שיטת החתכים הטלואים

באסטרודינמיקה, שיטת החתכים הטלואים או שיטת החתכים הקוניים (באנגלית: patched conic approximation[1][2]) היא שיטה מקורבת לחישוב מסלול בין פלנטרי של גוף בחלל בסביבה מרובה בגרמי שמיים.

השיטה

לכל גרמי השמיים (השמש, כדור הארץ, ירח וכו') שדה כבידה המשפיע על סביבתו. נניח ולכל גרם שמיים קיימת מעטפת השפעה, מרחק סופי מגרם השמיים, שבתוכה, גוף קטן ממדים (לוויין, רכב חלל) מושפע בקירוב מגרם שמיים יחיד ודומיננטי.

השיטה מבוססת על חלוקת המסלול בחלל למספר חלקים, "טלאים", שנבדלים במעטפות ההשפעה.

כך למעשה מפשטים בעיה מורכבת של בעיית N הגופים על ידי כך שפותרים N פעמים את בעיית שני הגופים עבור כל חלק במסלול; לבעיה זו פתרון ידוע כאחד מחתכי חרוט לפי מסלולי קפלר: אליפסה, פרבולה או היפרבולה.

קירוב זה אינו ממדל את נקודות לגראנז'.

דוגמה

איור גרפי של מסלול מכדור הארץ למאדים, בסביבת שמש

עבור תכנון מסלול של מערכת המשוגרת לחלל מכדור הארץ למאדים ובסביבת השמש:

  • בשלב הראשון - נבצע מסלול היפרבולי ביחס לכדור הארץ, לבריחה משדה הכבידה של כדור הארץ.
  • בשלב השני - כשאנו במעטפת ההשפעה של השמש, נבצע מסלול אליפטי או היפרבולי ביחס לשמש, על מנת להגיע למעטפת ההשפעה של מאדים.
  • בשלב השלישי - נבצע תמרון על מנת לבצע מסלול אליפטי סביב מאדים.

כמו כן יש להתאים את וקטורי המיקום והמהירות בגבולות המעטפת, בין החלקים, לצורך קבלת פתרון רציף.

ראו גם

הערות שוליים

  1. ^ Bate, R. R., D. D. Mueller, and J. E. White [1971], Fundamentals of Astrodynamics. Dover, New York.
  2. ^ Lagerstrom, P. A. and Kevorkian, J. [1963], Earth-to-moon trajectories in the restricted three-body problem, Journal de mecanique, p. 189-218.

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