ExoCube is the latest National Science Foundation (NSF) funded space weather CubeSat and is a collaboration between PolySat, Scientific Solutions Inc. (SSI), the University of Wisconsin, NASA Goddard and SRI International. The 3U will carry a mass spectrometer sensor suite, EXOS, in to low earth orbit (LEO) to measure neutral and ionized particles in the exosphere and thermosphere. Measurements of neutral and ion particles are directly impacted by the angle at which they enter EXOS and which leads to pointing requirements. A combination of a gravity gradient system with a momentum bias wheel is proposed to meet pointing requirements while reducing power requirements and overall system complexity. A MATLAB simulation of dynamic and kinematic behavior of the system in orbit is implemented to guide system design and verify that the pointing requirements will be met. The problem of achieving the required three-axis pointing is broken into four phases: detumbling, initial attitude acquisition, wheel spin-up, and attitude maintenance. Ultimately, this configuration for attitude control in a CubeSat could be applied to many future missions with the simulation serving as a design tool for CubeSat developers.