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SATELLITES' ORBITS
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The MPS system was designed to provide a minimum of 4 satellite MPS signals to a receiver anywhere on the surface of Mars, as shown in the 3D view Figure 1 below. Figure 1 represents four satellites and their respective look angles.
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Figure 1: satellites and their look angles
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A look angle of 10 degrees, similar to that used in the Earth GPS system, was used to help reduce the background thermal noise from Mars for the received GPS signal. A satellite with a circular orbital radius of 12650.7 km (or an altitude of 9253.66 km) is equivalent to half a Martian sidereal day, or two satellite orbital revolutions over the same point during a sidereal period. This is similar to the Earth based GPS system. Using this altitude also precludes any collisions with or any signal shadowing by Phobos, Mars’ nearest moon, and reduces free space path loss. The diagram below demonstrates the diminishing return of increasing satellite radius to hemisphere coverage.
Note: it is not possible to achieve 100% hemisphere coverage, regardless of satellite radius distance.
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Figure 2: diminishing return of increasing satellite radius to hemisphere coverage
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This 10 degree look angle is represented as angle A in the 2D view figure. Angle B is therefore 64.68 degrees, and half of angle C is 15.32 degrees. Angle C is the key angle required to determine the required number of satellites for GPS coverage.
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Figure 3: 2D view
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Using half of angle C, the radius of Mars, and the radius of satellite orbit, angle theta shown in the diagram below is determined to be 74.68 degrees. This angle represents only half of the coverage of the satellite signal, however, in order to ensure a minimum of 4 satellites of coverage, this is the angle used to provide double signal reception on the surface. Using this angle of 74.68 degrees and 360 degrees for a circle, the number of satellites needed to provide coverage is 4.8, which results in rounding up to 5 satellites. Therefore, a Mars GPS constellation should have 5 satellites in order to provide double signal reception on the surface.
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