Visibility analysis between satellites or between satellites and ground stations is an important research area due to its influence on satellite communications and navigation. Although this research area has a long history, no extendible mathematical method was introduced so far, with which visibility analysis can be performed with the appropriate level of detail, using definite integrals.This motivated the work presented in this thesis. The objective of this thesis is to provide a mathematical method that helps to develop an analytical way to perform satellite visibility analysis. Mathematical formulas are provided using definite integrals for several visibility statistics - mean visibility time, mean revisit frequency, long-term visibility ratio - and the relationship among them is shown. The results produced with the analytical method match with simulation results without perturbations. Early simulations show that the results produced with the introduced method provide a good approximation in case of circular satellite orbits with perturbations.It is also possible to perform satellite communications related tasks, based on the mathematical method. As an example, questions, like the minimum bandwidth an Earth observation satellite needs in order to download in each pass all the images that were collected during one orbit period can be answered. The example application areas introduced in this thesis include among others intersatellite link analysis, data relay link analysis, and satellite altitude optimization to maximize mean throughput per pass.