What Is the Satellite Gravity-Gradient Stabilization Torque Calculator?
Gravity-gradient torque is an environmental torque arising from the non-uniform gravitational field across an extended satellite body.
How Does the Satellite Gravity-Gradient Stabilization Torque Calculator Work?
Integrates differential gravitational force across the mass distribution of the spacecraft.
Satellite Gravity-Gradient Stabilization Torque Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
T_{ ext{gg}} = rac{3 mu}{2 r^3} |I_x - I_z| sin(2 heta)
First-order differential gravitational torque on an asymmetric rigid body.
How to Use the Satellite Gravity-Gradient Stabilization Torque Calculator
- Input orbit altitude, principal moments of inertia Ix and Iz, and angular deviation from nadir.
Step-by-Step Example Calculation
Earth-Pointing LEO CubeSat/SmallSat
Input Values:
orbitAltitudeKm:600
pitchInertiaIxKgM2:250
yawInertiaIzKgM2:80
pitchDeviationAngleDeg:12
Worked Steps: Restoring torque T_gg = 60.1 µN·m with orbital mean motion n = 1.08 mrad/s.
Understanding Your Result
Shows stabilizing restoring torque in micro-Newton-meters (µN·m) and orbital mean motion.
Factors That Affect the Result
- Torque decays rapidly with distance as 1/r^3; most pronounced in Low Earth Orbit (LEO).
When Should You Use This Calculator?
- Passive attitude stabilization design (using gravity-gradient deployable booms) and reaction wheel momentum dumping budget.
Assumptions & Limitations
- Assumes circular orbit around a spherical central body; rigid body mechanics.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard spacecraft attitude dynamics perturbation model.