# Modeling and Analysis of Staged Constellation Deployment from a Single-Unit System
## 1 Introduction  
Satellite constellations have traditionally been deployed through multiple launches, either releasing one satellite at a time or dedicating each launch to a specific orbital plane [1]. For pico- and nano-satellites, this approach presents additional challenges due to dependence on rideshare opportunities, which restrict control over launch timing and orbit insertion [2]. A notable example is the PlanetScope constellation of 130 3U CubeSats, which required deployment via multiple launch vehicles, including Falcon 9, Electron, and PSLV [3]. Although widely adopted due to the lack of practical alternatives, this deployment strategy is costly, logistically demanding, and complicates financial planning because of fluctuating prices between launches. Moreover, rideshare missions struggle to synchronize orbital plane insertions, leading to orbital misalignments that necessitate post-deployment corrections, leading to prolonged phase times unless propulsion is available [1], a limitation compounded by the fact that propulsion is often impractical for mass- and volume-constrained satellites [4]. To overcome these limitations, we propose a single-launch deployment strategy, where multiple satellites are assembled into a single unit that separates in orbit through a staged disengagement sequence. Each disengagement introduces a controlled change in velocity, or \(\Delta v\), which is enhanced via differential drag control to phase the constellation. The approach reduces launch scheduling complexity, eliminates multi-launch coordination, and enables scalable deployments in low-Earth orbit (LEO). Differential drag control is a technique that modulates atmospheric drag via satellite reorientation or deployable surfaces. It allows along-track control for formation flying, constellation phasing, and collision avoidance. Demonstrated by various missions such as Planet Labs' Flock, CYGNSS, AeroCube-4, and ORBCOMM [5; 6; 7; 8], it has become a standard method for managing relative satellite motion. More recently, [PERSON] et al. demonstrated its applicability to periodic rendezvous missions in their design of a coronagraph consisting of two CubeSats [9]. Advanced control strategies for differential drag include linear programming [10], LQR- and Lyapunov-based adaptive methods [11], convex optimization [12], and hybrid schemes combining drag with limited propulsion or lift modulation [13; 14; 15]. These strategies explore centralized and decentralized architectures, some leveraging inter-satellite communication and nodal precession for limited cross-track control. Differential drag control also has its limitations. Particularly, its effectiveness depends on altitude and atmospheric density, which varies with solar activity [6]. Phasing is inherently slower than thruster-based methods, often requiring weeks to months, and is largely restricted to in-plane maneuvers. Additionally, it relies on limited drag-state resolution and pointing accuracy [12]. Nonetheless, it remains an attractive option for satellites without onboard propulsion, offering a viable means of achieving relative positioning using only attitude control. Despite being developed using a variety of methods, existing differential drag control strategies generally assume that the initial relative positions and velocities are solely determined by the deployment conditions imposed by the launch vehicle. In contrast, the proposed deployment method provides additional control over the initial relative orbital parameters by leveraging its disengagement mechanics. Therefore, the novelty of this work lies not only in the proposed deployment architecture and dispersal strategy but also in the extension of existing research to make such a framework feasible. In particular, this work builds upon Planet Labs' model in [5] to provide an algorithm that selects the disengagement \(\Delta v\) magnitude and timing range to determine phase times.