Abstract: A satellite communications system is disclosed. One of the embodiments of the present invention includes six to fourteen satellites (12) which operate in a single Equatorial orbit (14). These satellites (12) are capable of providing communications services to locations on the Earth (E) which are within thirty degrees of the Equator (16). Another embodiment of the invention utilizes both the single Equatorial orbit plane (14) in combination with other satellites (12) moving in polar or inclined orbits (60, 63, 210). The embodiment that combines satellites (12) in Equatorial (14), polar (60) and inclined (63, 210) orbits will provide a wide variety of data services to virtually any point on the globe. In the preferred embodiments, the satellites (12) are designed to operate in a circular low Earth orbit at an altitude of from 800 to 1852 kilometers.

Abstract: Method and apparatus for optimizing the operational state of a system employing iterative steps that approximately follow a projective scaling trajectory or an affine scaling trajectory, or curve, in computing from its present state, x.sub.0 to a next state x.sub.1 toward the optimum state. The movement is made in a transformed space where the present (transformed) state of the system is at the center of the space, and the curve approximation is in the form of a power series in the step size. The process thus develops a sequence of tentative states x.sub.1, x.sub.2, x.sub.n . . . . It halts when a selected suitable stopping criterion is satisfied, and assigns the most recent tentative state as the optimized operating state of the system.