نویسندگان

1 کارشناسی ارشد، دانشکده مهندسی هوافضا، دانشگاه صنعتی خواجه نصیر الدین طوسی، تهران، ایران

2 استاد، دانشکده مهندسی هوافضا، دانشگاه صنعتی خواجه نصیرالدین طوسی،تهران، ایران

چکیده

در این مقاله، حل تحلیلی ماموریت تغییر مسیر جرم فضایی باالقوه خطرناکی که حیات بر روی کره زمین را با مخاطره روبه رو می‌سازد در مدارهایی با لحاظ اثر خروج از مرکز مورد بررسی قرار گرفته است. سیارک فضایی آپوفیس به عنوان نمونه بررسی در این تحقیق مورد مداقه قرار گرفته همچنین از تکنولوژی پرواز آرایشمند نیز به دلیل مزایای آن استفاده شده است. روش های متفاوتی برای ماموریت تغییر مسیر  این اجرام آسمانی پیشنهاد گردیده است که در این میان استفاده از تکنولوژی کشنده گرانشی کاربرد گسترده تری پیدا کرده است. روش حل کاملا تحلیلی با به کارگیری سری فوریه برای حل مساله بازآرایی در دینامیک حرکت نسبی استفاده گردیده است و همچنین نیاز به کارگیری کنترل فعال برای دست یابی به دقت بالاتر نیز با نمودارهای مربوطه بیان گردیده است. روش به کارگرفته شده کاملا تحلیلی و عمومی بوده و هیچ محدودیتی برای استفاده ندارد و در تمامی مدارهای بیضوی با دقت بالا قابل به کار گیری می‌باشد.

کلیدواژه‌ها

عنوان مقاله [English]

Analytical Solution to relative dynamic of gravity tractors in Formation Flying in Asteroid Deflection Mission

نویسندگان [English]

  • Javad Shams 1
  • Jafar Roshanian 2

1 M.Sc. Department of Aerospace Engineering, K. N. Toosi University of Technology, Tehran, IRAN

2 Professor, Department of Aerospace Engineering, K. N. Toosi University of Technology, Tehran, IRAN

چکیده [English]

In this paper, an analytical solution to deflection mission of asteroid as potentially hazardous spatial mass that threat humanity in future is investigated . The mission of deflecting potentially hazardous asteroids in recently years with possibility of their collision with Earth and the priority to carry out the mission of mitigate risk of these objects from its original space trajectory in recent years has been studied with interest in scientific research. Different methods have been proposed for execute the deflecting these celestial objects, among which the use of gravity tractor technology has become more widely used. In addition, the increasing use of formation flying technology in space missions is increasingly increasing, which has led to the use of this technology in this survey.

کلیدواژه‌ها [English]

  • Asteroid Apophis
  • asteroid deflection mission
  • gravity tractor
  • relative dynamic motion
  • formation flying
  • elliptical space orbits
 
