引用本文: 齐毅, 祁瑞. 限制性三体问题轨道能量与雅可比常数概念辨析. 力学与实践, xxxx, x(x): 1-5.
Qi Yi, Qi Rui. Discussion on orbital energy and jacobi constant in the restricted three-body problem. Mechanics in Engineering, xxxx, x(x): 1-5.
 Citation: Qi Yi, Qi Rui. Discussion on orbital energy and jacobi constant in the restricted three-body problem. Mechanics in Engineering, xxxx, x(x): 1-5.

## DISCUSSION ON ORBITAL ENERGY AND JACOBI CONSTANT IN THE RESTRICTED THREE-BODY PROBLEM

• 摘要: 在轨道力学教学中，学生容易将圆型限制性三体问题的航天器轨道能量与雅可比常数混淆。针对该问题，本文推导了轨道能量变化表达式，揭示了轨道能量变化机理，给出了一种新的推导雅可比常数表达式的简便方法，明晰了轨道能量和雅可比常数概念的区别。相关教学研究将帮助学生厘清三体轨道动力学学习难点。

Abstract: In the college classroom teaching of the orbital mechanism, students easily confuse Jacobi constant of the circular restricted three-body problem with the orbital energy of the spacecraft. To solve this issue, in this paper, we derive the expression of the derivation of orbital energy, and uncover the mechanism of the gravity assist or flyby. Then, a new and concise approach to derive Jacobi constant is proposed. Finally, the difference between the orbital energy and Jacobi constant is clarified. The result in this paper can help students figure out the key point in the orbital dynamics.

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