Daniele Mortari

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Flower Constellations

What are the Flower constellations? “Flower constellations” represent a design methodology for satellite constellations with elliptical orbits, wherein the arrangement of satellites is described with respect to a rotating reference frame. For satellite constellations in Earth orbit, this reference frame is typically chosen to be Earth-centered and Earth-fixed. Consequently, Flower constellations are particularly well-suited for addressing coverage problems, whether they involve localized regions or global areas. From a mathematical perspective, the theory underlying Flower constellations is rooted in the principles of number theory. Specifically, it is shown that for satellites in Keplerian orbits, the spatial distribution of satellites can be mathematically represented as a lattice on a two-dimensional torus. When the J2 perturbation (caused by the Earth’s oblateness) is included in the analysis, this lattice is extended to a three-dimensional torus. The name “Flower constellations” derives from the aesthetic patterns created by the relative motion of the satellites in the rotating reference frame, which often resemble petals of flowers. This methodology not only provides an elegant geometrical description of satellite orbits but also enables the optimization of their configuration to achieve specific design objectives, such as maximizing coverage, minimizing revisit times, or maintaining specific spatial symmetries. By leveraging the mathematical structure of lattices and tori, the Flower constellations framework offers a systematic approach to designing satellite constellations that can adapt to the constraints of different orbital regimes and mission requirements, making it a powerful tool in the field of astrodynamics and satellite mission design.

