With the recent boom in the private-sector space industry, more and more satellites are being sent into orbit every year. Satellites in Low Earth Orbit (LEO) experience a small, yet non-insignificant, amount of air drag causing their orbits to slowly decay. After enough time, any satellite in LEO without means of self-propulsion will fall back to Earth. The purpose of this paper is to investigate how dissipative forces affect orbits and find equations of motion that can be used to analyze a satellite's orbital decay. To do this, we used a model gravity well that allows us to simulate the motion of satellite orbits using marbles. By using Lagrangian mechanics and taking measurements of the simulation, we were able to derive equations that can be used to describe the motion of the orbiting marble. We found that we could describe the orbital decay by using a relationship between the Period and the Energy lost to friction. By measuring how much the Orbital Period changes as Energy is lost, we can see how friction causes the orbit to decay. We also found a way to analyze the dissipative force of friction on the marble by using the so-called Rayleigh dissipation function. These techniques proved effective at analyzing the simulated orbits, and we believe that they can also be applied to study the dissipative forces and orbital decay of a satellite.