Analysis of satellite formation flying models including j2 effect

Paper number

IAC-06-E2.1.05

Author

Mr. Giuseppe Del Gaudio, University of Rome "La Sapienza", Italy

Year

2006

Abstract

Nowadays clusters of small satellites represent a cheap and efficient alternative to big spacecrafts, as they are convenient to launch and more reliable. Payload can be spread on the cluster, but it is necessary that all satellites keep exactly their relative position. Therefore, formation flying becomes a quite important research topic. 
   Satellite formation flying is traditionally studied through Hill’s equations, a set of linear differential equations that describe the relative motion of two spacecrafts in similar near circular orbits, with the hypotheses of spherical Earth and small disturbances. Writing of Hill’s equations both in terms of relative position/ velocity vectors and in terms of orbital elements provides a substantial insight into the dynamics of nearby objects. 
   In particular, four cluster designs have been considered: in-plane, in-track, circular and projected circular. Each design is based on a set of constraints imposed on the initial components of relative position and velocity vectors. Values for the set of initial conditions have been analytically obtained for the designs under investigation. Furthermore, a 3D real time orbit simulator has been prepared to easily sketch the behaviour in time of the clusters.
   The attractive solutions to Hill’s equations under these ideal conditions lose their interest when perturbations are included in the model. In this work, the perturbing effect due to Earth’s oblateness, so-called ‘J2 effect’, has been investigated and secular motion of the right ascension of the ascending node, argument of perigee, and mean anomaly have been therefore included in the 3D orbital simulator. In particular, J2 disruptive effect on the circular and projected circular clusters has been clearly shown: the initial separation between satellites increases of ten percent over four days.
   To reduce the need of station-keeping thrust, attention has been moved to models taking into account Earth’s oblateness. The analytical linearized model proposed by Sabol-Burns-McLaughlin has been studied, evaluating its accuracy with respect to the numerical results offered by the orbital simulator.
   Then, Sabol-Burns-McLaughlin approach has been modified to produce a different, new model, which seemed to provide a behaviour closer to the real one as far as it concerns the J2 perturbation effects. The performances of the new model and the remaining differences with respect to the numerical case are discussed in depth.

Abstract document

IAC-06-E2.1.05.pdf

Manuscript document

IAC-06-E2.1.05.pdf (🔒 authorized access only).

To get the manuscript, please contact IAF Secretariat.