Model of $$J_2$$ J 2 perturbed satellite relative motion with time-varying differential drag

Abstract

This work revisits the modeling of the relative motion between satellites flying in near-circular low-Earth-orbits. The motion is described through relative orbital elements and both Earth's oblateness and differential drag perturbations are addressed. With respect to the former formulation, the description of the J 2 effect is improved by including also the changes that this perturbation produces in both relative mean longitude and relative inclination vector during a drifting phase, when a non-vanishing relative semi-major axis is required. The second major improvement consists in a general empirical formulation to include the mean effects produced by non-conservative perturbations, such as the differential aerodynamic drag acceleration. As a result, in addition to the well-known actions on the relative semi-major axis and on the mean along-track separation, the model is able to reflect the mean variation of the relative eccentricity vector due to atmospheric density oscillations produced by day and night transitions.

Minimum-Fuel Control Strategy for Spacecraft Formation Reconfiguration via Finite-Time Maneuvers

“…To this purpose, the relative position vector expressed in Cartesian coordinates, xδαu c , must lie outside a safety box centered in the chief spacecraft. In this study, the linear mapping originally presented in [17] and discussed more in detail in [18] is used to map the mean ROE vector to the Cartesian relative state, i.e.,…”

New State Transition Matrices for Relative Motion of Spacecraft Formations in Perturbed Orbits

“…This DMF-A model is inspired by the work done by Gaias on modeling relative motion subject to time-varying differential drag in near circular orbits. 27 Specifically, the state is augmented with three drift terms as opposed to the single term used in the previous section. For example, the singular ROE are augmented with the time derivatives of the relative semi-major axis, δȧ drag , differential eccentricity, δė drag , and differential argument of perigee, δω drag , due to differential drag.…”

“…This model has since been expanded to include the effect of differential drag on the relative semi-major axis, 26 and the effect of time-varying differential drag on the relative eccentricity vector. 27 This state formulation was first used in flight to plan the GRACE formation's longitude swap maneuver 28 and has since found application in the GN&C systems of the TanDEM-X 29 and PRISMA 3 missions as well as the planned AVANTI experiment. 30 However, to date neither of these approaches has produced an STM including both J 2 and differential drag in eccentric orbits.…”

“…Additionally, a generalized DMF differential drag model for orbits of arbitrary eccentricity is developed using approach inspired by Gaias' model of time-varying differential drag in near-circular orbits. 27 2. STMs for three mean ROE state definitions are derived using a simple, two-step method that allows inclusion of multiple perturbations in orbits of arbitrary eccentricity.…”

Semianalytical Solutions of Relative Motions with Applications to Periodic Orbits about a Nominal Circular Orbit

“…The results in the case of elliptic reference orbit were studied and extended by many researchers [5][6][7][8][9]. Some researchers studied the relative motions, starting from the solutions of HCW equations and latter moving to consider some perturbations, such as oblateness [10][11][12][13][14][15], drag [16,17], and third-body effects [18].…”