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The complex interplay between the Solar Wind and the lunar surface serves asa quintessential example of space weathering. However, uncertainties persistregarding 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 ionflux from Earth to the Moon under varying solar wind conditions.The objectiveof this study is to adapt a kinetic model for the challenging conditions ofhaving both the Earth and the Moon in a single simulation box. IAPIC, theParticle-In-Cell Electromagnetic Relativistic Global Model was modified tohandle the Sun-Earth-Moon system. It employs kinetic simulation techniques thathave proven invaluable tools for exploring the intricate dynamics of physicalsystems across various scales while minimizing the loss of crucial physicsinformation such as backscattering. The modeling allowed to derive the shapeand 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 escapetowards the dayside magnetopause, while $\mathrm{H^+}$ travels deeper into themagnetotail, extending up to the Lunar surface. In addition, plasma temperatureanisotropy and backstreaming ions were simulated, allowing for futurecomparison with the experiment. This study shows how a kinetic model cansuccessfully be applied to study the transport of ions in the Earth-Moonenvironment. A second paper will detail the effect on the Lunar environment andthe impact on the Lunar water.

The Sun-Earth-Moon Connection: I--3D Global Kinetic Simulation