The Orbital library is a Java class library providing object-oriented representations and algorithms for logic, mathematics, and computer science. It comprises theorem proving, computer algebra, search and planning, as well as machine learning algorithms. Generally speaking, the conceptual idea behind the Orbital library is to provide extensional services and components that surround the heart of many scientific applications, hence the name "Orbital library". In order to satisfy the requirements of high reusability, the design of this foundation class library favors flexibility, conceptual simplicity, and generalization. Many sophisticated problems can be solved easily with its adaptable components.