During the Space Race, NASA calculated lunar rocket trajectories by using Euler’s Method to estimate the differential equation obtained by numerically integrating Newton’s Laws of Motion. At the time, computing power was scarce, costly, and primitive. The objective of this project is to develop an interactive MATLAB application that leverages modern computing architecture to accurately and efficiently approximate lunar rocket trajectories based on multiple variables relating to a rocket's journey to the Moon using the Runge-Kutta method. The Runge-Kutta method is a more accurate and sophisticated version of Euler’s method as it uses a multi-stage algorithm that involves slope calculations at discrete time values. This project will bring valuable input to the feasibility of using such numerical methods in approximating lunar trajectories to the industry. The rocket emulated in the program will be based on NASA's Saturn V rocket. Our application will simulate three phases of travel to the moon: achieving Earth orbit, lunar transfer orbit, and lunar orbit. It will consider variables such as time, distance, velocity, acceleration, position, rocket thrust, exhaust velocity, mass flow rate, and aerodynamic drag. The application will allow users to adjust various parameters in real time and see results graphically.