A hopping rover is a robot that can move in low gravity planets by the characteristic motion called the hopping motion. For its autonomous explorations, the so-called SLAM (Simultaneous Localization and Mapping) is a basic function. SLAM is the combination of estimating the position of a robot and creating a map of an unknown environment. Most conventional methods of SLAM are based on odometry to estimate the position of the robot. However, in the case of the hopping rover, the error of odometry becomes considerably large because its hopping motion involves unpredictable bounce on the rough ground on an unexplored planet. Motivated by the above discussion, this paper addresses a problem of finding an optimal movement of the hopping rover for the estimation performance of the SLAM. For the problem, we first set the model of the SLAM system for the hopping rover. The problem is formulated as minimizing the expectation of the estimation error at a pre-specified time with respect to the sequence of control inputs. We show that the optimal input sequence tends to force the final position to be not at the landmark but in front of the landmark, and furthermore, the optimal input sequence is constant on the time interval for optimization.