In this study, a preliminary trajectory design is conducted for a conceptual spacecraft mission to a near-Earth asteroid (NEA) (99942) Apophis, which is expected to pass by Earth merely 32,000 km from the Earth’s surface in 2029. This close approach event will provide us with a unique opportunity to study changes induced in asteroids during close approaches to massive bodies, as well as the general properties of NEAs. The conceptual mission is set to arrive at and rendezvous with Apophis in 2028 for an advanced study of the asteroid, and some near-optimal (in terms of fuel consumption) trajectories under this mission architecture are to be investigated using a global optimization algorithm called monotonic basin hopping. It is shown that trajectories with a single swing-by from Venus or Earth, or even simpler ones without gravity assist, are the most feasible. In addition, launch opportunities in 2029 yield another possible strategy of leaving Earth around the 2029 close approach event and simply following the asteroid thereafter, which may be an alternative fuel-efficient option that can be adopted if advanced studies of Apophis are not required.

1. INTRODUCTION
2. PROBLEM FORMULATION
    2.1 Cost Function
    2.2 Ballistic Trajectory
    2.3 1DSM Trajectory
    2.4 MGA-1DSM Trajectory
3. MONOTONIC BASIN HOPPING ALGORITHM
4. RESULTS
    4.1 Feasible Sequence Identification
    4.2 Detailed Analyses on Feasible Sequences
    4.3 Ballistic Rendezvous Opportunities in 2029
5. CONCLUSIONS
REFERENCES

• Sungki Cho(Korea Astronomy and Space Science Institute)
• Jung Hyun Jo(Korea Astronomy and Space Science Institute)
• Sang-Young Park(Astrodynamics and Control Lab., Department of Astronomy, Yonsei University) Corresponding Author
• Pureum Kim(Astrodynamics and Control Lab., Department of Astronomy, Yonsei University)