  We investigate the implication of the non-linear and non-local multi-particle
Schroedinger-Newton equation for the motion of the mass centre of an extended
multi-particle object, giving self-contained and comprehensible derivations. In
particular, we discuss two opposite limiting cases. In the first case, the
width of the centre-of-mass wave packet is assumed much larger than the actual
extent of the object, in the second case it is assumed much smaller. Both cases
result in non-linear deviations from ordinary free Schroedinger evolution for
the centre of mass. On a general conceptual level we include some discussion in
order to clarify the physical basis and intention for studying the
Schroedinger-Newton equation.
