• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.43 no.8
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• pp.692-698
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• 2015

This paper represents a trajectory design and analysis technique which uses invariant manifolds of the circular restricted three body problem. Instead of the classical patched conic method based on 2-body problem, the equation of motion and dynamical behavior of spacecraft in the circular restricted 3-body problem are introduced, and the characteristics of Lyapunov orbits near libration points and their invariant manifolds are covered in this paper. The trajectories from/to Lyapunov orbits are numerically generated with invariant manifolds in the Earth-moon system. The trajectories in the Sun-Jupiter system are also analyzed with various initial conditions in the boundary surface. These methods can be effectively applied to interplanetary trajectory designs.

• Publications of The Korean Astronomical Society
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• v.30 no.2
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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 ${\mu}$.

• Publications of The Korean Astronomical Society
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• v.30 no.2
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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 ($q_1$).

• Publications of The Korean Astronomical Society
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• v.30 no.2
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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.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.38 no.7
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• pp.684-692
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• 2010

Based on the planar restricted three body problem formulation, optimized trajectories for the Earth-Moon transfer are obtained. Mixed impulsive and continuous thrust are assumed to be used, respectively, during the Earth departure and Earth-Moon transfer/Moon capture phases. The continuous, dynamic trajectory optimization problem is reformulated in the form of discrete optimization problem by using the method of direct transcription and collocation, and then is solved using the nonlinear programming software. Representative results show that the shape of optimized trajectory near the Earth departure and the Moon capture phases is dependent upon the relative weight between the impulsive and the continuous thrust.

• The Bulletin of The Korean Astronomical Society
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• v.43 no.1
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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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• v.13 no.1
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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.

• Journal of Information Technology Services
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• v.10 no.1
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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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• v.20 no.4
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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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• v.5 no.1
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• pp.19-30
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• 1988

The existence of the j-type collision periodic orbit is examined on the condition of mass ratio 0.9878449 and Jacobian constant 2.9∼3.4. Using the Birckhoff's regularization method and the 5th order Runge-Kutta variable step-sized numerical roution introduced by Fehlberg (1968). we test their periodicities. As the results, 4 j-type collision orbits and 5 peculiar orbits are represented. There are good agreements in this collision orbits with the relationship between the period and the shape of orbit proposed by Pinotsis Zikides(1984).