[1] Wie, B., “Astrodynamic Fundamentals for Deflecting Hazardous Near-Earth Objects,” IAC conference, sout korea, 2009.
[2] Chen, D.H. and Ozaki, S., “Numerical Study of Axially Crushed Cylindrical Tubes With Corrugated Surface,” Thin-Walled Structure, Vol. 47, No. 11, 2009, pp. 1387-1396.
[3] “Near-Earth Objects Survey and Deflection Analysis of Alternatives,” NASA, Mar. 2007.
[4] Hill, G. W., “Researches in the Lunar Theory,” American Journal of Mathematics, Vol. 1, No. 1, 1878, pp. 5–26.
[5] Lawden, D. F., Optimal Trajectories for Space Navigation, Butterworths, London, 1963, pp. 77–86.
[6] Inalhan, G., Tillerson, M., and How, J. P., “Relative Dynamics and Controlof Spacecraft Formations in Eccentric Orbits,” Journal of Guidance, Control, and Dynamics, Vol. 25, No. 1, 2002, pp. 48–59.
[7] Spencer, D., “The Effects of Eccentricity on the Evolution of an Orbiting Debris Cloud,” American Astronautical Society, AAS Paper 87-473, Aug. 1987. Formation Flying Design and Evolution” Journal of Spacecraft and Rockets, 2001.
[8] Vaddi, S.S., Vadali, S.R. and Alfriend, K.T., “Formation Flying: Accomodating Nonlinearity and Eccentricity Perturbation”, Journal of  Guidance, Control and Dynamics, Vol. 26, No. 2, 2003, p. 224.
[9] Bae, J., Kim, Y., “Revisiting the General Periodic Relative Motionin Elliptic Reference Orbits”, Acta Astronautica, Vol. 85, 2013, pp. 100-112.
[10]Palmer, P., Optimal Relocation of Satellites Flying in Near-Circular-Orbit Formations, Journal of Guidance, Control, and Dynamics, Vol. 29, No. 3, 2006, pp. 519–526.
[11]Carter, T. E., and Humi, M., “Fuel-Optimal Rendezvous near a Pointin General Keplerian Orbit,” Journal of Guidance, Control, and Dynamics, Vol. 10, No. 6, 1987, pp. 567–573.
[12]Carter, T.E., “New Form for the Optimal Rendezvous Equations neara Keplerian Orbit,” Journal of Guidance, Control, and Dynamics, Vol. 13, No. 1, 1990, pp. 183–186.
[13]Cho, H.C. and Park, S.Y., “Analytic Solution for Fuel- Optimal Reconfiguration in Relative Motion,” J Optim Theory Appl, Vol. 141, 2009, pp. 495–512.
[14]Cho, H., Park, S.Y., Yoo, S. M. and Choi, K.H., “Analytical Solution to Optimal Relocation of Satellite Formation Flying in Arbitraryelliptic Orbits,” Journal of Aerospace Science and Technology, Vol. 25, Issue 1, 2013, pp. 161-176.
[15]Navvabi, M. and Hamrah, R., “Close Approach Analysis of Space Objects and Estimation of Satellite-Debris Collision Probability,” Journal of Aircraft Engineering and Aerospace Technology, Vol. 87, No. 5, 2015, pp. 483-492.
[16]Navvabi, M. and Hamrah, R., Modeling of Space Objects Propagation, Prediction of Closest Approaches Among Satellites, and Assessment of Maximum Collision Probability, Journal of Space Science and Technology (JSST), Vol. 6 , No. 1 (14), spring 2013 , pp. 57-67.
[17]Roshanian, J., Shams, J., shafieenejad, I. Motalebi, A.A., “Investigating Un-stability Phenomena in Deflection of Asteroid Apophis,” the 13th Iranian Aerospace Society Conference, march 2014
[18]Chesley, S., Potential Impact Detection for Near Earth Asteroids: The Case of 99942 Apophis (2004 MN4);'IAU Symposium No. 229: Asteroids, Comets, Meteors, Rio de Janeiro, Brazil, August 7-12, 2005.
[19]McInnes, C., “Near Earth Object Orbit Modification UsingGravitational Coupling,” Journal of Guidance, Control, and Dynamics, Vol. 30, No. 3, 2007, pp. 870–873.
[20]Lu, E.T. and Love, S.G., “Gravitational Tractor for TowingAsteroids,” Nature, Vol. 438, Nov. 2005, pp. 177–178.
[21]M.Navvabi, M.Barati, “A Comparative Study of Dynamics Models and a Control Strategy for Satellite Formation Flying,” Journal of Advances in the Astronautical Sciences, Vol. 145, 2012, pp. 549-561.
[22]Navvabi, M., Barati, M. and Khamseh, H.B., “A Comparative Study of Dynamics Models for Satellite Formation Flying - Cartesian Ordinary Differential Equations Description,” Recent Advances in Space Technologies (RAST), 5th International Conference on, IEEE, 2011, pp.829-832.
[23]Navvabi, M., Barati, M. and Bonyan, H., “Algebraic Orbit Elements Difference Description of Dynamics Models for Satellite Formation Flying,” Recent Advances in Space Technologies (RAST), 6th International Conference on, IEEE, 2013, pp. 277-280.
[24] Bong Wie, “Dynamics and Control of Gravity Tractor Spacecraft for Asteroid Deflection,” Journal of Guidance, Control, and Dynamics, Vol. 31, No. 5, September October 2008.
[25]Gong, Sh., Li, J. and BaoYin, H., “Formation Flying Solar- Sail Gravity Tractors in Displaced Orbit for towing Near- Earth Asteroids,” Journal Celestial Mechanics and Dynamical Astronomy, Vol. 105, Isuue 1-3, 2009, pp. 105-159.
[26] Navabi, M. and Barati, M., “A Comparative Study of Dynamics Model and a Control Strategy for Satellite Formation Flying,
[27] Navvabi, M. and Barati, M., “Dynamics Modeling of Spacecraft Formation Flying and Evaluating the Models Accuracy under the Effects of Relative Distance, Eccentricity and Earth Gravitational Perturbation,” Journal of Space Science and Technology (JSST), Vol. 5, No. 1, 2012, pp. 51-59.