The terminal navigation of the Near Earth Asteroid Rendezvous (NEAR) spacecraft during its close flyby of asteroid 253 Mathilde involved coordinated efforts to determine the heliocentric orbits of the spacecraft and Mathilde and then to determine the relative trajectory of the spacecraft with respect to Mathilde. The gravitational perturbation of Mathilde on the passing spacecraft was apparent in the spacecraft tracking data. As a result of the accurate targeting achieved, these data could be used to determine Mathilde's mass as 1.033 (+/- 0.044) x 10(20) grams. Coupled with a volume estimate provided by the NEAR imaging team, this mass suggests a low bulk density for Mathilde of 1.3 grams per cubic centimeter.