Gravity Gradient Satellite Torque Calculator
Spacecraft Attitude Dynamics: Calculate gravity gradient disturbance torque ($\mathbf{T}_{gg}$) and passive gravitational nadir stabilization moments.
Principal Moments of Inertia
Attitude Deviation Angles & Orbit
Disturbance Torque Output
Pitch Torque ($T_{gg,y}$)
-- µN·m
In N·m: --
Roll Torque ($T_{gg,x}$)
-- µN·m
In N·m: --
Mean Motion ($\omega_0$)
-- rad/s
Period: -- min
Stabilization Condition
--
Iy > Ix > Iz criteria
Gravity Gradient Formulation:
• Vector torque: $\mathbf{T}_{gg} = \frac{3 \mu}{R^3} \mathbf{u}_e \times (\mathbf{I} \cdot \mathbf{u}_e) = 3 \omega_0^2 \mathbf{u}_e \times (\mathbf{I} \cdot \mathbf{u}_e)$.
• For small angles: $T_{gg,x} = \frac{3}{2} \omega_0^2 (I_z - I_y) \sin(2\phi)$, $T_{gg,y} = \frac{3}{2} \omega_0^2 (I_z - I_x) \sin(2\theta)$.
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