וקטור האקסצנטריות

פרמטרי המסלול האליפטי

באסטרודינמיקה, וקטור האקסצנטריות הוא וקטור המצביע לכיוון הפריאפסיס ושווה בגודלו לאקסצנטריות המסלול.

הפלנטה נמצאת על מוקד הנקרא ממשי, ואילו המוקד השני נקרא מדומה (Vacant focus). הנקודה הקרובה ביותר לפלנטה נקראת במקרה הכללי פריאפסיס (במקרה של כדור הארץ - פריגיאה, ובמקרה של השמש - פריהליון). מגדירים את וקטור האקסצנטריות:

כאשר:

  • v - מהירות הגוף אשר נמצא במסלול.
  • h - התנע הזוויתי הסגולי.
  • μ - קבוע הגרביטציה עבור הפלנטה.
  • r - המרחק של הגוף מן המוקד הממשי של המסלול.

מסלול סביב פלנטה יכול להיות כל חתך חרוט בעל תנע זוויתי (כלומר כל חתך פרט לקו ישר). מגדירים:

  • a - חצי ציר גדול.
  • b - חצי ציר משני.
  • c - חצי המרחק בין המוקדים.
  • p - פרמטר המסלול.
  • e - אקסצנטריות המסלול.
  • ν - זווית אנומליה אמיתית.
  • x - מרחק הגוף מן הדירקטיקס.
מעגל אליפסה פרבולה היפרבולה

מתקיימים הקשרים:

  • מיקום הגוף: .
  • מיקום הדירקטיקס באליפסה ובהיפרבולה: ; בפרבולה: .
  • האקסצנטריות: .
  • פרמטר המסלול: .
  • גובה הפריאסיס: .
  • גובה האפואפסיס: .

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