• 한국항공우주학회지
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• 제43권8호
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• pp.692-698
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• 2015

본 논문에서는 원형 제한 3체 문제의 불변위상공간을 이용하여 지구-달 또는 행성간의 궤적을 설계하고 해석하는 기법을 소개한다. 2체 문제를 조합하는 고전적인 방식 대신에 원형 제한 3체 문제에 대한 운동방정식, 궤적의 동적 특성, 평형점 주변의 리아프누프 궤도와 불변위상공간의 특성을 기술한다. 원형 제한 3체 문제의 불변위상공간을 이용했을 때, 지구-달 시스템의 궤적설계 방식과 태양-목성 시스템의 경계면에서의 초기조건에 따른 궤적 특성을 수치 시뮬레이션을 통해 확인한다. 본 논문에서 제안한 원형 제한 3체 문제의 불변위상공간을 이용한 궤적설계 기법은 저추력 또는 저에너지를 이용한 달탐사 또는 행성탐사 임무 등에 활용 가능할 것이다.

• 천문학논총
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• 제30권2호
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• pp.297-299
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• 2015

In this paper we have examined the linear stability of triangular equilibrium points in the photogravitational restricted three body problem when both primaries are triaxial rigid bodies, the bigger one an oblate spheroid and source of radiation. The orbits about the Lagrangian equilibrium points are important for scientific investigation. A number of space missions have been completed and some are being proposed by various space agencies. We analyze the periodic motion in the neighbourhood of the Lagrangian equilibrium points as a function of the value of the mass parameter. Periodic orbits of an infinitesimal mass in the vicinity of the equilibrium points are studied analytically and numerically. The linear stability of triangular equilibrium points in the photogravitational restricted three body problem with Poynting-Robertson drag when both primaries are oblate spheroids has been examined by A. Kumar (2007). We have found the equations of motion and triangular equilibrium points for our problem. With the help of the characteristic equation we have discussed stability conditions. Finally, triangular equilibrium points are stable in the linear sense. It is further seen that the triangular points have long or short periodic elliptical orbits in the same range of ${\mu}$.

• 천문학논총
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• 제30권2호
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• pp.295-296
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• 2015

This study deals with the generalization of the Elliptic Restricted Three-Body Problem (ER3BP) by considering the effects of radiation and oblate spheroid primaries. This may illustrate a gas giant exoplanet orbiting its host star with eccentric orbit. In the three dimensional case, this generalization may possess two additional equilibrium points ($L_{6,7}$, out-of-plane). We determine the existence of $L_{6,7}$ in ER3BP under the effects of radiation (bigger primary) and oblateness (small primary). We analytically derive the locations of $L_{6,7}$ and assume initial approximations of (${\mu}-1$, ${\pm}\sqrt{3A_2}$), where ${\mu}$ and $A_2$ are the mass parameter and oblateness factor, respectively. The fixed locations are then determined. Our results show that the locations of $L_{6,7}$ are periodic and affected by $A_2$ and the radiation factor ($q_1$).

• 천문학논총
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• 제30권2호
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• pp.293-294
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• 2015

This work considers the elliptic restricted three-body problem under effects of radiation of the bigger primary, and an oblate spheroid for the smaller primary to mimic an exoplanetary system with a gas giant planet. Under the influences of both effects we look for the existence of the triangular equilibrium points and the influences of the radiation and oblateness on the locations and motion of the points. We set the system in a normalized rotating coordinate system and derive equations of motion for the third infinitesimal object. Our study shows that the effects modify the equilateral/isosceles triangle shape with respect to the primaries. The triangular points also have non-planar motion with period depending on the value of the planet oblateness.

• 한국항공우주학회지
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• 제38권7호
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• pp.684-692
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• 2010

본 논문에서는 지구-달 천이를 위한 최적 궤도 설계에 관한 연구를 수행하였다. 지구와 달의 인력을 동시에 고려한 평면상 제한 3체 궤도 운동 모델을 바탕으로 지구 출발시에는 순간 추력을, 지구-달 천이 과정 및 달 임무궤도 투입시에는 연속 추력을 사용하는 혼합형 궤도전이 방법을 제시하였다. 최적화 풀이 방법으로서 Direct Transcription 및 Collocation을 이용한 비선형 프로그래밍 기법을 적용하였으며, 지구 출발 및 달 임무궤도 투입 궤적의 형상은 순간 추력의 연속 추력에 대한 상대 가중치 및 비행시간에 의하여 매우 달라질 수 있음을 파악하였다.

