This dissertation presents the development of a guidance algorithm for the re-entry of a low Lift-to-Drag (L/D) ratio vehicle returning from the Moon, employing a skip entry strategy inspired by the Apollo re-entry guidance. The primary goal of the algorithm is to guide the vehicle from the first atmospheric entry interface to the second, while ensuring that structural stress and thermal loads remain within tolerable limits for the vehicle. To achieve this, a Numerical Predictor-Corrector technique was implemented, utilizing bank angle modulation to control the vehicle trajectory. The predictor component numerically integrates the complete, unsimplified equations of motion, ensuring a more accurate representation of the vehicle dynamics compared to simplified models, which may introduce approximation errors affecting guidance precision.