2018 Fiscal Year Final Research Report
Breakthrough integrator for the gravitational N-body problem and its application to extrasolar systems
| Project/Area Number |
16K13781
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Tokushima Bunri University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Keywords | 保存量 / 時間可逆性 / スケーリング変換 / N 体問題 / 安定運動可能領域 / 平衡解 |
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| Outline of Final Research Achievements |
The general N-body problem has some equilibrium solutions and conserved quantities. Further, it is time-reversible. We designed a numerical integrator which maintains all the properties. Because these conserved quantities and equilibrium solutions have important roles in deciding the motion regions for the general three-body problem, our new integrator can precisely trace these regions. Actually, we numerically utilized our integrator to the motion regions of a planet in a binary or two-planet system. By observing the regions, we can clarify whether the orbit of this planet is stable or not.
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| Free Research Field |
数値計算 可積分系
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| Academic Significance and Societal Importance of the Research Achievements |
太陽系外惑星が持つ軌道の安定性を数値的に評価する際，複雑な座標変換や惑星質量を無視するなどの近似が行われることが多かった．このような操作なしに数値計算を行っても，軌道を正確に計算できる保障はなかったからである．研究代表者が開発した新解法はこの問題を克服した．二重星内の一惑星や単独星を周回する二惑星に新解法を適用することで，それらの軌道安定性を簡便・高速・極めて長時間かつ高精度に判定できるようにした．
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