New approach in dynamics problems of Earth

satellite formations flying

Alexei R.Golikov

Keldysh Institute of Applied Mathematics, RAS

Miusskaya pl., 4, Moscow, 125047, Russia

 

At present, it is in great request the projects with using the satellites flying in formation. The formations of inexpensive satellites have substantial advantage in comparison with individual, but costly spacecrafts: the "volumetric" configuration of similar formation allow to obtain the measurements (image data, etc.) directly in the spatial form, to realize complicated structural operations, to transform disposition of satellites relative to each other as well as to ground-based units.

The problem of relative motion evolution of large satellite systems is actual for various purposes: operational support, orbit determination and specification, project design, maneuvers of satellite orbits, etc. Direct numerical integration may be inefficient in this case because of large quantity of spacecrafts and complexity of examined tasks.

The semianalytical theory THEONA developed in the 1980s-1990s by the author provides the satellite motion prediction with high rapidity (100-1000 times faster than numerical propagators) and good accuracy (relative errors ~ 10^-9). For the problem examined here, an efficiency of the theory increase some more: it has developed additional methods where there are united structures of integrals and special functions. Accordingly, this lead to speed up the computations, relative error achieves 10^-12. Thus, new version of THEONA permits to provide almost all necessary operative and research calculations for the problems with formation flying.

As an example of efficient use of THEONA it is supplied the sudy of relative motion evolution of formation flying (the contributions of various perturbative forces). It is given the estimations of accuracy of absolute and relative motion.

THEONA is efficient as a tool for the study of Satellite Formation Flight. It provides high accuracy of calculations of relative motion with high speed. This efficiency increases for the formation flight because THEONA computes this motion as the motion of one object ( = guiding centre) with the deviations of other satellites ( = assistants). Moreover, THEONA permits to obtain separate contributions (caused by different perturbations) in the evolution of relative motion of formation.

THEONA works with both passive and active SC taking into account all essential forces in the satellite motion. Therefore it is effective for various space flight dynamics problems: mission design, mission analysis, formation keeping, orbit determination. It can be also applied for real-time orbit control (including on-board software).