[논문]A Preliminary Impulsive Trajectory Design for (99942) Apophis Rendezvous Mission

Kim, Pureum; Park, Sang-Young; Cho, Sungki; Jo, Jung Hyun

doi:10.5140/jass.2021.38.2.105

A Preliminary Impulsive Trajectory Design for (99942) Apophis Rendezvous Mission 원문보기

Journal of astronomy and space sciences, v.38 no.2, 2021년, pp.105 - 117

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

Abstract ▼ AI-Helper

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.

주제어

표/그림 (12)

표 Table 1. Some selected orbital and physical parameters of Apophis (epoch May 31, 2020). The data were retrieved from the JPL Small-Body Database Browser
그림 Fig. 1. Simplified illustration of a ballistic trajectory. Planetary orbits and heliocentric spacecraft trajectory are represented by thin black lines and thick gray lines, respectively. Each heliocentric arc making up the trajectory is labeled with its leg number (following L) and segment number (following S).
그림 Fig. 2. Simplified illustration of a 1DSM trajectory. Planetary orbits and heliocentric spacecraft trajectory are represented by thin black lines and thick gray lines, respectively. Each heliocentric arc making up the trajectory is labeled with its leg number (following L) and segment number (following S). DSM, deep space maneuvers.
그림 Fig. 3. Simplified illustration of an MGA-1DSM trajectory with two gravity assists. Planetary orbits and heliocentric spacecraft trajectory are represented by thin black lines and thick gray lines, respectively. Each heliocentric arc making up the trajectory is labeled with its leg number (following L) and segment number (following S). Delta-v vectors are not explicitly shown for the sake of simplicity. DSM, deep space maneuvers. MGA-1DSM, multiple gravity assists with one deep space maneuver per leg.
그림 Fig. 4. Schematic procedure of parallelized MBH algorithm. In this example, it is assumed that two perturbed points are generated in one step. MBH, monotonic basin hopping.
그림 Fig. 5. Simplified pseudocode for the parallel MBH algorithm. MBH,monotonic basin hopping.
그림 Fig. 6. Comparison of the most optimal solution of each sequence in the total trip time vs. total delta-v graph, where the optimal solution is defined as requiring the least total delta-v. MGA-1DSM sequences are denoted by abbreviations of the visiting order; for instance, EVMA stands for Earth-Venus- Mars-Apophis.
표 Table 2. Parameter bounds used for feasible sequence identification
그림 Fig. 7. Minimum total delta-v required for the three feasible sequences, for different Earth departure and Apophis arrival dates. (a) 1DSM trajectories, (b) EVA trajectories, (c) EEA trajectories. Yellow diamonds represent selected trajectories that require total delta-v values of less than 5.5 km/s. Refer to Table 3 for more information on the selected trajectories. DSM, deep space maneuvers; EVA, Earth- Venus-Apophis; EEA, Earth-Earth-Apophis.
표 Table 3. Detailed information on example trajectories
그림 Fig. 8. Trajectories for four selected example cases. (a) Case 3, (b) Case 4, (c) Case 8, and (d) Case 10. Spacecraft trajectories are represented by thick black lines. Thin blue and red lines represent heliocentric orbits of Earth and Apophis (before being deflected by Earth's gravity), respectively. Information about impulsive maneuvers (except for DSMs that are less than 0.001 km/s) is shown on tooltips. DSM, deep space maneuvers.
그림 Fig. 9. Analyses of 2029 ballistic trajectories, for different Earth departure date and Apophis rendezvous date. (a) Total delta-v required, (b) C3 energy required to leave Earth, (c) Delta-v required to rendezvous with Apophis. Each tick refers to the beginning of each month. Yellow diamond represents a selected example trajectory; refer to Table 3 for more information on this trajectory.

AI 본문요약
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제안 방법

In this study, preliminary trajectory design and analyses for a future mission to visit and inspect asteroid (99942) Apophis around its 2029 close approach to Earth were performed under the assumption of using impulsive maneuvers. Several different types of trajectories that may or may not include gravity assists were analyzed, and relatively simple trajectories, such as multi-revolution ballistic trajectories, 1DSM trajectories, and MGA-1DSM trajectories with a single gravity assist from Earth or Venus, were found to be the most feasible.

