Our objective is to (a) investigate the variation of insolation at the top of the atmosphere (TOA) under secular changes of astronomical elements (e.g., Earth’s heliocentric distance, Sun’s apparent geocentric declination) during the past four centuries, and (b) assess the accuracy of historical work on insolation in this historic context. Therefore, we predict the insolation at the TOA for timescales from the diurnal course to the annual course and arbitrary periods of days using a 10-minute timestep and an increment of 5？. Our predications are based on the ICRS geocentric-rectangular coordinates and their rates provided by the JPL planetary and lunar ephemeris DE440 and the adjustment of them to the equator and the equinox-of-date using the subroutines for aberration, frame-bias, precession, and nutation of the Naval Observatory Vector Astrometry Software, Version F3.1. At 1AU, we apply the solar constant of the respective year, taken from the reconstructed total solar irradiance (TSI) based on the “Community-Consensus TSI Composite” and SATIRE-T model. We quantify the variation as the differences in the daily mean solar irradiance over the annual course compared to 2010. Although the reconstructed TSI varies only by about 2.2 W？m？2, seasonal daily mean solar radiation differs notably from that of 2010, particularly for the polar regions of the southern hemisphere (SH) and the northern hemisphere (NH). There, the differences have mainly opposite signs, resulting in a butterfly-like distribution across latitudes and seasons. The 1910 daily mean solar irradiance differs the largest from that of 2010 (SH: ？7.3 W？m？2 to 7.4 W？m？2; NH: ？7.4 W？m？2 to 7.3 W？m？2) followed by 1810 (SH: ？5.0 W？m？2 to 5.5 W？m？2; NH: ？5.8 W？m？2 to 5.2 W？m？2). For 1910, 1810, 1950, and 1710, the daily mean solar irradiance is most sensitive to smooth changes in the astronomical elements from the polar circles poleward and least sensitive around the equator. The smallest differences compared to 2010 occur for 1750 (SH: ？1.9 W？m？2 to 1.1 W？m？2; NH: ？2.0 W？m？2 to 1.2 W？m？2), when the largest positive differences occur around the equator. Our results reveal a noteworthy nonlinear relationship between the annual course of daily
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