*3.1. Effect of Orbit Inclincation on Constellation Coverage*

One critical design feature of a constellation is the orbit inclination of its satellites. The inclination of a satellite's orbit determines the maximum possible latitude of its surface observations and hence affects the global distribution of its spatial coverage. The inclination will also affect the frequency with which samples are made at different latitudes, which in turn determines the ZTC. These two performance considerations should both be considered in the design optimization process.

For this study, we consider design options in which one third of the total number of satellites is distributed between each of three orbit planes at distinct inclinations. We analyzed three cases, one where all three planes have an inclination of 30◦, another where the three planes have inclinations of 30◦, 60◦ and 90◦, and a third where all three planes have an inclination of 90◦.

The ZSC results of these simulations are illustrated in Figures 2–4. Although these images depict a single orbit of these three constellations over a period of 1 h, 40 min, and 30 s, they can be extrapolated to form the full 24 h spatial coverage maps. The maximum inclination of the constellation can be seen to limit its latitudinal coverage. The coverage will not exceed the inclination by more than 10◦ north or south. For instance, the constellation with three planes at an inclination of 30◦ has non-zero ZSC at latitudes slightly lower than 40◦ north and south. However, after extrapolating the three orbit maps, this truncated coverage will contrast with the almost 100% ZSC performance demonstrated by the 30◦-60◦-90◦ and 90◦-90◦-90◦ inclination constellations. In these situations where the maximum inclination of the constellation is set to 90◦, the constellations are capable of taking measurements over the entire Earth.

**Figure 2.** Single-Orbit Spatial Coverage for 3-Plane 30◦-30◦-30◦ constellation at 800 km, 16 parallel measurements per sampling, and operating with an RCG Threshold of 15. The lower maximum inclination limits spatial coverage to below 40◦ latitude.

**Figure 3.** Single-Orbit Spatial Coverage for 3-Plane 30◦-60◦-90◦ constellation at 800 km, 16 parallel measurements per sampling, and operating with an RCG Threshold of 15. The inclination distribution provides greater coverage at the various orbit peaks, allowing for a greater GSC than the 30◦-30◦-30◦ constellation.

The ZTC results of these simulations are illustrated in Figure 5. When all constellation planes operate at the same inclination, the ZTC peaks around those latitudes. However, when the plane inclinations are more evenly spaced between latitude levels, as shown by the 30◦-60◦-90◦ constellations, we get more well-distributed sampling across the Earth at the cost of smaller coverage peaks.

**Figure 5.** 24 h Temporal Coverage measurements at different latitudes for 3-Plane constellations at 800 km, 16 parallel measurements per sampling, and operating with an RCG Threshold of 15. Raising the inclination of individual planes or the entire constellation can alter which latitudes are visited most often.

#### *3.2. Effect of Orbit Planes on Constellation Coverage*

The second critical design feature of a constellation is how its satellites are distributed between orbit planes. In this series of design options, an orbit plane is defined as a group of satellites orbiting with the same ascending node longitude. With that definition in mind, we find that when a singular plane satellite constellation is divided into a constellation with multiple planes, its ZTC increases. However, when only looking at certain latitude zones on the globe, this trend may not be uniform.

To better understand how the temporal coverage depends on the distribution of planes, two experiments were conducted where the total number of satellites and satellite inclination were held constant. These experiments first simulate the performance of a single plane of 24 evenly distributed satellites all orbiting at the same inclination. Then, the simulation is repeated for a second constellation in which the plane is split into two planes of twelve evenly distributed satellites separated by 180◦ longitude. Finally, a third constellation is considered in which the satellites are further split into three planes of eight evenly distributed satellites separated by 120◦ longitude. These results are presented in Figure 6, where the orbit inclination is set to 30◦.

**Figure 6.** 24 h Temporal Coverage measurements at different latitudes for 24-satellite constellations at 800 km, 30◦ inclination, 16 parallel measurements per sampling, and operating with an RCG Threshold of 15. Increasing the number of constellation planes while keeping the total number of satellites constant will increase the constellation's Zonal and Global Temporal Coverage.

In this scenario, the ZTC in the zone near the orbit peaks grows when the original constellation is divided into more planes. There is also a ZTC increase at latitudes lower than the peaks when the constellation is redistributed from one plane to three planes. However, when observing the two-plane constellation, the ZTC measurements at latitudes near the equator can remain near stagnant.

Using this understanding of orbit planes and inclinations, designers can better tune their constellation orientations so that both spatial and temporal coverage metrics are optimized. For this experiment, we consider a constant number of satellites all at the same inclination and in the same plane. In this case, a 24-satellite constellation at 30◦ inclination is selected. The performance of this constellation is seen in the blue curve of Figure 7. Note that coverage is lacking near 60◦. To improve it, we divide the plane into a constellation of two 12-satellite planes, one of which orbits at 30◦ and the other at 60◦, resulting in the red curves in Figure 7. As these curves demonstrate, adding this second plane at a higher inclination has the desired effect of increasing coverage above 30◦. Furthermore, if coverage at even higher latitudes was desired, the constellation could be divided into a third plane with an inclination of 90◦. This third plane will also eliminate the coverage drop near the equator present in constellations with two planes.

**Figure 7.** 24 h Temporal Coverage measurements at different latitudes for 24-satellite constellations at 800 km, 16 parallel measurements per sampling, and operating with an RCG Threshold of 15. As the initial 30◦ inclination plane of 24 satellites is divided in smaller planes with raised inclinations allows the constellation's Zonal and Global Temporal Coverage to be shaped and increased.
