Passive magnetic attitude control (PMAC)

Definition#

Passive magnetic attitude control (PMAC) combines two magnetic parts. A permanent magnet aligns one body axis with the local geomagnetic field, the way a compass needle does. Hysteresis dampers, rods or strips of a soft-magnetic alloy, turn rotational energy into heat as the field component along them cycles, so the spin and the libration around the field line die out[1]. The system has no power supply, software, sensors or moving parts. That is why it is the most common attitude control of 1P and 1.5P PocketQubes, and why it flew on Grizu-263A.

How it works#

As the spacecraft moves along its orbit the field direction turns, roughly twice per orbit relative to an inertial frame, and the magnet drags the stabilized axis along. In a dipole field the inclination $I$ of the field line follows $\tan I=2\tan {\lambda }_m$, where ${\lambda }_m$ is the magnetic latitude: the axis lies almost horizontal over the magnetic equator and almost vertical near the poles[1]. The magnet’s restoring torque $mB\sin \theta$ makes the axis oscillate around the field line with an undamped libration period $2\pi \sqrt{I/(mB)}$; the dampers remove the energy of that oscillation and of the initial spin.

flowchart LR
  M["Permanent magnet"] -->|"restoring torque m × B"| BODY["Spacecraft body"]
  BODY -->|"rotation"| ROD["Hysteresis dampers"]
  ROD -->|"loss per cycle, heat"| BODY
  EARTH["Geomagnetic field"] --> M
  EARTH --> ROD

Why a 1P is different#

Methods developed for CubeSats and microsatellites still apply[2][3], but three effects change at 50 mm[1][4]:

1. The magnet does not shrink with the spacecraft. Disturbance torques of a 1P are tiny, but the torque of a residual dipole does not depend on size, so the moment the rules call for stays near a few hundredths to a tenth of an A·m².
2. The magnet sits close to everything. The field of a dipole decays as $r^{-3}$, so at the walls of a 1P it is eight times stronger than at the walls of a 1U. Dampers biased by that field stop working, and magnetometers saturate.
3. The dampers are short. Only about 45 mm fit, against 95 mm in a 1U, which lowers dissipation per element, although the much lower inertia more than compensates.