대상 데이터

As the pre- 2029 nominal heliocentric orbit of Apophis lies between the orbits of Venus and Mars, Venus, Earth, and Mars were chosen as candidate swing-by planets, and the number of gravity assists was limited to two; thus, the number of possible MGA-1DSM sequences is 12. In total, 14 sequences (three with a single gravity assist, nine with two assists, and two without any assists) were chosen as candidates for this feasibility analysis. From now on, MGA-1DSM sequences are denoted by abbreviations of the visiting order; for instance, the EVMA sequence indicates that it is an MGA- 1DSM sequence with two gravity assists that begins from Earth and performs two swing-by’s at Venus and then Mars, and then reaches Apophis in the end.

성능/효과

Several different types of trajectories that may or may not include gravity assists were analyzed, and relatively simple trajectories, such as multi-revolution ballistic trajectories, 1DSM trajectories, and MGA-1DSM trajectories with a single gravity assist from Earth or Venus, were found to be the most feasible. For the spacecraft to rendezvous with Apophis before the end of 2028, the latest departure opportunity requiring a delta-v that is less than 5.5 km/s is in November 2027. It was also found that in the event that it is not necessary to arrive at Apophis before the close approach event, the strategy of letting the spacecraft accompany Apophis along its deflected orbit immediately after the close approach event may require an even less total delta-v of approximately 4.
5 km/s is in November 2027. It was also found that in the event that it is not necessary to arrive at Apophis before the close approach event, the strategy of letting the spacecraft accompany Apophis along its deflected orbit immediately after the close approach event may require an even less total delta-v of approximately 4.6 km/s.
In this study, preliminary trajectory design and analyses for a future mission to visit and inspect asteroid (99942) Apophis around its 2029 close approach to Earth were performed under the assumption of using impulsive maneuvers. Several different types of trajectories that may or may not include gravity assists were analyzed, and relatively simple trajectories, such as multi-revolution ballistic trajectories, 1DSM trajectories, and MGA-1DSM trajectories with a single gravity assist from Earth or Venus, were found to be the most feasible. For the spacecraft to rendezvous with Apophis before the end of 2028, the latest departure opportunity requiring a delta-v that is less than 5.
It should be noted that the result itself will change under a different departure scenario (such as a change in the altitude of the parking orbit or the use of a launch vehicle from Earth), but the general procedure of the preliminary design used in this study can still be followed. Starting from the preliminary design obtained through this procedure, high-fidelity trajectories can be built and fine-tuned. Such high-fidelity trajectories should reflect both complex dynamics and more realistic constraints, and are likely to require more maneuvers than those used in the preliminary trajectory.
Starting from the preliminary design obtained through this procedure, high-fidelity trajectories can be built and fine-tuned. Such high-fidelity trajectories should reflect both complex dynamics and more realistic constraints, and are likely to require more maneuvers than those used in the preliminary trajectory.
The preliminary analyses in this study were conducted under the assumption that the spacecraft leaves from a 600- km altitude Earth parking orbit, and the cost function was defined simply as the total delta-v required to depart from the parking orbit until the rendezvous. It should be noted that the result itself will change under a different departure scenario (such as a change in the altitude of the parking orbit or the use of a launch vehicle from Earth), but the general procedure of the preliminary design used in this study can still be followed.

후속연구

The preliminary analyses in this study were conducted under the assumption that the spacecraft leaves from a 600- km altitude Earth parking orbit, and the cost function was defined simply as the total delta-v required to depart from the parking orbit until the rendezvous. It should be noted that the result itself will change under a different departure scenario (such as a change in the altitude of the parking orbit or the use of a launch vehicle from Earth), but the general procedure of the preliminary design used in this study can still be followed. Starting from the preliminary design obtained through this procedure, high-fidelity trajectories can be built and fine-tuned.

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