Context: The complex interplay between the Solar Wind and the lunar surface serves as a quintessential example of space weathering. However, uncertainties persist regarding the influence of plasma originating from Earth’s ionosphere, necessitating a comprehensive understanding of its quantitative impact. Hitherto, the dearth of reliable models has impeded accurate computation of ion flux from Earth to the Moon under varying solar wind conditions. Aim: The objective of this study is to adapt a kinetic model for the challenging conditions of having both the Earth and the Moon in a single simulation box. Methods: \(\mathrm{IAPIC}\), the Particle-In-Cell Electromagnetic Relativistic Global Model was modified to handle the Sun-Earth-Moon system. It employs kinetic simulation techniques that have proven invaluable tools for exploring the intricate dynamics of physical systems across various scales while minimizing the loss of crucial physics information such as backscattering. Results: The modeling allowed to derive the shape and size of the Earth’s magnetosphere and allowed tracking the O⁺ and H⁺ ions escaping from the ionosphere to the Moon: \(\mathrm{O^{+}}\) tends to escape towards the dayside magnetopause, while \(\mathrm{H^{+}}\) travels deeper into the magnetotail, extending up to the Lunar surface. In addition, plasma temperature anisotropy and backstreaming ions were simulated, allowing for future comparison with the experiment. Conclusion: This study shows how a kinetic model can successfully be applied to study the transport of ions in the Earth-Moon environment. A second paper will detail the effect on the Lunar environment and the impact on the Lunar water.