## 4 Results
The Light Time Delay model is essential for accounting for the duration required for light, or in this context, a signal, to traverse the distance from Earth to Mars, which is pivotal for grasping communication delays. The Apparent Position model calculates the perceived location of Mars orbiters from Earth, factoring in the finite speed of light and the orbital motion of both planets [56]. The data were exported to CSV files following the establishment of the required orbital propagations and communication links in STK. After this, the data underwent post-processing to facilitate the analysis of several metrics critical to comprehending the Earth-Mars communication link. These metrics include the following:  
* Range: The distance (million kilometers) throughout the period. * One-Way-Light Time (OWLT): The time it takes for a signal to propagate at the Earth-Mars range. * Averaged Daily Contact Frequency: The average number of contacts every 24 h.
* Averaged Daily Contact Time: The aggregated contact time per day. These metrics are vital for assessing the viability and reliability of communications between Earth's DSN and the Mars orbiters and are discussed below. The code for creating the STK scenario, exporting the data, and processing and plotting the results can be seen in the repository of the Data Availability Statement. The characterization of the Earth-to-Mars link dynamics is essential for successful interplanetary communications. The analysis presented in this section explores the complex relationship between the range, communication time, and frequency of contacts as orbital mechanics and the positioning of ground stations on Earth influence them. Insights into the optimal conditions for establishing a stable communication link with Mars orbiters are provided, considering the inherent challenges presented by the relative movements of Earth and Mars and the limitations imposed by the planets' horizons. Figure 10 (top) illustrates the dynamic nature of the Earth-to-Mars link, depicting the variation in range and OWLT between NASA's DSN ground sites and Mars. The data indicate a periodic oscillation ranging from 96 to 362 million kilometers, occurring over two years, which aligns with Earth and Mars's relative positions in their orbits. Correspondingly, OWLT varies between 5.3 and 20.1 min. These values indicate Earth's closest approach to Mars, known as opposition, and when they are on opposite sides of the Sun, known as conjunction. This cyclic pattern directly results from the orbital mechanics of the two planets and defines the planning backhauling strategies for Mars missions (see Figure 11). Figure 9: Message capacity per SF during the orbital period of a satellite on Mars. Figure 10 (bottom) depicts the varying involvement of each DSN ground site in maintaining communication with Mars-orbiting spacecraft. The graph highlights a notable trend: The Canberra station in Australia consistently provides the highest communication frequency, particularly when Mars is optimally positioned for the southern hemisphere. Conversely, the Goldstone and Madrid stations exhibit increased contact when Mars is better aligned with the northern hemisphere. This pattern underscores the need for strategic planning in ground station resource allocation to accommodate the periodic nature of Earth-Mars connectivity for optimal mission support. Figure 12 provides a detailed temporal analysis of daily contact frequency and duration between Earth's DSN and Mars orbiters, segmented by altitude and inclination. Note that the aggregated daily contact time in Figure 12 considers the cumulative communication windows from all three DSN sites, so the total can exceed 24 h in a single day (see snapshot in Figure 13a). Figure 11: Far (**a**) and close (**b**) ranges between Earth and Mars. Figure 10: Range, OWLT (**top**), and participation of NASA’s DSN ground sites (**bottom**) in the contacts between Earth and Mars segments.