Having completed the individual case analysis for both electric and chemical propulsion methods, the orbit group provided the results to the bus group and launch group for consideration in their associated trades. Strictly from an orbit standpoint, chemical propulsion not only requires less overall ∆V, but also takes less transit time to complete and is therefore the best candidate of the two methods. Given the mission operations concept – in particular, the use of the launch vehicle for a significant portion of the transfer ∆V – the integration group selected chemical propulsion for the MINERVA system design.
Figure 6.10: Coverage Trade Space 6.5.1 Constellation Design Trade Space
6.5.1.1 Availability and Revisit Time
Two separate requirements placed on the MINERVA system affect the coverage of the satellite constellation. Firstly, a satellite shall be available to an MSE at least 50% of the time, and secondly, the time between satellite passes shall not exceed three hours.
Using these two constraints, a separate trade space was created for each type of constellation.
For example, constellations with a different number of orbital planes, or phasing angles have their own trade space.
In each trade space the minimum number of satellites needed to satisfy the requirements was calculated for different inclinations and altitudes.
The coverage trade spaces were then combined and the resulting composite trade space is shown in Figure 6.10. From the plot we can see that as altitude increases, the number of satellites decreases. This follows from the fact that as the satellites increase in altitude, the size of their footprint also increases. The number of satellites also increases as the
inclination increases. This is because as the inclination increases, the satellites are directly above the ±15° latitude band for a smaller percentage of the orbital period.
Figure 6.11: Minimum Altitude for Inter-Satellite Links 6.5.1.2 Inter-Satellite Links
Each satellite has the ability to communicate with the other satellites in orbit via inter-satellite links. In order for these links to work, the inter-satellites require line of sight visibility.
This constraint imposes a minimum altitude on the satellite constellation. Figure 6.11 shows the approximate minimum altitude necessary for line of sight communication. The figure assumes that the satellites are evenly spaced around the planet in circular orbits.
Also included in the figure is the requirement that the communication links must pass 200 km above the surface. This additional requirement provides a margin of safety that takes into account the atmospheric effects and orbit insertion errors.
6.5.1.3 Position Determination Constraint
As described in section 10.2 the satellites need to be in an inclined orbital plane relative to the equator. This inclination allows the MINERVA system to calculate the position of an MSE with greater accuracy and in less time. The required inclination is 25°-30° with higher inclinations preferred.
6.5.2 Final Constellation Design
The above trade spaces placed restrictions on the constellation design. After they had been combined, they produced a set of constellations that were feasible. From this set, the final design was chosen.
The parameters that were varied include, number of satellites, inclination, and altitude.
The first parameter that was chosen was the number of satellites. From the ICE sessions it was confirmed that four satellites is the maximum number of satellites that could be afforded. The decision to use four satellites was based mainly on the altitude restriction placed on the constellation by the inter-satellite links. Having four satellites allow as the constellation to orbit at a much lower altitude than three satellites. (1700 km compared to 3700 km). At 3700 km, the antenna needed to communicate to the surface would be much larger than necessary.
Figure 6.12: Final Constellation
Once four satellites had been chosen, the altitude and the inclination were determined. An increase in altitude increases the coverage area, but at the same time increases the antenna size. A decrease in inclination also increases the coverage within the latitude band, but at the same time decreases the performance of the position determination system. From these two trades, the final altitude was chosen to be 2000 km. This altitude corresponds to the altitude where the beamwidth of the antenna allows users to communicate with the satellite as long as the satellite is 10° above the horizon (see Figure 6.12).
Once the altitude had been set at 2000 km, the inclination was set so that the satellite can communicate with any MSE in the ±15° latitude band during every orbital period. The required inclination is 27°. This can be seen graphically in Figure 6.12. Generated in MATLAB, the figure shows the satellites in their final constellation around Mars. The yellow cones represent the areas covered by each individual satellite. The green lines represent the ±15° latitude band. In the figure, one of the satellites is at the highest point (with respect to the equator) in its orbit.
The final design is a Walker-Delta pattern, which consists of four satellites in two orbital planes. The satellites are in circular orbits with an altitude of 2000 km and an inclination of 27°.
6.5.3 Constellation Statistics
Once the constellation had been determined, the statistics of the constellation were determined. These statistics were used to evaluate different point designs. The payload group used this information to determine the communication abilities of the system.
Figure 6.13: Availability Contours
Shown on Figure 6.13, Figure 6.14 and Figure 6.15 are the results of the statistical analysis of the final constellation. Figure 6.13 is a contour plot showing the percentage of time that a satellite is in view. Around the equator, a satellite is in view for at least 80%
of the time, and at 15° N and 15° S, the satellite is in view 70% of the time. Above 65°
the satellites are never in view.
Figure 6.14: Contours of Maximum Revisit Time
Figure 6.14 shows the maximum time in minutes that a satellite will not be in view. Near the equator, this is less than 20 minutes, and less than 30 minutes at the ±15° latitudes.
Just outside of this band, the maximum revisit time increases to 60 minutes. This large jump is due to the fact that during an orbit period, an MSE outside of the latitude band may not see all four satellites.
Figure 6.15: Contours of Average Time in View
Figure 6.15shows the average amount of time in minutes that a satellite will stay in view.
From -30° N to 30° S, a satellite will stay in view for about 50 minutes. Notice that this corresponds to the inclination of the orbital planes, as is to be expected.