Variable and Fixed Step Integrations for Dynamic Orbit Determination of LEO Satellites

Multi-step integrators can be classified either as single or double integrators. The single integrators are designed for first-order differential equations whereas the double integrators solve second-order differential equations and calculate position of the satellite directly from its acceleration. When force model include drag effect, we also need satellite’s velocity. Therefore, single integrators are required. The most popular single integrators are Adams-Bashforth-Moulton and Shampine-Gordon which the former is a multi step fixed step-size technique and the latter is a multi step variable step-size technique. Our numerical results illustrate the Shampine-Gordon method is more stable than the Adams-Bashforth-Moulton method.