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The Sun is the primary source of energy for the Earth. The small changes intotal solar irradiance (TSI) can affect our climate in the longer timescale. Inthe evolutionary timescale, the TSI varies by a large amount and hence itsinfluence on the Earth's mean surface temperature (T$_{s}$) also increasessignificantly. We develop a mass-loss dependent analytical model of TSI in theevolutionary timescale and evaluated its influence on the T$_{s}$. Wedetermined the numerical solution of TSI for the next 8.23 Gyrs to be used asan input to evaluate the T$_{s}$ which formulated based on a zero-dimensionalenergy balance model. We used the present-day albedo and bulk atmosphericemissivity of the Earth and Mars as initial and final boundary conditions,respectively. We found that the TSI increases by 10\% in 1.42 Gyr, by 40\% inabout 3.4 Gyrs, and by 120\% in about 5.229 Gyrs from now, while the T$_{s}$shows an insignificant change in 1.644 Gyrs and increases to 298.86 K in about3.4 Gyrs. The T$_{s}$ attains the peak value of 2319.2 K as the Sun evolves tothe red giant and emits the enormous TSI of 7.93$\times10^{6} Wm^{-2}$ in 7.676Gys. At this temperature Earth likely evolves to be a liquid planet. In ourfinding, the absorbed and emitted flux equally increases and approaches thesurface flux in the main sequence, and they are nearly equal beyond the mainsequence, while the flux absorbed by the cloud shows opposite trend.

The Total Solar Irradiance variability in the Evolutionary Timescale and its Impact on the Mean Earth's Surface Temperature