Free-space optical communication between satellites in a distributed network can permit high data rates of communication between different places on Earth. To establish optical communication between any two satellites requires that the line of sight of their optics be aligned during the entire communication time. Because of the large distance between the satellites and the alignment accuracy required, the pointing from one satellite to another is complicated because of vibrations of the pointing system caused by two fundamental stochastic mechanisms: tracking noise created by the electro-optic tracker and vibrations derived from mechanical components. Vibration of the transmitter beam in the receiver plane causes a decrease in the received optical power. Vibrations of the receiver telescope relative to the received beam decrease the heterodyne mixing efficiency. These two factors increase the bit-error rate of a coherent detection network. We derive simple mathematical models of the network bit-error rate versus the system parameters and the transmitter and receiver vibration statistics. An example of a practical optical heterodyne free-space satellite optical communication network is presented. From this research it is clear that even low-amplitude vibration of the satellite-pointing systems dramatically decreases network performance.