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Near-Earth Object (NEO) initial orbit determination typically uses astrometric measurements during a close approach over a time window much shorter than the orbital period of the NEO. The initial orbit is only weakly determined with dominant uncertainties in the distance of the NEO from the Earth. Topocentric astrometric measurements allow us to estimate NEO distances using observed nonlinear motions of the NEOs relative to observers, which come from the relative orbital motion of the NEOs to the Earth plus the topocentric parallax (parallax) from the diversity of observatory locations relative to the Earth center. We calculate the ratio of the contributions to the nonlinear motion from the relative orbital motion and the parallax to be approximately (TΔ/(day au))2, where T is the arc length measured in days and Δ is the distance of close approach. The dominant nonlinear motion for ranging the NEO comes from the relative orbital motion of the NEO to the Earth center, due to mainly the differential solar gravitational acceleration, when TΔ ≳ 1 day au and the parallax when TΔ ≲ 1 day au. This is confirmed by simulation data and supported by observational data of real NEOs. In the regime TΔ ≲ 1 day au, the orbit determination uncertainties are inversely proportional to the amplitude of the parallax. Introducing diversities of hour angles and observatory latitudes (especially alternating between extreme values) into scheduled follow-up observations can improve the parallax amplitude, thus the orbit accuracy. Most of the newly discovered NEOs are in this regime, we recommend optimizing parallax by properly scheduling observations when the NEO is very close to the Earth and using synthetic tracking to improve astrometry accuracy for initial orbit determination.