Orbit Design and Control for Non-Heliocentric Small-Body Missions

非日心小天体任务的轨道设计与控制

• 批准号: 22K14424
• 负责人: 陳 泓儒
• 金额: $ 2.91万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Early-Career Scientists
• 财政年份: 2022
• 资助国家: 日本
• 起止时间: 2022-04-01 至 2025-03-31
• 项目状态: 未结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-22K14424/
• 关键词: Hamiltonian function; Canonical tranformation; Quasi-periodic orbits; J2-peturbed problem; Elliptic problem; small planetary moons; Small bodies; Nonheliocentric missions; Orbit design; Stability analysis; Orbit perturbations

To guide orbiting operations around a non-heliocentric moon, it is necessary to take into account the nonspherical gravity field of the planet and the eccentricity of the moon's orbit. It is difficult to compute bounded orbits in such a non-spherical field perturbed elliptic three-body problem. The applicantworked with Prof. Stefano Caletta on the Hamiltonian function of the perturbed elliptic problem and we attempt to establish the canonical transformation between the circular-restricted three problems (CR3BP), such that the Hamiltonian function of the perturbed problem has a form identical to the one in CR3BP. We can then convert the periodic orbits in the CR3BP to the bounded orbits in the perturbed elliptic problem. The applicant is also working on the development of the J2-perturbed elliptic-restricted three-body problem and the computation of the invariant torus (or quasi-periodic orbits), which are bounded, in the developed model.

为了指导围绕非日心月球的轨道运行，有必要考虑行星的非球形重力场和月球轨道的偏心率。在这种非球面场扰动椭圆三体问题中计算有界轨道是很困难的。申请人与Stefano Caletta教授合作研究扰动椭圆问题的哈密顿函数，并尝试建立循环限制三问题（CR3BP）之间的规范变换，使得扰动问题的哈密顿函数具有与CR3BP中的哈密顿函数相同的形式。然后我们可以将 CR3BP 中的周期轨道转换为扰动椭圆问题中的有界轨道。申请人还致力于J2扰动椭圆限制三体问题的开发以及所开发模型中有界的不变环面（或准周期轨道）的计算。