radiation in the terrestrial atmosphere. This means the terrestrial temperature will continue increasing up to

C by 2375 when the second modern GSM2 will occur (2375–2415). During GSM2

C since 1700 because of SIM effects. Because of the

C higher than it was in 1700. After 2053, the solar

C giving

magnitude by about 1.3 *W=m*<sup>2</sup> derived from the mean monthly S-E distances, which is close to the magnitude of 1–1.5 *W=m*<sup>2</sup> reported for the similar period from the current TSI observations [34]. However, the annual TSI magnitudes, calculated from the daily S-E distances reveal a much larger annual increase of the total solar irradiance by about 20–25 *W=m*<sup>2</sup> by 2500 in M2 compared to millennium M1. This means there is an excess of solar radiation input into the terrestrial atmosphere in millennium M2 not accounted for by any other consideration that has to be considered for the solar forcing. This additional solar input should have different redistribution between Northern and Southern hemispheres, in addition to normal variations of the Earth position on elliptic orbit [49] linked to their exposure time to

towards Southern polarity as it was reported before [19, 52].

the solar input not discussed in the current paper.

increased by 2020 by 1.5<sup>∘</sup>

3.0<sup>∘</sup>

**50**

the resulting temperature of 0.5<sup>∘</sup>

forces of the four large planets.

*Solar System Planets and Exoplanets*

V. Zharkova wishes to express her deepest gratitude to the funding by the public supporters raised through 'Fund-me'sites. Their support inspired the author to undertake the investigation of the ephemeris of the Sun-Earth distances and relevant variations of the solar irradiance associated with the changes of the Sun-Earth distances induced by orbital effects. The author also wishes to thank the Paris Observatory, France and JPL ephemeris websites, JPL, Pasadena, US for providing the ephemeris of the Sun-Earth distances for a few millennia. The work was partially supported by the US Airforce grant PRJ02156.
