Long-term predictive assessments of solar and geomagnetic activities made on the basis of the close similarity between the solar inertial motions in the intervals 1840–1905 and 1980–2045

The solar inertial motions (orbits) (SIMs) in the years 1840–1905 and 1980–2045 are of a disordered type and they are nearly identical. This fact was used for assessing predictive capabilities for the sizes of three future sunspot cycles and for the time variation of the geomagnetic aa-index up to 2045. The author found that the variations in sunspot numbers in the interval 1840–1867 and in the interval 1980–2007 are similar, especially after 1850 (1990). The differences may be ascribed to the lower quality of the sunspot data before 1850. A similarity between the variations in geomagnetic aa-index in the intervals 1844–1867 and 1984–2007 is also found. Moreover, the aa-index in these intervals have the same best fit lines (the polynomials of the fourth order) with close positions of the extrema. The extrema of the best fit line for the aa-index in the interval 1906–1928 which corresponds to the first half of the ordered, trefoil interval of the SIM have the opposite positions to them. The correlation coefficient between the aa-indices in the interval 1844–1866 and in the interval 1984–2006 is 0.61. In contrast, the correlation coefficient between the aa-indices in the interval 1844–1866 and in the interval 1906–1928 is −0.43. Cautious predictions have been made: the author believes that the cycles 24–26 will be a repeat of cycles 11–13, i.e. they could have heights around 140 (100), 65 and 85, they will have lengths of 11.7, 10.7 and 12.1 years. The maxima of the cycles should occur in 2010, 2023 and 2033, the minima in 2007, 2018, 2029 and 2041. Up to 2045, the aa-index could repeat its values for the interval 1868–1905. The results indicate that solar and geomagnetic activities are non random processes. If these predictions may come true, then further evidence of the primary role of the SIM in solar variability is established.