## 6 Methodology  
A change probability is a number calculated to indicate the possibility of change in space and is often obtained via temporal investigation of historical datasets. This value estimates the chance of change occurring in an area. Forecasting future circumstances is essential for planning-related research, and identifying the likelihood of change permits this capability. Both non-periodic and periodic datasets may be examined to conclude trajectory change detection [35]. The pattern is a parameter that could be figured out from observations made at either regular intervals or irregular intervals. Most of the time, trends from observations that do not happen at regular intervals are found in large amounts of data, such as annual or other regularly collected observations [36]. When analyzing patterns, curve fitting may be employed in non-periodic sampling. Estimating pattern parameters may be accomplished using conventional statistical methods such as regression. It is worth mentioning that our current dataset is periodic. The model has additional flexibility in choosing which filters to use in threshold queries, thanks to the dynamic query parameters. Whereas descriptive statistics describe a dataset's features, inferential statistics allow us to draw inferences and establish predictions depending on the data. Upon acquiring the dataset, we applied inferential statistics to  
Figure 8: Boxplot of the snap component (for the time interval 7 August 2011 until 4 January 2023). gain insights into the broader population from which the sample originated. Inferential statistics enable us to draw conclusions about the larger population based on the sample data. A formal approach to conducting statistical analysis through inferential methods is hypothesis testing, which aims to analyze populations or investigate relationships between variables using sample data. With the use of statistical tests, hypotheses or predictions are examined. A valid conclusion may be drawn using statistical tests that evaluate sample errors. Utilizing stationary or non-stationary decomposition strategies allows for the collection of pattern characteristics [37]. The interpretation of stationary temporal patterns may restrict the use of these approaches to events that exhibit certain material change features. The stationarity criteria are violated when sudden changes significantly depart from a temporal curve of biophysical parameters. Natural occurrences like volcanic eruptions might cause these kinds of changes and therefore do not satisfy the stationarity criterion. The spacecraft dynamics must be mathematically represented as an initial step in approaching the spacecraft trajectory analytic aspect. A route or time history of the location and velocity of the spaceship may be represented by a collection of ordinary differential equations, which is how the spacecraft trajectory scheme is defined. These equations can be thought of as spacecraft trajectory modeling. In a broad sense, the movement equations for the spacecraft [38; 39] used as the model may be stated in a first-order notation. We have represented the state of the object (\(\overline{\text{U}}\)) with the formula as follows:  
\[\overline{\text{U}}(t)=f(\overline{r}(x,y,z),\overline{v}(x,y,\ z),t), \tag{1}\]  
We denote the relative position and relative velocity of Juno around Jupiter by \(\overline{X}=\overline{X}(t)\) and \(\overline{X}^{\prime}=\overline{X}^{\prime}(t)\) as two-column vectors dependent on time \(t\), respectively. Movement of Juno in the solar system is executed and conforms to a non-linear differential equation:  
\[\overline{v}=\frac{d}{dt}\overline{r}=\overline{r}^{\prime}=g(\overline{r},t). \tag{2}\]  
where the position vector has the following formula:  
\[\overline{r}^{\prime}=\left[x^{\prime}\ y^{\prime}\ z^{\prime}\right]^{T}= \left[\frac{dx}{dt}\ \frac{dy}{dt}\ \frac{dz}{dt}\right]^{T}=\left[v_{x}\ v_{y}\ v_{z}\right]^{T}. \tag{3}\]  
And \(f,\ g\) are control functions of the trajectory and velocity, respectively.