Very recently, Heinze & Metchev proposed a novel method for calculating precise distances to the main-belt asteroids using only two nights of data from a single observatory. In this paper, we re-derive the solution but use easily understood spherical astronomy. Our derivation is based on the premise that the geocentric angular velocity of an asteroid changes linearly with time, which is closer to the real situation. Therefore, a possible extra error of rotational reflex velocity, in some cases, is eliminated. A total of 193 frames of CCD images over four nights for 10 asteroids in a conventional stare mode taken with the 1 m telescope at Yunnan Observatory were used to test the improved solution and precise distances were evaluated.