A perturbative analysis of geopotential disturbances for satellite cluster formation flying

Abstract

Effects of the second order perturbative term of the Earth's geopotential on clusters of satellites are analyzed by adding the linearized J2 force onto the right side of Hill's equations as a forcing function. A continuation of previous work, the equations of motion are generalized to orbits of all inclinations, and terms are identified that account for rotation of periapsis within the orbital plane, as well as precession of the longitude of the ascending node. The effect of the periapsis rotation on the cluster is identified as a 'tumbling' mode of the system. Accuracy of the linearization is determined by comparison of the analytic solutions with those obtained using an orbit propagator.

High-Precision, Symplectic Numerical, Relative Orbit Propagation

“…Keplerian solution to include the effects of J 2 [3,4,5,6,7,8], eccentricity [9,10,11,12,13] and drag [14]. There were also some attempts at incorporating higher order geopotentials into the solution but with eccentricity limitations [15,16,17,18].…”

Relative State Estimation of Satellite Formation Flying Using Kalman Filter

“…In reality, however, it is not true. In this section, we take the effect of 2 J on relative orbit dynamics into account by adding the 2 J induced gravitational acceleration to the right side of the HCW equations as a forcing term [Schweighart et al 2001]. The gravitational potential of the earth, accounting for only latitude variation, takes on the following 2 1(…”

Output Regulation Control for Satellite Formation Flying Using Differential Drag

“…However, the HCW equations contain a great source of error in that Earth is assumed to be a perfect sphere. Several papers have contributed to the development of relative motion equations to incorporate the effects of various perturbations with significant effects on the relative motion [6][7][8][9][10][11][12]. These approaches involve different representations of relative states: translational relative states, curvilinear relative states, and orbital elements illustrating unperturbed and perturbed relative motion [13].…”

“…Schweighart and Sedwick then partially incorporated the mean motion of satellites into the relative motion equations by including the time average of the gradient of the J 2 potential to form a new set of constant coefficient linearized equations. Their model in [7] is referred to as the SS model in this paper. This model was further modified to provide a fairly accurate model of the cross-track motion under the influence of the J 2 potential in [8].…”