The Spacecraft Interaction Plasma Software package (SPIS), a three-dimension particle in cell (PIC) code, was used to model the Parker Solar Probe (PSP) spacecraft and FIELDS instrument and their interactions with the Solar wind. Our SPIS modeling relied on material properties of new spacecraft materials that we had obtained in previous work. The model was used to find the floating potentials of the spacecraft and FIELDS antennas at different distances from the Sun (from 1AU to 0.046AU). We find the following results: At greater distances from the Sun, the shadowed spacecraft charges negatively while the illuminated Thermal Protection System (TPS) charges positive due to the high resistance of the TPS Alumina shield at low temperatures. As the spacecraft approaches the Sun, the temperature of the TPS increases, the resistance between it and the spacecraft drops, and its photoemission increases, driving the spacecraft more positive. At the same time, an electrostatic barrier forms near the illuminated surface of the TPS and reflects the photoelectrons back leading to negative charging of some surfaces. The FIELDS antennas and shield also see this barrier forming but on a smaller scale. The FIELDS antennas charge positively at all distances modeled when no current bias is applied. Current biasing of the antennas affects their floating potential.