External torque analysis

There will be many external torques affecting the satellite’s attitude and orbit such as the atmospheric drag, radiation pressure and gravity gradient. Of these, gravity gradient must be considered later on in the spacecraft’s development cycle as it depends on the craft’s internal mass layout. Torques produce an angular acceleration equal to:

(1)
\begin{equation} a=T/I \end{equation}

where a is acceleration, T is torque in newton meters and I is moment of inertial. For now we can assume our satellite will have an even mass distribution to give us a moment of inertia of 1/240 kg m^2

++Atmospheric Drag++
Even at such a high altitude, there is residual atmosphere that will produce a retarding drag force and torque proportional to the spacecraft’s speed squared.

(2)
\begin{align} F=\frac{1}{2}CArv^2 \end{align}

Where C is the drag coefficient, which describes the smoothness of the surface, r is the atmospheric density, and A is the cross sectional area. The rotational drag torque obeys a similar set of relations. The atmospheric density varies by several orders of magnitude as it is governed by solar weather, but it can be approximated using the exponential pressure relation, which gives us 1.963e-44 kg/m3 at 800km. This massive factor reduces the force to around 1e-36N. Clearly the main factor limiting the mission if it starts from this altitude is more likely to be radiation damage than orbital degradation. Similarly, the torque produced from atmospheric drag is going to be far too small to help detumble the satellite.