Variable cosmological "constant" and motion of a test particle in a cloud of dust

We find that Einstein's like field equations with coordinate-dependent cosmological "constant" Lambda(x (i)) imply a non geodesic law of motion for test particles moving in a continuous distribution of incoherent matter ("dust"). The deviation from the geodesic law depends on the derivatives partial derivative Lambda/partial derivative x(i) and, in the weak field approximation, causes an anomalous acceleration A similar to (Vc (2)/gamma rho)partial derivative Lambda/partial derivative t+(c(4)/gamma rho)partial derivative Lambda/partial derivative r where V=dr/dt, c=the speed of light, gamma=8 pi G with G=the gravitational coupling, rho=the mass density of the cloud, r and t are the radial and time coordinate respectively. Reasonable assumptions on Lambda=Lambda(t) give A < 10(-8) cm/s(2) when rho > 10(29) g/cm(3) i.e. in all known astrophysical systems. A possible connection with the anomalous Pioneer acceleration is shortly discussed in the case of a cosmological "constant" coupled to matter.