This thesis examines how to keep a satellite in a stable orbit in Low Earth Orbit (LEO) using a continuous low-thrust engine. We specifically look at the challenges caused by shadow phases, when the satellite is in Earth’s shadow. The physical model is set up in a 3D spherical coordinate system and includes the effects of atmospheric drag. Because the engine can’t operate in the shadow, this eclipse constraint is a key factor in how we can control the satellite and what thrust strategy is needed. To handle environmental forces, we use the MSISE-00 model for atmospheric density. We also use SPICE data to accurately track the positions of the Sun and Earth, which helps us precisely determine when the satellite is in shadow.