Van der Waals forces between atoms and molecules are universally assumed to
act along the line separating them. Inspired by recent works on effects which
can propel atoms parallel to a macroscopic surface via the Casimir--Polder
force, we predict a lateral van der Waals force between two atoms, one of which
is in an excited state with non-zero angular momentum and the other is
isotropic and in its ground state. The resulting force acts in the same way as
a planetary gear, in contrast to the rack-and-pinion motion predicted in works
on the lateral Casimir--Polder force in the analogous case, for which the force
predicted here is the microscopic origin. We illustrate the effect by
predicting the trajectories of an excited caesium in the vicinity of
ground-state rubidium, finding behaviour qualitatively different to that if
lateral forces are ignored
