Empirical Models for CubeSat Stability Indices based on the Gravity-Gradient Stabilization
CubeSat, Gravity-Gradient Stabilization (GGS), Passive Attitude Stabilization, Stability Indices, Rotational Kinetic Energy, Attitude Determination and Control System (ADCS), Inertia Ratios, Low Earth Orbit (LEO), Electrical Power Subsystem (EPS), Systems Tool Kit (STK), CubeSat Design Specifications (CDS), Magnetorquers, Reaction Wheels, Control Performance, Design Optimization
Optimizing CubeSat subsystems for size, weight, power consumption, and performance is essential given the inherent constraints of CubeSat missions. The CubeSat Design Specifications (CDS) allow for mechanical designs with inertia values across five stability regions on the Gravity-Gradient Stability Map (GGSM): Lagrange, Debra-Delp, Pitch, Roll-Yaw, and Unsteady. This work investigates the application of Gravity-Gradient Stabilization (GGS), which utilizes external gravitational torque for passive stabilization, by analyzing rotational kinetic energy patterns and introducing empirical models for stability indices based on the GGSM, principal moments of inertia, and characteristic equation roots for CubeSat standards. Python-based numerical simulations and polynomial curve fitting validate the effectiveness of these models, providing a robust framework for evaluating mechanical designs and identifying configurations that enhance CubeSat attitude stability. One application of these empirical model-based indices compares GGS with commonly used active Attitude Determination and Control Systems (ADCS) - specifically magnetorquers and reaction wheels - within the CubeSat standard. The analysis focuses on control performance, power consumption, and implications for design optimization, the latter useful for structural modeling. The results indicate that configurations with lower rotational kinetic energy improve control response and overall efficiency, demonstrating the potential advantages of integrating active attitude control and GGS using the proposed empirical model-based indices. Case study scenarios were simulated considering a 500 km altitude circular orbit and were performed using the two-body method. The impact of GGS on the power generation of CubeSats was also considered in the numerical simulations. The results compare the performance of gravity gradient stability regions in terms of power generation for different CubeSat sizes. The results demonstrated that GGS provides uniform power generation for all GGSM regions. Numerical simulations were performed using Python and also the Systems Tool Kit (STK) software.