Time series forecasting is one of the most critical challenges in statistics and
data science. Human activities and health are significantly influenced by solar activity. The
sunspot number is one of the most commonly used measures of solar activity. The solar
cycle’s quasi-periodic nature makes it an excellent choice for time series forecasting. Four
models include three singular models, consisting of LSTM, ARIMA, and SARIMA, as well
as a hybrid model were implemented to forecast maximum sunspot number of cycles 25 and
26. The hyperparameters of the singular models were optimized using Bayesian optimization.
The LSTM-ARIMA hybrid model was able to achieve the best performance. The outstanding
results of the LSTM-ARIMA model shows the potential of hybrid methods in improving the
overall performance. Moreover, the LSTM model was able to outperform the ARIMA model,
which demonstrates the ability of LSTM networks in learning from time-series data. The final
model forecasts a peak sunspot number of 137.04 for Solar Cycle 25 in September 2024 and
164.3 for Solar Cycle 26 in December 2034, which is comparable to NASA’s prediction of
134.4 in October 2024 and 161.2 in December 2034.

In the present paper, we investigate the impact of solar activity on Low Earth Orbiting (LEO) satellites. How the increase in the number of coronal mass ejections and solar flares raises the likelihood that sensitive instruments in space and will be damaged by energetic particles accelerated in these events. So, we study the effect of perturbation forces on the Keplerian orbital elements of two LEO satellites using atmosphere model NRLMSISE00. The equation of motion and the effect of all perturbation are solved by using a High-Precision Orbit Propagation (HPOP) model, with Runge-Kutta 7 method, this method was treated by Cowell’s technique. In this respect we deduce that solar activity influences the upper atmosphere; this influence is mediated through rapid geomagnetic disturbances.