Journal articles

  1. D. Mortari, M. P. Wilkins, and C. Bruccoleri, “The Flower Constellations,” AAS The Journal of the Astronautical Sciences, vol. 52, no. 1 and 2, pp. 107–127, January–June 2004, special Issue: The “John L. Junkins” Astrodynamics Symposium.
  2. D. Mortari and M. P. Wilkins, “The Flower Constellation Set Theory Part I: Compatibility and Phasing,” IEEE Transactions on Aerospace and Electronic Systems, vol. 44, no. 3, pp. 953–963, July 2008.
  3. M. P. Wilkins and D. Mortari, “The Flower Constellation Set Theory Part II: Secondary Paths and Equivalency,” IEEE Transactions on Aerospace and Electronic Systems, vol. 44, no. 3, pp. 964–976, July 2008.
  4. D. Mortari, “Flower Constellations as Rigid Objects in Space,” ACTA Futura, vol. 2, pp. 7–22, 2006, published also as ESA SP-633.
  5. Marzano, F.S., Cimini, D., Memmo, A., Montopoli, M., Rossi, T., De Sanctis, M., Lucente, M., Mortari, D., and Di Michele, S. “Flower Constellation of Millimeter-Wave Radiometers for Tropospheric Monitoring at Pseudo-Geostationary Scale,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 47, No. 9, September 2009, pp. 3107-3122.
  6. S. K. Bourgeois and D. Mortari, “Rock Around Orbits,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 34, No. 4, pp. 810–819, 2011.
  7. Mortari, D., De Sanctis, M., and Lucente, M. “Design of Flower Constellations for Telecommunication Services,” Proceedings of the IEEE, Vol. 99, No. 11, November 2011, pp. 2008-2019.
  8. M. E. Avendaño and D. Mortari, “New Insights on Flower Constellations Theory,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 48, No. 2, pp. 1018-1030, April 2012.
  9. Davis, J.J., Avendaño, M.E., and Mortari, D. “The 3-D Theory of Lattice Flower Constellations,” Celestial Mechanics and Dynamical Astronomy, Vol. 116, No. 4, 2013, pp. 339-356.
  10. Avendaño, M.E., Davis, J.J., and Mortari, D. “The 2-D Theory of Lattice Flower Constellations,” Celestial Mechanics and Dynamical Astronomy,Vol. 116, No. 4, 2013, pp. 325-337.
  11. Casanova, D., Avendaño, M.E., and Mortari, D. “Design of Flower Constellations using Necklaces,” IEEE Transactions on Aerospace and Electronic Systems,Vol. 50, No. 2, April 2014, pp. 1347-1358.
Conferences
  1. Mortari, D., Wilkins, M.P., and Bruccoleri, C. “The Flower Constellations,” AAS 03-274, AAS “John L. Junkins” Astrodynamics Symposium, Texas A&M University, College Station, TX, May 23-24, 2003.
  2. Wilkins, M.P., Bruccoleri, C., and Mortari, D. “Constellation Design Using Flower Constellations,” AAS 04-208, Space Flight Mechanics Meeting Conference, Maui, HI, February 9-13, 2004.
  3. Park, K., Wilkins, M.P., Bruccoleri, C., and Mortari, D. “Uniformly Distributed Flower Constellation Design Study for Global Positioning System,” AAS 04-297, Space Flight Mechanics Meeting Conference, Maui, HI, February 9-13, 2004.
  4. Mortari, D., Wilkins, M.P., and Bruccoleri, C. “On Sun-Synchronous Orbits and Associated Constellations,” 6-th DCSSS Conference, July 18-22, 2004, Riomaggiore, Italy.
  5. Wilkins, M.P. and Mortari, D. “Constellation Design via Projection of an Arbitrary Shape Onto a Flower Constellation Surface,” AIAA/AAS Astrodynamics Specialist Conference, August 16-19, 2004, Providence, RI.
  6. Mortari, D., Abdelkhalik, O., and Bruccoleri, C. “Synodic and Relative Flower Constellations with Applications for Planetary Explorations,” AAS 05-151, AAS/AIAA Space Flight Mechanics Meeting, January 23-27, 2005, Copper Mountain, CO.
  7. Bruccoleri, C. and Mortari, D. “The Flower Constellations Visualization and Analysis Tool,” IEEE Aerospace Conference, March 5-12, 2005, Big Sky, MT.
  8. Park K., Ruggieri, M., and Mortari, D. “Comparisons Between GalileoSat and Global Navigation Flower Constellations,” IEEE Aerospace Conference, March 5-12, 2005, Big Sky, MT.
  9. Mortari, D. “Satellite Ballet by Flower Constellations,” Renaissance Banff Bridges Conference, Banff, Alberta, Canada, July 31 – August 3, 2005.
  10. Mortari, D. and Wilkins, M.P. “Dual-Compatible Flower Constellations,” AAS 06-202, AAS/AIAA Space Flight Mechanics Meeting Conference, Tampa, FL, January 22-26, 2006.
  11. Henderson, T. and Mortari, D. “Uni-Flower: A Novel Proposal for University-Built Nanosatellites in Flower Constellations,” AAS 06-204, AAS/AIAA Space Flight Mechanics Meeting Conference, Tampa, FL, January 22-26, 2006.
  12. Mortari, D. “Flower Constellations as Rigid Objects in Space,” Invited paper, Innovative System Design Concepts Workshop, Space Research and Technology Center of European Space Agency (ESTEC/ESA), Noordwijk, The Netherlands. Edited by ESA’s publication division, pp. 7-22. February 21, 2006.
  13. De Sanctis, M., Rossi, T., Lucente, M., Ruggieri, M., Bruccoleri, C., Mortari, D., and Izzo, D. “Flower Constellations for Telemedicine Services,” Tyrrhenian International Workshop on Digital Communications (TIWDC’06) – Satellite Navigation and Communications Systems Conference, September 6-8, 2006, Island of Ponza, Italy.
  14. Lucente, M., Rossi, T., De Sanctis, M., Ruggieri, M., Bruccoleri, C., and Mortari, D. “Flower Constellations for Interplanetary Missions,” IEEE Aerospace Conference, Big Sky, MT, August 3-7, 2007.
