## 4 Materials and Methods for Designing Tether-Deployed Constellations
### Orbit Design  
General constellation design entails choosing orbit parameters and satellite quantities specific to each application. For the sake of brevity, the basics of constellation design is not described in this article, but they are well-described in references [16; 17; 18; 19; 20]. In general, however, key factors to consider when designing a constellation include, but are not limited to, the following:  
* Speed of communication between satellites and ground stations (affecting how fast information can be communicated, such as internet speed). * Line-of-sight ranges (affecting how long ground links can last, such as length of a connection between one or more internet satellites before needing to connect to others to maintain connection). * Revisit rate or frequency of repeated positioning of spacecraft over key locations (affecting how frequently location-specific data can be updated, such as monitoring the actively changing boundary of a wildfire). * Range of coverage (such as limits in latitudes, affecting the limits of what regions, ground stations, and people can be covered). Typically, constellations are constructed from one or more \"rings\" of satellites in orbital planes (such as a [PERSON] constellation), but this is not necessarily always the case (such as with a Molniya-based constellation). These orbital rings are constructed in a manner where two or more spacecraft share an orbit and follow each other through the progression of their orbit path. These rings can be populated sparsely (such as with GPS), or densely (such as with Starlink). When describing the orbits throughout this article, only simple elliptical orbits and in-plane maneuvers will be considered. While plane change maneuvers enabled by tethers are possible, they are not the primary focus of this article and will not be discussed in depth. The general geometry and parameters referenced from this point on are shown in Figure 14. Note that figures throughout this article depicting orbits have had their features exaggerated to assist in explanation, particularly regarding orbit radii and eccentricity. Some of the key orbit parameters to consider are orbit radius \(R\), apoapsis \(R_{a}\), periapsis \(R_{p}\), semimajor axis \(a\), true anomaly \(\theta\), orbital period \(T\), gravitational parameter of the central planetary body \(\mu\), and the change in velocity needed to execute orbital maneuvers \(\Delta V\). As the tether concept allows for near-instantaneous imparting of velocity change to deployed payloads, the largest orbit changes can be made by directing this \(\Delta V\) in a direction tangent to the current trajectory of the payload-deployer system. It is also possible to direct velocity changes by tethers into directions other than directly tangent with the direction of orbital motion, but it is not as energy efficient when looking mainly to spread satellites immediately after launch. If, however, it desired to execute maneuvers such as plane changes, these maneuvers are still possible if the involved systems are designed and operated properly. These kinds of maneuvers are beyond the scope of this article, but will be addressed in future work. This \(\Delta V\) tangent to the direction of orbital motion can be directed prograde or retrograde to increase or decrease a payload's orbit apoapsis \(R_{a}\) or periapsis \(R_{p}\), thereby also affecting its semimajor axis \(a\), eccentricity \(e\), and orbital period \(T\). A basic visualization of the orbits produced by prograde or retrograde release from a deployer are shown in Figure 15.  
The process of deploying payloads into particular orbits forces some decisions to be made regarding the final orbit configurations of each payload and the deployer. For this system, there are currently five primary options to consider, each yielding their own benefits and drawbacks that can be selected for specific constellation design depending on application and the resources available to produce it.