## 8 Limitations and Future Work  
In order to identify orbital deviations, we used high-resolution velocity and acceleration data to evaluate Juno's trajectory using classical Newtonian physics. Although this method offers a strong foundation for comprehending the velocity of the spacecraft, relativistic effects--which may cause minute but detectable variations in trajectory calculations--are not specifically taken into consideration. General relativity foresees that a spacecraft traveling in the gravitational field of a large body, like Jupiter, is subject to time dilation and gravitational redshift. Moreover, the spacetime curvature around Jupiter also moderately changes the path more than is anticipated in Newtonian mechanics. Such relativistic effects are mainly applicable in long-duration missions with high-precision tracking, since tiny perturbations can build up over time. With the time resolution of our dataset (intervals of one minute) and the interest in finding changes in velocity and acceleration, skipping relativistic corrections can cause small errors in our findings. Nevertheless, it has been demonstrated in earlier research that for spacecraft orbiting Jupiter in elliptical orbits, the general relativistic effect on trajectory prediction is generally in the order of millimeters per second in velocity and several meters in position over extended periods of time [43]. Though small in comparison to the size of Juno's orbital fluctuations, these effects might be considerable in high-precision anomaly detection. The Hilbert transform is commonly used to analyze instantaneous frequency fluctuations in stationary and linear signals. Juno's orbital trajectory is non-stationary and non-linear owing to the complicated interactions with Jupiter's gravitational field, magnetosphere, and solar radiation pressure. These dynamic forces cause time-dependent fluctuations that Hilbert-based spectrum analysis may not capture. The Hilbert transform may introduce spectrum distortions when processing non-stationary data. Juno's rapid motion shifts may distort the retrieved frequency components. The Hilbert transform accentuates localized fluctuations, but it does not account for the spacecraft's trajectory non-linearities, which may lead to misinterpretations of severe occurrences. To address these problems, we used the Hilbert transform as an exploration tool rather than a diagnostic measure of trajectory abnormalities. We also cross-validated our resultsusing wavelet transformations, which are superior for non-stationary data. The wavelet-based findings matched the Hilbert-based methodology, validating our event detection technique. However, adaptive time-frequency decomposition approaches like empirical mode decomposition (EMD) or variational mode decomposition (VMD) might improve spectrum analysis in complicated orbital dynamics. Future research may include relativistic corrections in the study, either by applying post-processing modifications using the Schwarzschild metric approximation or by including relativistic equations of motion into the orbital modeling procedure. Moreover, juxtaposing the outcomes of classical and relativistic trajectory calculations may provide additional insights into the importance of these effects in spacecraft motion analysis. Based on the findings of this research, a number of opportunities for future research are available to complement the analysis of Juno's trajectory dynamics further. This work lays the foundation for future research on space mission trajectory analysis. Potential areas for further investigation include the following:  
* Adapting our methods for real-time trajectory analysis and anomaly detection during ongoing missions. * Integrating machine learning techniques to further enhance the prediction accuracy and pattern recognition in trajectory data. * Extending our approach to analyze and optimize multi-body trajectories for future complex mission designs.