  15. Salvini, P., Nicolai, V., Ruggieri, M., and Mortari, D. “Deployment and Reconfigurability of Flower Constellations,” IEEE Aerospace Conference, Big Sky, MT, August 3-7, 2007.
  16. Mortari, D., Nicolai, V., Ruggieri, M., and Salvini, P. “Reconfiguring Flower Constellations using Continuous Firing,” IEEE Aerospace Conference, Big Sky, MT, August 3-7, 2007.
  17. Mortari, D. and Tonetti, S. “The Flower Formation Flying. Part I: Theory,” AAS 08-185, AAS/AIAA Space Flight Mechanics Meeting Conference, Galveston, TX, January 27-31, 2008.
  18. Tonetti, S.,  Hyland, D., and Mortari, D. “The Flower Formation Flying. Part II: Applications,” AAS 08-186, AAS/AIAA Space Flight Mechanics Meeting Conference, Galveston, TX, January 27-31, 2008.
  19. Marzano, F.S., Cimini, D., Montopoli, M., Memmo, A., Ferretti, R., Rossi, T., De Sanctis, M., Lucente, M., Mortari, D., Oricchio, D., Varchetta, S., Pavia, P., Nassisi, A., Balduccini, M., Scorzolini, A., Reboa, L., Tozzi, P., Bruno, A., Greco, F., Perrotta, G., Giuliani, G., and Giusto, R. “FLORAD: Micro-satellite Flower Constellation of Millimeter-wave Radiometers for Atmospheric Remote Sensing,” Specialist Meeting on Microwave Radiometry and Remote Sensing of the Environment, Firenze, Italy, March 11-14, 2008.
  20. Avendaño, M. and Mortari, D. “Rotating Symmetries in Space: The Flower Constellations,” AAS 09-189, AAS/AIAA Space Flight Mechanics Meeting Conference, Savannah, GA, February 9-12, 2009.
  21. Marzano, F.S., Cimini, D., Montopoli, M., Rossi, T., Mortari, D., Di Michele, S., and Bauer, P. “Flower Elliptical Constellation of Millimeter-Wave Radiometers for Precipitating Cloud Monitoring at Geostationary Scale,” European Geosciences Union General Assembly 2009, Vienna, Austria, April 19-24, 2009
  22. Varchetta, S., Marzano, F.S., Cimini, D., Rossi, T., and Mortari, D. “FLOMIR: the Light-Weight Conical-Scan Millimetre-Wave Imaging-Sounding Radiometer,” ESA Workshop on Millimetre Wave Technology and Applications and ESA Antenna Workshop Millimeter and Sub-Millimeter Waves: From Technologies to Systems. ESTEC, Noordwijk, The Netherlands, May 18-20, 2009.
  23. M. E. Avendaño, J. J. Davis, and D. Mortari, “The Lattice Theory of Flower Constellations,” AAS 10–172, AAS/AIAA Space Flight Mechanics Meeting Conference, San Diego, CA, February 8–12, 2010.
  24. J. J. Davis, M. E. Avendaño, and D. Mortari, “Elliptical Lattice Flower Constellations for Global Coverage,” AAS 10-173, AAS/AIAA Space Flight Mechanics Meeting Conference, San Diego, CA, February 8–12 2010.
  25. D. Casanova, M. E. Avendaño, and D. Mortari, “Necklace Theory on Flower Constellations,” AAS 10-126, AAS/AIAA Space Flight Mechanics Meeting Conference, New Orleans, LO, February 13-17 2011.
  26. Mortari, D. and Avendaño, M.E. “Evolution of Flower Constellations Theory,” Mini-symposium Algebraic Geometry Applied to Celestial Mechanics of SIAM Conference on Applied Algebraic Geometry, North Carolina State University, Raleigh NC, October 6-9, 2011.
  27. Davis, J., and Mortari, D. “Reducing Walker, Flower, and Streets-of-Coverage Constellations to a Single Constellation Design Framework,” AAS 12-147, AAS/AIAA Space Flight Mechanics Meeting Conference, Charleston, SC, Jan. 29 – Feb. 2, 2012.
  28. Casanova, D., Avendaño, M.E., and Mortari, D. “Flower Constellation Optimization using Evolutionary Algorithms,” XIII Jornadas de Trabajo en Mecánica Celeste, Zaragoza, June 18-19, 2012.
  29. D. Mortari, M. E. Avendaño, and S. Lee, “J2-Propelled Orbits and Constellations,” AIAA/AAS Astrodynamics Specialists Conference, Minneapolis, MN, August 13-16 2012.
  30. Casanova, D., Avendaño, M.E., and Mortari, D. “Optimizing Flower Constellations for Global Coverage,” AIAA/AAS Astrodynamics Specialist Conference, Minneapolis, MN, August 13-16, 2012.
Two generations (from left: Dr. C. Bruccoleri, Dr. M. Wilkins, Prof. D. Mortari, Dr. J. Davis, Prof. M. Avendaño)
MS Thesis and PhD Dissertations
  1. M. P. Wilkins, “The Flower Constellations – Theory, Design Process, and Applications,” PhD Thesis, Texas A&M University, October 2004.
  2. C. Bruccoleri, “Flower Constellation Optimization and Implementation,” PhD Thesis, Texas A&M University, December 2007.
  3. J. J. Davis, “Constellation Reconfiguration: Tools and Analysis,” PhD Thesis, Texas A&M University, December 2010.
  4. E. Mandakh, “BOUQUET: A Satellite Constellation Visualization Program for Walker’s and Lattice Flower Constellations,” Aerospace Engineering, Texas A&M University, August 2011.
Reports
  1. M. Ruggieri, M. D. Sanctis, T. Rossi, M. Lucente, D. Mortari, C. Bruccoleri, P. Salvini, and V. Nicolai, “The Flower Constellation Set and its Possible Applications,” European Space Agency, ESTEC, Noordwijk, The Netherlands, Final Report, Ariadna ID: 05/4108, Contract #19700/06/NL/HE, June 2006.
  2. D. Mortari, T. Henderson, J. J. Davis, and M. E. Avendaño, “Satellite Constellation Design Optimization Methods Study,” Air Force Research Laboratory, AFRL Contract FA9453-06-C-0342. Final Report, September 2009.

With John Draim (from left: Prof. D. Casanova, Prof. M. Avendaño, Dr. J. Draim, Dr. J. Davis, Prof. D. Mortari)