• 천문학회보
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• 제43권1호
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• pp.46.3-47
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• 2018

We present a general N-body exasolar system simulator in anticipation of upcoming searches for exoplanets and even exomoons by next generation telescopes such as James Webb Space Telescope. For habitable zones, traditionally defined by temperature, we here address the essential problem of dynamical stability of planetary orbits. Illustrative examples are presented on P-type orbits in stellar binary systems, that should be fairly common as in Kepler 16b. Specific attention is paid to reduced orbital lifetimes of exoplanets in the habitable zone by the stellar binary, that is propoesed by Maurice van Putten (2017). Especially, we focused on a classic work of complex three-body problem that is well known by Dvorak(1986). We charge his elliptic restricted three-body problem to extend unrestricted three-body problem to look into dynamical motions in view of circumbinary planet, furthermore, we suggest that opposite angular orientation of the planet is relative to the stability of orbits. In here, counter-rotation case is relatively more faster than co-rotation case for being stable. As a result, we find that various initial conditions and thresholds to approach dynamical stability and unstability with unexpectable isolated islands over enormous parameter space. Even, superkeplerian effect of binary is important to habitability of the exoplanet and we can verify that superfaster binary doesn't effect on th planet and increases survivality of planet around the binary.

• International Journal of Aeronautical and Space Sciences
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• 제13권1호
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• pp.106-116
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• 2012

Optimal transfer trajectories based on the planar circular restricted three body problem are designed by using mixed impulsive and continuous thrust. Continuous and dynamic trajectory optimization is reformulated in the form of discrete optimization problem. This is done by the method of direct transcription and collocation. It is then solved by using nonlinear programming software. Two very different transfer trajectories can be obtained by the different combinations of the design parameters. Furthermore, it was found out that all designed trajectories permit a ballistic capture by the Moon's gravity. Finally, the required thrust profiles are presented and they are analyzed in detail.

• 한국IT서비스학회지
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• 제10권1호
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• pp.65-72
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• 2011

In this paper, we consist of three dimensional acceleration sensor as a small-sized sensor module to acquire base technologies that need to estimate exhibition audience' moving distance. and that we developed algorism and device that can calculate acceleration in gravity direction with attaching it to people's body part without regard to three dimensional direction. By making use of the sensor module, we have to process the data that let it quantitatively process possible to measure people's walk and movement by computer system. We normalized sensor output data in the process of change from sensor module to acquisition of data, rectangular coordinates and single scalar acceleration value in gravity direction. Printed out sensor data attaching sensor module to people's body part is used for motion pattern detection after normalization, Motion sensor devised mode change algorism because it print data of other pattern according to attached position of body. For algorism design, we collected data occurring during walking about subject and we also defined occurring problem domain after analyzing the data. We settle defined problem domain and that we simulated the walking number measuring instrument with highly efficient in restricted environment.

• Journal of Astronomy and Space Sciences
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• 제20권4호
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• pp.313-318
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• 2003

A communications satellite system placed in three-Lagrange points, $L_3$, $L_4$ and $L_5$, of the restricted three-body problem in Earth-Moon system is proposed in this paper. LEO satellite constellation has been another choice of communications system. The proposed system which is alternatives of limited geostationary orbit resources, has some weak points such as long distance from the Earth, relatively expensive launch cost, long delay time, more required power, and so on. It has good points like less efforts (fuel) for station keeping, less eclipses, etc. This system has limitations for applications to provide commercial services but it is still some attractive points.

• Journal of Astronomy and Space Sciences
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• 제5권1호
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• pp.19-30
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• 1988

지구-달계의 질량비인 $\mu$-0.9878449 와 Jacobi 상수 2.9~3.4인 범위의 조건일 때 j종족 충돌궤도가 존재하는가를 조사하였다. 수치적인 방법으로는 Birckhoff의 정칙화 평면에서 Fehlberg(1968)의 5차 Runge-Kutta가변구간 수치적분방법을 사용하여 궤도의 주기성을 검증하였다. 그 결과 4개의 j종족 충돌궤도와 5개의 특이형궤도를 얻었고, 또한, 이 j 종족 충돌궤도가 Pinotsis와 Zikides(1984)가 제시한 주기와 궤도형태의 상관관계를 보였다.