Source: https://ntrs.nasa.gov/api/citations/20110007876/downloads/20110007876.pdf
Theory: Earth has a magnetic field and satellites tend to have a weak magnetic field of their own. The two magnetic fields want to align, causing the satellite to rotate accordingly. Earth’s magnetic field is complex, asymmetric, not aligned with Earth’s spin axis, varies with geographical movement of the dipole and changes in solar particle flux.
Type: Cyclic
Formula: For the purposes of ADCS design, sufficient to model Earth’s magnetic field as a dipole and determine the maximum possible value of the magnetic torque for a spacecraft’s altitude.
$$ T_m=DB $$
$$ D=\frac{M}{R^3}\lambda $$
$T_m$ is the magnetic torque
$D$ is the spacecraft’s residual dipole moment in $A\times m^2$
$B$ is the magnetic field strength in tesla
$M$ is the magnetic moment of the Earth multiplied by the magnetic constant ($M=7.8\times 10^{15}\space tesla\space m^3$)
$R$ is the distance between the spacecraft and the Earth’s center in $m$
$\lambda$ is a unitless function of the magnetic latitude that ranges from 1 at the magnetic equator to 2 at the magnetic poles (A polar orbit will se roughly twice the maximum magnetic torque of an equatorial orbit)
From SMAD (2005) Table 11-9A
Type: Cyclic
Influenced Primarily By:
Formula: