  Bogoliubov quasiparticles moving in the background of superfluid
$\text{He}^3$-A see an apparently curved space-time metric when the background
superfluid vacuum is in motion. We study how this curvature couples with the
spins of the effectively massless quasiparticles. First, we set up the problem
in null Fermi coordinates for radial as well as circular geodesics and then use
it in the context of the analog metric seen by the quasiparticles. We obtain an
effective magnetic interaction due to curvature coupling, and provide numerical
estimates. Some possible implications of these results are then pointed out.
