Journal of the Korean earth science society (한국지구과학회지)

The Korean Earth Science Society (한국지구과학회)
권호 표지
DOI QR코드

DOI QR Code

Detailed Re-derivation of Keplerian Orbit and Kaula's Satellite Orbit Perturbation Theory

케플러궤도운동과 카울라의 인공위성궤도 섭동이론의 상세한 재유도

  • Na, Sung-Ho (Space Science Division, Korea Astronomy and Space Science Institute) ;
  • Bae, Tae-Seok (Department of Geoinformation Engineering, Sejong University) ;
  • Jo, Jung-Hyun (Space Science Division, Korea Astronomy and Space Science Institute) ;
  • Park, Jong-Uk (Space Science Division, Korea Astronomy and Space Science Institute)
  • 나성호 (한국천문연구원 우주과학연구부) ;
  • 배태석 (세종대학교 지구정보공학과) ;
  • 조중현 (한국천문연구원 우주과학연구부) ;
  • 박종욱 (한국천문연구원 우주과학연구부)
  • Received : 2012.01.04
  • Accepted : 2012.02.22
  • Published : 2012.02.29
Download PDF
⟨ Previous Next ⟩

Abstract

Kaula's theory of satellite orbit and Kepler's law are re-visited. All the mathematical steps of derivation are thoroughly shown including the ones, which had been omitted in Kaula's original publication. Particularly in evaluations of the 15 independent Lagrange brackets, simplicity and clarity are attained by using orthogonal property of transformation matrix. Explanations of important physical concepts are included as well in the midway of derivation. One conceptual blunder of Kaula's is corrected.

카울라에 의해 완성되었던 인공위성궤도이론과 케플러의 법칙을 다시 다루었다. 카울라의 원문에서는 생략되었던 부분을 포함한 모든 수식유도과정을 상세히 기술하였다. 특히 15개의 독립적인 라그랑지 괄호들을 계산하는 데에 변환행렬의 직교성을 사용하여, 간결성과 명확성을 이루었다. 여러 중간단계에서 중요한 물리적인 개념들에 대한 설명도 추가하였다. 카울라의 개념적 오류 한 개를 정정하였다.

Keywords

References

  1. Brouwer, D. and Clemence G. M., 1961, Methods of Celestial Mechanics, Academic Press.
  2. Danby, J. M. A., 1962, Celestial Mechanics, The Macmillian Company.
  3. Gradshteyn, I. S. and Ryzhik, I. M., 1965, Table of Integrals, Series, and Products, Academic Press, Inc., 2.261.
  4. Kaula, W. M., 1966, Theory of Satellite Geodesy, Blaisdell Publishing Company. (Dover reprint available)
  5. Pollard, H, 1966, Mathematical Introduction to Celestial Mechanics, Prentice-Hall Inc.
  6. Seeber, G., 2003, Satellite Geodesy 2nd edition, Walter de Gruyter.
  7. Sterne, T. E., 1960, An Introduction to Celestial Mechanics, Interscience Publishers, Inc.