Source: https://ntrs.nasa.gov/api/citations/20110007876/downloads/20110007876.pdf

Theory: caused when a spacecraft’s center of gravity is not aligned with its center of mass with respect to the local vertical. Center of gravity of spacecraft is dependent on its attitude relative to Earth. Cg is not, in general, the same as the center of mass. Gravity gradient torque increases with the angle between the local vertical and the spacecraft’s principal axes, always trying to align the minimum principal axis with the local vertical.

Type: Constant

Formula:

$$ T_g=\frac{3\mu}{2R^3}|I_z- I_y|\sin{(2\theta)} $$

$T_g$ is the gravity gradient torque about the X principal axis

$\mu$ is the Earth’s gravitational constant $(3.986\times 10^{14}\space m^3/s^2)$

$R$ is the distance from the center of the Earth in $m$

$\theta$ is the angle between the local vertical and Z principal axis

$I_y$ and $I_z$ are the moments of inertia about Y and Z in $kg \space m^2$

Other resources:

https://www.jhuapl.edu/Content/techdigest/pdf/APL-V03-N05/APL-03-05-Fischell.pdf

https://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1035&context=aerosp

https://upcommons.upc.edu/bitstream/handle/2117/329895/REPORT sense dades confidencials.pdf