Step proof mass dynamics

Abstract

The Satellite Test of Equivalence Principle (STEP) is a joint European–US project to investigate one of the most fundamental principles in physics, the Equivalence of inertia and passive gravitational mass. As STEP matures into a flight program, the development of a precise spacecraft dynamics simulator becomes crucial. The simulator is primarily needed for design, test and verification of the drag-free control (DFC) system and the flight software. The drag-free concept involves centering the proof mass located inside a satellite. As the proof mass is free of external disturbances (drag free), it follows a purely gravitational orbit. Since the satellite is forced to follow the proof mass, it too follows the same gravitational orbit, canceling all non-gravitational forces. For the STEP Mission, the DFC system is required to attenuate any disturbance forces acting on the spacecraft to achieve residual acceleration at location of the accelerometer of less than 3×10 −14 m/s 2 (rms) across the measurement bandwidth. While the simulator is based on a high-fidelity six-degree-of-freedom numerical simulation, a simplified model is used to analyze the proof mass dynamics. The stability analysis of the proof mass motion is performed by transformation of the simplified model into the standard form of the Mathieu differential equation. The stability regions of the solution are applied to choose proper values for parameters like coupling forces between satellite and proof mass as a function of spacecraft rotation. The paper describes the calculation of the spacecraft/payload dynamics and the assumptions used to derive the underlying algorithms with a special emphasis on numerical precision issues.