Granular materials exhibit complex rheological behavior that is strongly influenced by external conditions, including gravity. Treating such media as a continuum allows their behavior to be represented as non-Newtonian fluids, enabling efficient numerical analysis of large-scale flows and intrusion problems. Although dense granular flows have been extensively studied under Earth gravity, the effect of gravity on the resistive forces experienced by intruding objects remains poorly understood. Quantifying this gravity-dependent rate sensitivity is crucial for planetary exploration in low-gravity environments and for geophysical and engineering applications, and thus constitutes a key challenge in granular mechanics and computational modeling. The μ(I) rheology has been widely used to describe granular flows, capturing the transition from quasi-static to inertial regimes through the inertial number. Building on this framework, we propose a generalized μ(I) constitutive model that incorporates gravity-dependent rate sensitivity. In this study, we focus on a cylindrical intruder moving through granular media, analyzing how resistive forces vary with intrusion speed and gravitational acceleration. The model is solved using an adaptive finite element method, which refines the mesh in regions of high estimated error, allowing accurate computation of the boundary-layer flow, stress distribution, and forces in the vicinity of the cylinder. Compared with results obtained from a microgravity experimental platform based on the Beijing Drop Tower, the numerical predictions show very good agreement. In particular, the resistance acting on the cylinder exhibits a strong dependence on intrusion speed under reduced gravity, while remaining weakly rate-dependent under Earth gravity. The proposed framework demonstrates strong predictive capability across different gravitational conditions and provides an effective numerical tool for the development and assessment of constitutive models for granular flows.