There are four sources of attitude disturbance in Earth's orbit. Solar (photon) pressure, atmospheric drag, gravity gradient and interaction with geomagnetic field. Let's examine possible effects on the ParkinsonSat from each one.
Solar pressure with the given satellite design has the tendency to keep increasing the angular velocity and it could possibly reach the limit where centrifugal forces tear the satellite apart. One caveat is that for the spin around desired axis of minimal principal moment of inertia, it must not already have a significant spin around the axis of maximal principal moment of inertia. Rotations are stable for both of this axes and it is hard to change the axis of rotation without first slowing down. Additionally, when rotation is around a non desired axis, the solar pressure will alternatively provide opposite torques depending on the side which is in the sunlight. Figure below shows angular velocity from a simulation of a ParkinsonSat with only solar pressure, neglecting orbit and eclipses.
Atmospheric drag can act to align the satellite's most aerodynamic direction with the velocity vector. However, CubeSats are not really aerodynamic and mostly symmetrical, thus this is very minor effect. On the other hand, the drag can directly act to slow down the spin of the satellite, as the satellite's sides sweep through the atmosphere. Next figure is a simulation of the ParkinsonSat with an initial angular velocity of 3 RPM, altitude of 350 km and only atmospheric drag effect. Orbit effects are not taken into account, which would vary the orbit velocity vector. Orbital velocity vector is kept normal to the satellite's angular velocity vector, in which case the torque is strongest. Variation of the atmospheric density, which changes on many factors, but mostly on the sunlight/eclipse, is also ignored.
Gravity gradient can only convert any available potential energy, due to the satellite's orientation, into kinetic and thus alter the angular velocity. Amount of angular momentum here is limited and often will be quite small, especially on a CubeSat like ParkinsonSat. At best, slight attitude oscillation can be expected from this effect, which is not of interest for this question.
Interaction with the Earth's geomagnetic field is complicated to account for as it varies with the orbit and the position in the orbit. ParkinsonSat did not use magnetic actuators to reach its spin state and this attitude disturbance source can will be at first ignored.
Therefore, taking solar pressure and atmospheric drag effects, we can find terminal velocity dependent on the orbit altitude. Terminal velocity is achieved when solar pressure and atmospheric drag torques cancel each other out. Following figure presents calculated torques.
With the orbital period of 95 minutes, the altitude is about 400 km and terminal velocity should be reached at around 80 RPM. However, this analysis is done without much knowledge of the ParkinsonSat, I had to estimate a whole lot from the available pictures. Still, I would expect that this is precise within 20% error margins.
Few conclusions given this analysis:
- It is unlikely that the ParkinsonSat reached its 6 RPM spin in 15 days due to the solar pressure disturbance. Even on their web site they state that they over did it. I can only guess that means it did not fit their designs either.
- Atmospheric drag is insignificant for satellite dynamics at around 15 RPM.
- Remaining torque source, which could explain the reached spin is geomagnetic field. ParkinsonSat was not designed to use this for its spin, but making sure your satellite is not affected by the geomagnetic field can take significant effort. Often the current from solar cells can induce dipole moment when the satellite is in the Sun. This corresponds with the observations and can be confused with the solar pressure torque. Quick calculation: 4 solar cells each producing about 2 W at 0.5 V, connected in series outputs (4x2)/(4x0.5) = 4 A current. Wire loop area of one solar panel could be maybe 50 mm^2, giving a dipole moment of 0.02 Am^2. With an average field strenght of 10 uT, we get torque of 0.2 uNm. Roughly 200 times stronger than the solar pressure torque. Of course, there are many other factors to consider, as this torque is not constant and depends on the magnetic field direction and would provide torque around other axes too. Still, axis of minor principal moments of inertia is favored, firstly because it is easier to spin around this axis, and secondly because that axis gets torque from all four solar panels, while the other two axes have to split panels two and two.
