# Inter-Satellite Link Prediction with Supervised Learning: An Application in Polar Orbits
## 3 Polar Orbits  
A polar orbit is characterized by a high inclination angle relative to the equator, which makes it pass near the Earth's geographic poles. These characteristics allow polar-orbiting satellites to provide global coverage, observing different parts of the Earth with each orbital pass. This property makes polar satellites highly useful for Earth observation and remote sensing applied in scientific research, disaster management, and environmental studies (e.g., weather monitoring). For this reason, polar satellites are found at low altitudes and are defined by orbital periods of less than 128 min. Figure 2 shows the inclination angle for all 6175 active LEO satellites present in Celestrak in February 2023. Satellites in the red region, with an inclination range of 66\({}^{\circ}\) to 114\({}^{\circ}\) (90\({}^{\circ}\)\(\pm\) 24 \({}^{\circ}\)), are defined as arctic polar satellites and represent approximately 42% of all LEO satellites. Within this range, satellites are commonly located in Sun-synchronous orbits (SSOs), where each successive orbital pass occurs at the same local time under similar lighting conditions. This characteristic allows satellites to retrieve consistent Earth observation data, making them suitable for studies of weather and geophysical phenomena. To accurately replicate real polar satellites with synthetic data, a detailed analysis of the two-line elements (TLE) information for all 2613 Celestrak LEO polar satellites is displayed in Figure 3. A TLE defines the position of a satellite in a given _epoch_ or at a given time with a set of six orbital elements (OEs) that define the orbit shape or eccentricity (\(e\)), the size or semi-major axis (\(a\)), and three orbit orientation angles (inclination (\(i\)), right ascension of the ascending node (\(\Omega\)), and argument of perigee (\(\omega\))), as well as the satellite position along the orbit or mean anomaly (\(M\)). Additionally, the TLE models the atmospheric drag force with the B-star term (\(B^{*}\)), as defined in Equation (1). \[B^{*}=\frac{\rho_{0}C_{d}A}{2m} \tag{1}\]  
Figure 1: Satellite-to-satellite distance, upper and lower bound thresholds (\(T_{min}\), \(T_{max}\)), and resulting encounter with 576 features corresponding to 48 h of SGP4 orbit determination with 5 min discretization intervals. where \(\rho_{0}\) is a reference air density, \(C_{d}\) is the drag coefficient, \(A\) is the frontal area, and \(m\) is the satellite's mass. Notice that \(B^{*}\) is not constant, since both \(A\) and \(C_{d}\) change over time with the satellite's orientation. Figure 3a shows the probability distribution of \(B^{*}\), measured in units of the inverse of the Earth's radius (\(R_{\rm F}^{-1}\)). The vast majority of the Celestrak polar satellites exhibit a small positive drag term. However, unexpectedly, approximately 1% of the satellites present a negative \(B^{*}\). Those negative values arise from unmodeled forces that alias the drag term, creating a negative force for orbit compensation. Since SGP4 can deal with negative drag forces, the range from \(-0.03\) to \(0.03\), containing more than 98% of the cases, has been considered to create synthetic satellites. Similarly, Figure 3b shows the distribution of the semi-major axis. As expected for LEO orbiting satellites (usually found between 160 km and 1600 km above the Earth) the semi-major axis ranges from 6500 km to 8000 km. To delimit the space and avoid outliers, only values from 6700 km to 7500 km are considered for synthetic representation, accounting for more than 99% of the cases. In Earth observation missions, LEO polar orbits are quasi-circular, with low eccentricity values. As shown in Figure 3c, the vast majority of satellites have eccentricities lower than 0.02.