Navigation of the orbit phase of the Near Earth Asteroid Rendezvous (NEAR) mission will require determination of certain physical parameters describing the size, shape, gravity field, attitude and inertial properties of (433) Eros. Prior to launch, little was known about Eros except for its orbit and spin rate, which could be determined with high precision from ground based telescope observations. Radar bounce and light curve data provided a rough estimate of Eros shape and a fairly good estimate of the pole and prime meridian. The determination of the NEAR spacecraft orbit requires a high precision model of Eros' physical parameters and the ground based data provides only marginal a priori information. The initial orbit determination strategy is therefore concerned with developing a precise model of Eros. On December 23, 1998, the NEAR spacecraft flew by Eros on a high velocity trajectory that provided a brief glimpse and allowed for an improved estimate of the Dole, prime meridian and mass of Eros. Estimates of Eros' physical parameters obtained from this flyby are presented. Application of this new knowledge to simplification of Eros orbital operations and the orbit determination strategy will be discussed.