Analysis of the Impact of Orbit-Attitude Coupling at Higher-Degree Potential Models on Spacecraft Dynamics

A novel representation of the gravitational force and gravity-gradient torque acting on a rigid-body spacecraft is presented. This formulation considers orbit-attitude coupling perturbations acting on the spacecraft when the gravitational field is modeled using spherical harmonics. Furthermore, the main contribution of this work is the generalization of these coupling terms to any degree and order of spherical harmonic representation. The magnitude of the accelerations are presented for point-mass and rigid-body spacecraft up to degree and order 256 for the case of a spacecraft in orbit around a central body. Numerical simulations are provided for spacecraft orbits near two different central bodies: The Moon and a “Bennu-like” object. The “Bennu-like” object is assumed to have the same size, mass, gravitational parameter, and angular velocity as those of the titular asteroid, but with spherical harmonic gravity constants of the Moon. It is shown that the magnitudes of the accelerations caused by the orbit-attitude coupling are orders of magnitude smaller than the accelerations derived from assuming a point-mass spacecraft. It is also observed that the difference in these orders of magnitudes has the tendency to decrease appreciably as the size of the celestial body decreases, suggesting the importance of consideration of higher order attitude terms in scenarios with large, low-mass spacecraft and/or in orbits around small celestial bodies with highly nonuniform gravitational fields. Therefore, the formalism in this study can be used as an accurate tool to quantify the effects of translational-rotational coupling in space operations