Returning to the Figure 1, we have determined that one constellation should have 5 satellites, and noting the 3D view diagram, in order to provide a minimum of 4 GPS signals for position accuracy, we introduce another constellation in an orthogonal orbit to the original.
Figure 1: satellites and their look angles
Above: Five MPS satellites coverage
For entire planet coverage, we introduce another satellite constellation orthogonal to the other two planes, resulting in a total of 15 satellites among 3 orthogonal constellations, resulting in entire Mars coverage with a minimum of 4 GPS satellite signals at any given location. While it would be possible to use pure equatorial and polar orbits for the 3 orthogonal constellations, in order to avoid one satellite loitering over a given area too long, orbital inclinations of 55 degrees were used, mimicking the Earth based GPS systems.
The final orbits are depicted below:
Figure 5: The final orbits
The pictures below show the coverage at polar and equatorial locations, and the area with the largest gap between the orthogonal planes.Click on the image to view the animations.
Figure 6: Polar coverage
Figure 7: Equatorial coverage
Figure 8: Area with the largest gap between planes
In order to avoid satellite collisions at the intersections of orthogonal orbits, the use of off set True Anomalies prevents satellites from arriving at the intersections at the same time, and also provides a margin of safety for orbital maneuvers to correct satellite positions over time.
The table below gives all the orbital elements for the 15 satellites.
