###### Abstract  
NASA's Juno mission, involving a pioneering spacecraft the size of a basketball court, has been instrumental in observing Jupiter's atmosphere and surface from orbit since it reached the intended orbit. Over its first decade of operation, Juno has provided unprecedented insights into the solar system's origins through advanced remote sensing and technological innovations. This study focuses on change detection in terms of Juno's trajectory, leveraging cutting-edge data computing techniques to analyze its orbital dynamics. Utilizing 3D position and velocity time series data from NASA, spanning 11 years and 5 months (August 2011 to January 2023), with 5.5 million samples at 1 min accuracy, we examine the spacecraft's trajectory modifications. The instantaneous average acceleration, jerk, and snap are computed as approximations of the first, second, and third derivatives of velocity, respectively. The Hilbert transform is employed to visualize the spectral properties of Juno's non-stationary 3D movement, enabling the detection of extreme events caused by varying forces. Two unsupervised machine learning algorithms, DBSCAN and OPTICS, are applied to cluster the sampling events in two 3D state spaces: (velocity, acceleration, jerk) and (acceleration, jerk, snap). Our results demonstrate that the OPTICS algorithm outperformed DBSCAN in terms of the outlier detection accuracy across all three operational phases (OP1, OP2, and OP3), achieving accuracies of 99.3%, 99.1%, and 98.9%, respectively. In contrast, DBSCAN yielded accuracies of 98.8%, 98.2%, and 97.4%. These findings highlight OPTICS as a more effective method for identifying outliers in elliptical orbit data, albeit with higher computational resource requirements and longer processing times. This study underscores the significance of advanced machine learning techniques in enhancing our understanding of complex orbital dynamics and their implications for planetary exploration. Article  
Astronomical Engineering, 2025
quantity, behavior, or other recurring measures of interest over time, is a key concept when analyzing longitudinal data [2]. Launched on 5 August 2011, NASA's Juno spacecraft is the first mission to explore beneath Jupiter's thick clouds, offering insights into the gas giant and the origins of the solar system. Now in its extended mission phase, Juno continues its pioneering research. This study investigates the trajectory characteristics of Juno during the initial phase of its mission, employing Hamiltonian mechanics to define the momentum and position concurrently. This research aims to develop a strategy for assessing Juno's trajectory and identifying related changes, contributing to a deeper understanding of spacecraft dynamics in deep-space exploration. Identifying causal effects is challenging, but analysis of temporal and spatial data trends allows for predictions and deep analysis, enhancing comprehension of trajectories. Analyzing precise trajectories and detecting changes within them is crucial to understanding object dynamics and the relationships between phenomena. Trajectory analysis provides timely and contextual information that is often unattainable through other means. Remote sensing data have become a key component of change detection due to its high temporal frequency, digital processing capabilities, comprehensive perspective, and enhanced spatial and multidimensional resolution. Human-controlled trajectory modification was considered an extreme event of the time series. The Hilbert transform of the amplitudes of the higher order derivatives of the position vector in the reference system connected to the solar system was used. There were analyzed derivatives up to order four of the position vector: velocity, acceleration, jerk, and snap. It was proved that information in the higher-order derivatives serves to identify extreme events. The novel aspect of our contribution is that it is incorporated into the supplied learning model, allowing it to be adapted to a non-stationary challenge.