Gravity Gradient Effect on a LEO Satellite with an Elliptic Orbit and Unsymmetrical Mass Properties

Abstract

The study presented in this paper investigates the dynamic behavior of a low earth orbit (LEO) satellite due to gravity gradient disturbances when the product of inertia terms of the spacecraft and the orbit eccentricity are considered. It is shown that the classical stable solution for the gravity gradient disturbance becomes unstable if at least one product of inertia term exceeds a critical value. Dimensional analysis technique is used to develop the significant dimensionless groups which were used to correlate the data generated from the response of the coupled roll, pitch and yaw dynamics. Based on the findings of these groups, stability maps are developed to predict the influence of the product of inertia terms on the long-term behavior of the spacecraft attitude dynamics. The developed stability maps are verified numerically and successful prediction of a spacecraft stability condition due to gravity gradient disturbance is achieved.