The objective of the NEAR-Earth Asteriod Rendezvous (NEAR) laser ranging investigation is to obtain high integrity profiles and grids of topography for use in geophysical, geodetic and geological studies of asteroid 433 Eros. The NEAR laser rangefinder (NLR) will determine the slant range of the NEAR spacecraft to the asteroid surface by measuring precisely the round trip time of flight of individual laser pulses. Ranges will be converted to planetary radii measured with respect to the asteroid center of mass by subtracting the spacecraft orbit determined from X band Doppler tracking. The principal components of the NLR include a 1064 nm Cr:Nd:YAG laser, a gold-coated aluminum Dall-Kirkham Cassegrain telescope, an enhanced silicon avalanche photodiode hybrid detector, a 480-MHz crystal oscillator, and a digital processing unit. The instrument has a continuous in-flight calibration capability using a fiber-optic delay assembly. The single shot vertical resolution of the NLR is <6 m, and the absolute accuracy of the global grid will be ~10 m with respect to the asteroid center of mass. For the current mission orbital scenario, the laser spot size on the surface of Eros will vary from ~4--11 m, and the along-track resolution for the nominal pulse repetition rate of 1 Hz will be approximately comparable to the spot size, resulting in contiguous along-track profiles. The across-track resolution will depend on the orbital mapping scenario, but will likely be <500 m, which will define the spatial resolution of the global topographic model. Planned science investigations include global-scale analyses related to collisional and impact history and internal density distribution that utilize topographic grids as well as spherical harmonic topographic models that will be analyzed jointly with gravity at commensurate resolution. Attempts will be made to detect possible subtle time variations in internal structure that may be present if Eros is not a single coherent body, by analysis of low degree and order spherical harmonic coefficients. Local- to regional-scale analyses will utilize high-resolution three-dimensional topographic maps of specific surface structures to address surface geologic processes. Results from the NLR investigation will contribute significantly to understanding the origin, structure, and evolution of Eros and other asteroidal bodies.¿ 1997 American Geophysical Union