As space exploration progresses, renewed attention has been given to advanced Lunar exploration technologies. The main objective is to address many open questions about the Moon, such as its origin or chemical components, as most of the current hypotheses are just inferences based on limited evidences. Unmanned subsurface investigation technologies for the Moon are of special significance for future exploration as it may enhance our knowledge of space science. This paper aims to develop a subsurface robotic explorer for the Moon in order to bury an instrument, such as a long period seismometer, for acquiring subsurface information. In previous work, the authors have showed the effectiveness of a novel screw drilling mechanism for burrowing an exploration robot with no-reaction to the body. This paper addresses anew a fundamental dynamics model for a robotic screw explorer. The model includes the geometric model of a conical screw drill and the soil mechanics, allowing us to mathematically estimate a frictional moment around the perimeter of the screw. This theoretical analysis is governed by complex soil behaviors and has not been thoroughly discussed previously. Hence, this challenging study can provide key insight into this matter. The validity of the model developed here is also presented in this paper.