Project/Area Number 
19F19328

Research Category 
GrantinAid for JSPS Fellows

Allocation Type  Singleyear Grants 
Section  外国 
Review Section 
Basic Section 17010:Space and planetary sciencesrelated

Research Institution  Japan Aerospace EXploration Agency 
Host Researcher 
藤本 正樹 国立研究開発法人宇宙航空研究開発機構, 宇宙科学研究所, 教授 (30242811)

Foreign Research Fellow 
LIANG YUYING 国立研究開発法人宇宙航空研究開発機構, 宇宙科学研究所, 外国人特別研究員

Project Period (FY) 
20191108 – 20220331

Project Status 
Granted (Fiscal Year 2020)

Budget Amount *help 
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2021: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 2020: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2019: ¥900,000 (Direct Cost: ¥900,000)

Keywords  Perturbation theory / satellite orbit family 
Outline of Research at the Start 
This research is devoted to the scientific exploration on space environment near Phobos. It consists of two phases: Firstly, the astrodynamic environment near Phobos is explored systematically by finitetime Lyapunov exponent and GPUaccelerating technique; Secondly, based on the refined stable orbits, the distribution and evolution of dust tori near Phobos is predicted by space density matrix and entropy map in highfidelity model. Especially, the transition due to solar wind and interaction of Deimos is investigated.

Outline of Annual Research Achievements 
Firstly, targeting at various fidelity requirements, the researcher established a series dynamical models of MarsPhobos system considering multiple perturbations. Then, based on the perturbation theory, the mechanism of Mars gravity on periodic motion in Phobos vicinity is discussed. By singleaveraging method, the Mars gravity perturbation on the periodic motion near Phobos is divided to secular and osculating parts mathematically. Importantly, the perturbed dynamics is established in two cases, i.e., outsides and insides the sphere of influence of Phobos, respectively. It is demonstrated numerically that its secular perturbation contributes to the continuous decreasing or increasing "ω" (the argument of pericenter) of distant retrograde orbit family outsides and insides the sphere of influence of Phobos, respectively. The osculating effect of Mars gravity perturbation is critical to the different variation of "ω" for two satellite orbit families, i.e., g and g’ families. Furthermore, in detecting the dynamical flow in energy space of satellite orbits, polygonallike resonant periodic families are gained and show multiple loops above the Phobos surface. Enlightened by the aforementioned results, the researcher is developing a jumping mechanism on the Phobos surface by arcs of g and g’ families and their invariant tori. The current results demonstrate a feasible pointtopoint transfer mechanism with flexible time of flight and proper initial relative velocity.

Current Status of Research Progress 
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
The current status of the research goes well as scheduled in JSPS application. So far, a series dynamical models of MarsPhobos system are established according to different fidelity requirements, which fundamentally support the research on interdisciplinary research of celestial mechanics and planetary science in next stage. Importantly, based on the perturbation theory, the mechanism of Mars gravity on periodic motion in Phobos vicinity is discussed. Wherein the dynamics near Phobos is described by six canonical variables. Not only some valuable results are obtained by so, but also the current analysis can be extended to the study of a mathematical problem, i.e., coplanar motion, explaining the disturbed motion very close to Phobos. Furthermore, instead of the “popular” distant retrograde orbit family, the potential application of two satellite families consisting of prograde orbits is being studied, which provides us a new view to examine the periodic motion around Phobos. As an assistance to the research, the engagement to the research group, and the institution is getting on the right track. The abundant resources both academic and industrial, and both domestic and international from the institution are promoting the researcher’s early career. However, the current research is suffering from the spread of Coronavirus inevitably to some degree. Remarkably amount of time and efforts are spent on the settledown and initialization in the early stage of the research in FY 2019. Thus, the current status is better to be regarded as moderate.

Strategy for Future Research Activity 
The researcher is planning to conduct and extend the current results from the following aspects: 1) study the coplanar motion near Phobos in the sense of formation dynamics by perturbation theory. The truncation of perturbation series function is avoided so the coplanar motion very close to Phobos with an altitude of 1050 km is better described. 2) apply the jumping dynamics to pointtopoint transfer along Phobos 3D surface. The spatial satellite orbit families are employed. A jumping strategy is developed. Through such chessjumping, routines between two and several valuable locations, e.g., craters Clustril and Drunlo are planned as an example. 3) combine weak stability boundary with periodic motion near Phobos. A new concept of dynamical influence of sphere of Phobos is developed considering periodic perturbations, such as Mars orbital eccentricity and solar perturbation. The capture by Phobos is achieved by implementing a proper kick at the apocenter of resonant orbits around Mars. 4) explore the potential distribution of dust tori around Phobos. A new description of the distribution of dust tori is employed by introducing the concept of space density matrix. The dynamics of dust tori is established by partial differential equations considering Mars orbital eccentricity and solar perturbation etc.
