  Ricci magnetic geodesic (RMG) motion in a k\"ahler manifold is the analogue
of geodesic motion in the presence of a magnetic field proportional to the
ricci form. It has been conjectured to model low-energy dynamics of vortex
solitons in the presence of a Chern-Simons term, the k\"ahler manifold in
question being the $n$-vortex moduli space. This paper presents a detailed
study of RMG motion in soliton moduli spaces, focusing on the cases of
hyperbolic vortices and spherical $\mathbb{C}P^1$ lumps. It is shown that RMG
flow localizes on fixed point sets of groups of holomorphic isometries, but
that the flow on such submanifolds does not, in general, coincide with their
intrinsic RMG flow. For planar vortices, it is shown that RMG flow differs from
an earlier reduced dynamics proposed by Kim and Lee, and that the latter flow
is ill-defined on the vortex coincidence set. An explicit formula for the
metric on the whole moduli space of hyperbolic two-vortices is computed
(extending an old result of Strachan's), and RMG motion of centred two-vortices
is studied in detail. Turning to lumps, the moduli space of static $n$-lumps is
$Rat_n$, the space of degree $n$ rational maps, which is known to be k\"ahler
and geodesically incomplete. It is proved that $Rat_1$ is, somewhat
surprisingly, RMG complete (meaning that that the initial value problem for RMG
motion has a global solution for all initial data). It is also proved that the
submanifold of rotationally equivariant $n$-lumps, $Rat_n^{eq}$, a
topologically cylindrical surface of revolution, is intrinsically RMG
incomplete for $n=2$ and all $n\geq 5$, but that the extrinsic RMG flow on
$Rat_2^{eq}$ (defined by the inclusion $Rat_2^{eq}\hookrightarrow Rat_2$) is
complete.
