  The effective capillary interaction potentials for small colloidal particles
trapped at the surface of liquid droplets are calculated analytically. Pair
potentials between capillary monopoles and dipoles, corresponding to particles
floating on a droplet with a fixed center of mass and subjected to external
forces and torques, respectively, exhibit a repulsion at large angular
separations and an attraction at smaller separations, with the latter
resembling the typical behavior for flat interfaces. This change of character
is not observed for quadrupoles, corresponding to free particles on a
mechanically isolated droplet. The analytical results for quadrupoles are
compared with the numerical minimization of the surface free energy of the
droplet in the presence of ellipsoidal particles.
