• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.45 no.9
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• pp.775-783
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• 2017

In this paper, an impulsive rendezvous problem by using minimum energy of spacecraft in different orbits is addressed. In particular, the orbits considered in this paper are the general orbits including the elliptic orbit, while most of the orbits considered in the literature have been restricted within co-planar or circular orbits. The constraints for solving this optimization problem are the Kepler's equation formulated with the universal variable, and the final position and velocity of two spacecraft. Also, the Lagrange coefficients, sometimes called as f and g solution, are used to describe the orbit transfer. The proposed method technique is demonstrated through numerical simulation by considering the minimum energy, and both the minimum energy and the wait time, respectively. Finally, it is also verified by comparing with the Hohmann transfer known as the minimum energy trajectory. Although a closed-form solution cannot be obtained, it shows that the suggested technique can provide a new insight to solve various orbital transfer problems.

• Journal of Astronomy and Space Sciences
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• v.22 no.3
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• pp.249-262
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• 2005

Optimization problems are formulated to calculate optimal impulses for deflecting Earth-Crossing Objects using a Nonlinear Programming. This formulation allows us to analyze the velocity changes in normal direction to the celestial body's orbital plane, which is neglected in many previous studies. The constrained optimization in the three-dimensional space is based on a patched conic method including the Earth's gravitational effects, and yields impulsive ${\Delta}V$ to deflect the target's orbit. The optimal solution is dependent on relative positions and velocities between the Earth and the Earth-crossing objects, and can be represented by optimal magnitude and angle of ${\Delta}V $ as a functions of a impulse time. The perpendicular component of ${\Delta}V $ to the orbit plane can sometimes play un-negligible role as the impulse time approaches the impact time. The optimal ${\Delta}V $ is increased when the original orbit of Earth-crossing object is more similar to the Earth's orbit, and is also exponentially increased as the impulse time reaches to the impact time. The analyses performed in present paper can be used to the deflection missions in the future.

• 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.