حل تناوبی متقارن حول سیارک 216 کلوپاترا و بررسی پایداری آن در حضور فشار تشعشع خورشیدی

نوع مقاله : مقالة‌ تحقیقی‌ (پژوهشی‌)

نویسندگان

1 عضو هیأت علمی دانشکده مهندسی هوافضا دانشگاه خواجه نصیرالدین طوسی، تهران، ایران

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

10.30699/jsst.2021.1233

چکیده

در این مقاله از مدل دمبلی برای میدان گرانشی سیارک 216 کلوپاترا استفاده شده است. با استفاده از این مدل، معادلات حاکم بر حرکت فضاپیما حول سیارک به فرم معادلات حرکت فضاپیما در مسئله سه جسم محدود دایروی در خواهند آمد. بر این اساس نقاط تعادل و نواحی ژاکوبی حول این سیارک محاسبه شده و با بهره‏گیری از روش‏های جست‏و‏جوی شبکه‏ای و پرتابی مدارهای تناوبی متقارن محاسبه شده‌اند. این تقارن نسبت به صفحه xz در نظر گرفته شده است. پس از استخراج مدارها، پایداری مدارهای تناوبی با تئوری فلوکه مورد ارزیابی قرار گرفته که بیانگر ناپایداری مدارها است. با اضافه کردن فشار تشعشع خورشیدی به معادلات حاکم، مجددا مدارهای تناوبی متقارن استخراج و شاخص پایداری آن‌ها محاسبه شده است. نتایج حاکی از آن است که فشار تشعشع خورشیدی هر چند مقادیر شاخص پایداری را تغییر می‌دهد ولی تغییری در پایداری یا ناپایداری آن ایجاد نمی‌کند. بنابراین پایدارسازی فضاپیما بر روی این مدارهای ناپایدار مستلزم اعمال کنترل بر روی فضاپیما است.

کلیدواژه‌ها


عنوان مقاله [English]

Symmetric periodic solution around asteroid 216 Kleopatra and its stability in the presence of solar radiation pressure

نویسندگان [English]

  • Mahdi Jafari Nadoushan 1
  • Kosar Aramkhah 2
1 Faculty of Aerospace Engineering, K.N.Toosi University of Technology, Tehran, IRAN
2 Faculty of Aerospace Engineering, K.N.Toosi University of Technology, Tehran, IRAN
چکیده [English]

In this paper, the dumbbell model is used for gravity field of asteroid 216 Kleopatra. Utilizing the model results in governing equations of motion of a spacecraft around an asteroid similar to those of motion of a spacecraft in the restricted circular three-body problem. The equilibrium points and Jacobi regions are calculated and symmetric periodic orbits are computed utilizing grid search and shooting methods. The xz-plane is considered as the symmetry plane. Stability of the periodic orbits is evaluated by Floquet theory that shows all the computed orbits are unstable. By adding the solar radiation pressure term to the governing equations of motion, the symmetric periodic orbits are recomputed and index of stability are examined. The results show that the solar radiation pressure, though change the values of the index of stability, does not affect the stability of computed periodic orbits. Therefore, stabilizing a spacecraft on the unstable periodic orbits requires controlling spacecraft.

کلیدواژه‌ها [English]

  • 216 Kleopatra Asteroid
  • Symmetric Periodic Orbit
  • Dumbbell Model
  • Solar Radiation Pressure
  • Floquet theory
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