Orbiting objects in space are exposed to the risk of collision with space debris over their lifetime. Space debris orbiting in space experiences orbital decay due to various orbital perturbations. This work considers only orbital perturbations due to aerodynamic forces, which spacecraft experience due to the presence of a rarefied atmosphere, causing tumbling motion and orbital decay. Analysis of the orbital decay of a spacecraft is carried out by considering the variation of the drag coefficient as a function of its shape, motion and angle-of-attack. An in-house Direct Simulation Monte Carlo (DSMC) solver is modified for aerodynamic analysis of a spacecraft orbiting in the free molecular regime in low Earth orbit. In addition, an orbital dynamics model is developed to simulate the tumbling motion of a spacecraft and its orbital decay. The orbital decay trajectory is predicted for two sample spacecrafts using the aerodynamic coefficients obtained from the in-house DSMC solver as inputs to the orbital decay model. This study analyses and explores in detail the effects of the aerodynamic coefficients and shape of a spacecraft on its orbital decay.