In August 2007, a group of American researchers from Texas A&M analytically confirmed the numerical results obtained by the Advanced Concepts Team (DG-PI) and the Department Me.Mo.Mat. of the University of Rome in the context of the Ariadna study 4104/05 "A search for invariant satellite motion".

During that study, a numerical investigation revealed a strange resonance phenomenon triggered by the oblateness of the Earth on the formation flight of satellites. In particular, it was claimed that four special values of the orbital inclination (49,131, 63 and 117 degrees) existed for which the relative dynamics resulted to be 'almost' periodical.

The result was published in peer-reviewed journals and attracted the attention of a leading group of researchers at Texas A&M University in the US, who confirmed the result using an elegant mathematical formulation and correctly relating the phenomenon to the matching of the in-plane and out of plane frequencies of the relative motion. This way, the exact values of 49.11 and 130.89 degrees could be evaluated for these new special inclinations.

"This previously unkown feature of the Earth geopotential field has remained unveiled for years, only know, thanks to the interest for formation flying missions and thus for relative satellite motion, we were able to find this resonance", says Dr. Dario Izzo of the Advanced Concepts Team.

In fact, sufficient scientific evidence has now been amassed as to claim that there are special inclinations values that are attractive for control purposes of formation flying missions as they simplify the task of the on board control system. First estimates show that one order of magnitude can be gained in terms of DV performance.

References:

[1] S.R. Vadali, P. Sengupta, H. Yan and K.T. Alfriend, "On the fundamental frequencies of relative motion and the control of satellite formations", 2007 AAS / AIAA Astrodynamics Specialist Conference, paper AAS 07-427

[2] Sabatini M. and Izzo D. and Bevilacqua, R., "Special Inclinations Allowing Minimal Drift Orbits for Formation Flying Satellites", accepted in Journal of Guidance Control and Dynamics [June 2007]

[3] Sabatini, M., Bevilacqua, R., and Pantaleoni, M., A Search for Invariant Relative Satellite Motion, European Space Agency, the Advanced Concepts Team, Ariadna Final Report (04-4104a), 2005.

[4] Sabatini, M., Bevilacqua, R., Pantaleoni, M., and Izzo, D., Periodic relative motion of formation flying satellites, Paper AAS 06-206, AAS/AIAA Space Flight Mechanics Conference, Tampa, Florida, 2006.

[5] Sabatini, M., Bevilacqua, R., Pantaleoni, M., and Izzo, D., Numerical Search of Bounded Relative Satellite Motion, Nonlinear Dynamics and Systems Theory, 6(4), pp.411-419, 2006.

[6] Sabatini, M., Izzo, D., and Palmerini, G., Analysis and control of convenient orbital configuration for formation flying missions, Paper AAS 06-120, AAS/AIAA Space Flight Mechanics Conference, Tampa, Florida, 2006.