Perturbations analysis of L4 and L5 points orbits in Sun-Earth system

• Material Type: 文書・図像類
• Title: Perturbations analysis of L4 and L5 points orbits in Sun-Earth system
• Author/Editor: 歌島, 昌由; Utashima, Masayoshi
• Author Heading: 歌島, 昌由; Utashima, Masayoshi
• Publication, Distribution, etc.: 宇宙開発事業団
• Publication Date: 2000-09-29
• Publication Date (W3CDTF): 2000-09-29
• Alternative Title: 太陽地球系におけるL4とL5点の摂動解析
• Periodical title: NASDA English Translation
• ISSN (Periodical Title): ISSN : 1345-7926
• Text Language Code: eng
• Subject Heading: 天体系; 太陽・地球系; 地球・月系; 太陽・木星系; ラグランジュ点; L1; L4; L5; 太陽観測所; 宇宙機運動; 3体問題; 惑星; 重力; 太陽輻射圧; 2等辺3角形; celestial body system; Sun Earth system; Earth Moon system; Sun Jupiter system; Lagrangian point; solar observatory; spacecraft motion; three body problem; planet; gravity; solar radiation pressure; equilateral triangle
• Target Audience: 一般
• Note (General): 太陽・地球系、地球・月系、太陽・木星系などの各天体は5個のラグランジュ点を持つ。これまで太陽・地球系のL1点のみが太陽観測ミッションに利用された。太陽・地球系のL5点に位置した新しい太陽観測所と太陽・地球系のL4またはL5に位置したSpace Guard Space Telescopeが、近い将来の新しいミッションとして提案された。これらL4とL5点の近くの宇宙機の運動は、円形に拘束された3体問題に基づいて参照文献1に記述された。本報告では、地球の離心率、惑星の重力、太陽・地球系のL4とL5点近傍の軌道への太陽輻射圧の効果を調べた。2章で、簡単な文献のサーベイの結果を示した。3章で、地球軌道の離心率の影響を調べた。解析的取り扱いから太陽と地球の瞬時点の2等辺3角形をなす点が、楕円形に拘束された3体問題でのL4かL5点になることがわかった。前述したL4かL5点の周りの周期運動が初速度を調整して実現できた。4章で、惑星の重力の影響を調べ、直接と間接両方の項を惑星の重力に対して考慮した。惑星の潮力による半主軸の短周期項が支配的であることが分かった。それらはある惑星の天体経度と元期での地球との差に依存し、惑星のほとんどの影響もまた初速度を調整して消去できた。調整の大きさは1m/sより小さかった。5章で、地球の離心率と惑星の重力を合成した影響を調べたが、その影響が単純な重ね合わせとして近似的に正確であった。6章で、移転に最小の燃料を必要とするL5ミッション軌道について簡単に述べ、L5点の入射誤差の影響を記述した。入射誤差を制御しないと5年間で最大ドリフトが約250×10(exp 4)kmであった。7章で、太陽輻射圧の影響を始めに解析的に調べ、その後、数値積分によって確認した。輻射圧はL4とL5点を地球からの距離を変えずに太陽方向に移動させ、移動したL4やL5点の周りの運動は、地球の質量を無視する近似内で輻射圧に影響されなかった。結局、太陽・地球系のL4とL5点近傍の軌道に対して、地球の離心率、惑星の重力、および太陽の輻射圧によるほぼ全ての影響は、初期位置と速度を調整することによって打ち消せることが分かった。; Each celestial body system such as Sun-Earth system, Earth-Moon system, Sun-Jupiter system, and so on has five Lagrangian points. Until now, only L1 point in the Sun-Earth system has been utilized for solar observatory missions. A new solar observatory positioned at L5 point in the Sun-Earth system and a positioned at L4 or L5 point in the Sun-Earth system are proposed as new missions in the near future. Spacecraft motion near these L4 and L5 points are described in reference 1 based on the circular restricted three body problem. This report studied effects of the eccentricity of the Earth, the gravity of planets, and the solar radiation pressure to orbits near the L4 and L5 points in the Sun-Earth system. In chapter 2, results of brief paper survey were shown. In chapter 3, effects of the eccentricity of the Earth orbit were studied. It was known from analytical treatment that the point which forms an equilateral triangle with the Sun and the instant position of the Earth becomes L4, or L5 point in the elliptical restricted three body problem. Periodic orbits around the L4 or L5 point mentioned above could be realized by adjusting the initial velocities. In chapter 4, effects of the gravity of planets were studied. Both direct and indirect terms were included for the gravity of planets. It was found that the short periodic terms of the semi-major axis due to the tidal force by planets are dominant. They depend upon the difference between the celestial longitudes of a planet and the Earth at the epoch, and most effects of planets could also be cancelled by adjusting the initial velocity. The magnitude of adjustment is less than 1 m/s. In chapter 5, the combined effects of the Earth's eccentricity and planetary gravities were studied, and it was confirmed that those combined effects could be accurately approximately as the simple superposition. In chapter 6, an L5 mission orbit with the minimum fuel for transfer was briefly stated, and effects of injection errors at L5 point were described. The maximum drift for 5 years by no control of the injection errors at L5 was about 250 x 10(exp 4) km. In chapter 7, effects of the solar radiation pressure were studied analytically at first, then confirmed by the numerical integrations. It was found that the radiation pressure makes the L4 and L5 points shift to the Sun direction with the unchanged distance from the Earth, and that the movement around the shifted L4 or L5 point was not affected by the radiation pressure in the approximation of neglect of the Earth's mass. After all, most effects of the eccentricity of the Earth, the gravity of planets, and the solar radiation pressure to orbits near the L4 and L5 points in the Sun-Earth system were found to be cancelled by adjusting the initial position and velocity.; 資料番号: AA0028932000; レポート番号: NASDA-ETR-000003; レポート番号: NASDA-TMR-980010
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