Abstract
In this paper novel trajectories that are particularly suitable for space-borne observation missions are introduced. Based on the framework of the spatial circular restricted three-body problem with the Sun and the Earth as the primaries and a special selection of a coordinate system, a family of trajectories with considerable displacements above the ecliptic plane is found. Stability analysis of these trajectories is carried out using practical stability theory. The normal component of motion results in significantly reduced noise from the interplanetary (zodiacal) dust and a concomitant reduction in the necessary size of the optical collecting area. The reduced size of the mirrors allows a considerable reduction in payload mass and manufacturing costs. The quest for optimal trajectories is performed using genetic algorithms. First, types of trajectories are characterized using a genetic search. Utilizing the results and insight obtained from the characterization process, optimal trajectories are designed. The first optimal trajectory requires low launch energy and yields a maximum decrease of 67% in the zodiacal cloud brightness. The second optimal trajectory requires higher launch energy, but it renders a dramatic 97% maximum noise decrease.
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References
NASA’s Origins Web Site, http://origins.jpl.nasa.gov.
LUBOW, S. “Controlling the NGST Orbit,” http://icarus.stsci.edu/~lubow/ngst/orbits.html.
The TPF Science Working Group, “Terrestrial Planet Finder,” NASA/JPL Publication 99–3, May 1999.
SZEBEHELY, V. Theory of Orbits, Academic Press, New York, 1967.
GOMEZ, G., MASSDEMONT, J., AND SIMO, C. “Lissajous Orbits around Halo Orbits,” Advances in the Astronautical Sciences, Vol. 95, 1997, pp. 117–134.
HOWELL, K. C., BARDEN, B.T., and LO, M. W. “Application of Dynamical Systems Theory to Trajectory Design for a Libration Point Mission,” The Journal of the Astonautical Sciences, Vol. 45, No. 2, April–June 1997, pp. 161–178.
GOUDAS, C. L. “Three Dimensional Periodic Orbits and Their Stability,” Icarus, Vol. 2, 1963, pp. 1–18.
HENON. M. “Vertical Stability in the Restricted Problem. II. Hill’s Case,” Astronomy and Astrophycis, Vol. 30, 1974, pp. 317–321.
KELSALL, T., WEILAND, J. L., FRANZ, B. A., REACH, W.T., ARENDT, R. G., DWEK, E., FREUDENREICH, H.T., HAUSER, M.G., MOSELEY, S.H., ODEGARD, N.P., SILVER-BERG, R. F., and WRIGHT, E. “The COBE Diffuse Infrared Background Experiment Search for the Cosmic Infrared Background. II. Model of the Interplanetary Dust Cloud,” The Astrophysical Journal, Vol. 508, No. 1, Part 1, Nov. 1998, pp. 44–73.
BELBRUNO, E. “Analytic Estimation of Weak Stability Boundaries with Applications to Low-Energy Trajectories for Space Travel,” paper preprint, June 2000.
GOLDBERG, D. E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading, MA, 1989.
HARTMAN, J. W., COVERSTONE-CARROLL, V. L., and WILLIAMS, S. N. “Optimal Interplanetary Spacecraft Trajectories via a Pareto Genetic Algorithm,” The Journal of the Astronautical Sciences, Vol. 46, No. 3, July 1998, pp. 267–282.
GOMEZ, G., MASDEMONT, J., and SIMO, C. “Quasihalo Orbit Associated with Libration Points,” The Journal of the Astronautical Sciences, Vol. 46, No. 2, April–June 1998, pp. 135–176.
MARCHAL, C., The Three-Body Problem, Elsevier, New York, 1990.
RABE, E. “Determination and Survey of Periodic Trojan Orbits in the Restricted Problem of Three Bodies,” The Astronomical Journal, Vol. 66, 1961, pp. 500–507.
BREAKWELL, J. V. “Trajectories Launched Normal to the Ecliptic,” Proceedings of the 14th International Astronautical Congress, Paris, 1963, pp. 128–141.
MICHEL, A. N. “Quantitative Analysis of Simple and Interconnected Systems: Stability, Boundedness and Trajectory Behavior,” IEEE Transactions on Circuits and Systems, Vol. CT-17, No. 3, August 1970, pp. 292–301.
WEISS, L. and INFANTE, E. F. “On the Stability of Systems Defined over a Finite Time Interval,” Proceedings of the National Academy of Science, Vol. 54, 1965, pp. 44–48.
WEISS, L. “Converse Theorems for Finite Time Stability,” Proceedings of the First Asilomar Conference on Circuits and Systems, Asylomar, California, 1968, pp. 1005–1014.
BUGLIA, J. J. “Planetary Flybys Resulting in Heliocentric Orbits Normal to the Ecliptic with Fixed Perihelia,” Journal of Spacecraft and Rockets, Vol. 10, No. 3, May 1973, pp. 601–602.
RENARD, M. L. “Practical Stability of High-Eccentricity Orbits Quasi-Normal to the Ecliptic,” Journal of Spacecraft and Rockets, Vol. 7, No. 10, October 1970, pp. 1208–1214.
MAHFOUD, S.W. “Niching Methods for Genetic Algorithms,” Illinois Genetic Algorithms Laboratory Report No. 95001, University of Illinois at Urbana-Champaign, 1995.
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Gurfil, P., Kasdin, N.J. Optimal Out-of-Ecliptic Trajectories for Space-Borne Observatories. J of Astronaut Sci 49, 509–537 (2001). https://doi.org/10.1007/BF03546222
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DOI: https://doi.org/10.1007/BF03546222