IN ORDER TO STUDY THE EFFECT OF LARGE SCALE COSMOLOGICAL EXPANSION ON SMALL SYSTEMS, WE ASSUME A FRW-TYPE COORDINATE SYSTEM IN PRESENCE OF A NON-ZERO Ù AND DERIVE A REISSNER-NORDSTROM TYPE METRIC. IT IS AN ANALYTIC FUNCTION OF R FOR ALL VALUES EXCEPT AT R=0 WHICH IS SINGULAR. BY DETERMINING THE EQUATION OF MOTION IN THIS METRIC, WE CAN ESTIMATE HOW THE EXPANSION OF THE UNIVERSE MAY EFFECT ON THE PIONEER’S MOTION.