## 4 Materials and Methods for Designing Tether-Deployed Constellations
### Orbit Design
#### 4.2.3 Orbit Design Question 3: Single or Multiple Semimajor Axes for Released Payloads  
When considering single or multiple semimajor axes being allowed, the key question is whether or not all payload orbits need to be dedicated to very similarly sized orbits. If this requirement is needed, this again results in requiring one of the asymmetrical payload release options. If there is allowance for variation in payload altitude however, symmetrical payload release becomes viable, and is a much more preferable option. 2.4 Orbit Design Question 4: Preference on Arguments of Periapses for a Prograde or Retrograde Payload Release Group  
With the utilization of a symmetrical release, more options are available, which revolve around potentially optimizing the distribution of deployed payloads in either the prograde  
Figure 19: Retrograde concentric circular release trajectory (prograde orbit hidden). Figure 20: Retrograde concentric elliptical release trajectory (prograde orbit hidden). or retrograde release orbits. This is not always necessary, but if it is, it would entail the deployer and either prograde or retrograde release orbits being configured in such a way that their orbital periods would allow for a uniform distribution of payloads along an optimized orbital ring, all with the same argument of periapses. The optimized payload group's orbits could be considered concentric, as they would be identical trajectories overlapping each other. It is possible that this optimized release payload orbit be made circular, but that would eliminate the need for a preference for the arguments of periapses of that payload group. Maintaining the same arguments of periapses would require the deployer to release payloads in the same direction at the same position in its orbit for each payload in the selected optimized group. Examples of these particular orbits are depicted in Figures 17-20. The basic progression behavior of the released payloads naturally results in the prograde payload \"lagging behind\" the deployer's position after one deployer orbit due to the increased orbital period of the prograde payload. The reverse is also true for the retrograde payload \"leading ahead\" of the deployer after one orbit due to the shorter period for the retrograde payload. A visualization of this behavior is shown in Figure 21. As more payloads get released, this will naturally produce a chain of payloads that will appear to either \"lag behind\" or \"lead ahead\" of the deployer over time as the prograde and retrograde orbits become populated. The primary benefit of the approach of optimizing one payload group is that it guarantees at least one payload group is released into a consistent pattern, uniformly distributed along a single release orbit path, but this comes at the expense of possibly producing gaps or overlaps in the distribution of payloads in the other release orbit and increasing its eccentricity, and can potentially take more time to execute when waiting for the deployer to intersect with the release orbits at the proper time to release each payload. A visualization of the different optimization options for prograde and retrograde orbit payload distributions and their resultant gaps or overlaps are shown in Figures 22 and 23. If this approach is used for optimizing specifically the prograde release orbit, the resultant geometry required for the deployer and retrograde release orbits should be carefully considered so as to not inadvertently release the retrograde payloads on a trajectory leading to a collision with the  
Figure 21: Basic payload orbit progression behavior post-release. central planetary body, unless the retrograde payloads are replaced with counterweights for an asymmetrical release approach as previously described. Figure 23: Basic payload orbit progression behavior with retrograde release orbit distribution optimization for an example set of 8 prograde-released payloads and 8 retrograde-released payloads.