  In this study we overview recent advances with prediction of solar activity
using as a proxy solar background magnetic field and detection of grand solar
cycles of about 400 years separated by grand solar minima (GSMs).The previous
GSM known as the Maunder minimum was recorded from 1645 to 1715. The
terrestrial temperature during Maunder Minimum was reduced by up to 1.0C that
led to freezing rivers, cold winters and summers. The modern GSM started in
2020 and will last for three solar cycles until 2053. During this GSM two
processes will affect the input of solar radiation: a decrease of solar
activity and an increase in total solar irradiance because of solar inertial
motion (SIM). For evaluation of the latter this study uses daily ephemeris of
the Sun-Earth (SE) distances in two millennia from 600 to 2600 showing
significant decreases of SE distances in the first 6 months of a year by 0.005
au in 600 to 1600 and by more than 0.01 au in 1600 to 2600 with consequent
increases of SE distances in the second halves of a year. Although, these
increases are not fully symmetric in the second millennium (1600 to 2600),
during which the longest SE distances are gradually shifted from 21 June to 15
July in 2600 while the shortest ones from 21 December to 15 January. These
distance variations impose significant increases of solar irradiance in the
first six months of each year in the two millennia, which are not fully offset
by the solar radiation decreases in the last six months in millennium 1600 to
2600. This misbalance creates an annual surplus of solar radiation to be
processed by the terrestrial atmosphere and ocean environments that can lead to
an increase of terrestrial temperature. We estimate that decrease of solar
activity during GSM combined with its increase imposed by SIM will lead to a
reduction of terrestrial temperature during the modern GSM to the levels of
1700.
