Potential Trajectory Options for the Korea’s Future Planetary Missions utilizing the Moon

다국어 초록 (Multilingual Abstract)

In this thesis, two potential planetary trajectories utilizing the Moon for future Korea’s planetary missions are suggested. The first mission is a multi-purpose mission that can explore both the Moon and Mars with a single launch. The proposed mission applies the concept of a piggyback ride to a small-sized lunar probe, i.e., the daughter-ship, of the main Mars orbiter, i.e., the mothership. For the trajectory design, the Earth-Moon-Mars gravity assist (EMMGA) trajectory is adopted for the mothership to reach Mars, and the daughter-ship is assumed to be released from the mothership during lunar flyby. Since this kind of mission has not been suggested previously, in order to investigate the early-phase feasibility of the proposed mission, the launch windows have been analyzed and the associated delta-Vs have been directly compared with the solutions obtained for the typical Earth-Mars direct (EMD) transfer options. Also, mass budget estimation is analyzed with existing heavy launch vehicles.
With the first study, we could verify the feasibility of the multi-purpose space mission which explore both the Moon and Mars by way of the Earth-Moon-Mars Gravity Assist (EMMGA) trajectory. However this research is of intermediate character in that it has not employed rigorous optimization so that future work needs to be conducted for the design of the trajectory utilizing optimization methods. In this sense, the suggested candidate launch window and mission opportunities from the first work will be a good starting point for more detailed trajectory design optimization.
The second mission is the Moon-to-Earth return flight trajectory with the concept of Point Return Orbit (PRO). To formulate the given problem, a numerical three-step approach is proposed. Each step properly adapts different equations of motion with design parameters suitable to each step’s primary objective. Three- and N-body equations of motion are used as a basis, and PRO is constrained by the parking orbit at the Moon and Earth re-entry corridor associated with the re-entry position. Consequently, the major trans-Earth-injection (TEI) maneuver condition at the Moon is optimized together with the right ascension of the ascending node and the argument of the latitude. Moreover, the TEI maneuver magnitude with its execution date and required time of flight is optimized to form PRO. Adopting this three-step approach, the effect of the Moon’s relative motion with respect to the Earth to form the optimal TEI condition is clearly analyzed. In addition, the direct insight on the TEI condition is obtained by expressing the M–E rotating frame, which is expected to save time and effort while generating initial guesses for TEI conditions. We could verify that this three-step numerical approach can be useful in designing the Moon-to-Earth return flight trajectory.
These two works are performed under numerous assumptions for a simplified problem. However, by combining the analytic and numerical methods, good convergence and precise trajectories can be found for the two given missions. The two foregoing studies serve as the basis that can be applied to the future Moon exploration and other planetary exploration missions.

목차 (Table of Contents)

• Abstract i
• Table of Contents iii
• List of Figures vii
• List of Tables x
• Chapter 1. Introduction 1
• 1.1. Overview 1
• 1.2. Earth to Mars Mission with Lunar fly-by 3
• 1.3. Earth Return Mission with Point Return Orbit (PRO) 7
• Chapter 2. Orbit Dynamics 12
• 2.1. Time and Coordinate System 12
• 2.1.1. Time 12
• 2.1.1.1. Time Scale 12
• 2.1.1.2. The Julian Day 15
• 2.1.2. Coordinate Systems 16
• 2.2. Lambert Problem 19
• 2.3. Patched Conic Approximation and Sphere of Influence (SOI) 20
• 2.4. Fly-by Maneuver (gravity assist maneuver) 23
• 2.5. Rocket Equation 25
• Chapter 3. Design of Earth-Moon-Mars Trajectory utilizing Lunar Fly-by 27
• 3.1. Introduction 27
• 3.2. EMMGA Design Models and Methods 29
• 3.2.1. Lunar Fly-by Trajectory Generation en Route to Mars 30
• 3.2.1.1. Earth-centered Phase (stage 1) 30
• 3.2.1.2. Sun-centered Phase (stage 2) 36
• 3.2.1.3. Mars-centered Phase (stage 3) 38
• 3.2.2. Released SmallSat Trajectory Generation 40
• 3.2.3. Mass Budget Estimation 42
• 3.3. Simulation Setup 43
• 3.4. Results and Analysis 45
• 3.4.1. EMMGA Trajectory Characteristics 45
• 3.4.1.1. Launch Opportunities 45
• 3.4.1.2. Spacecraft Mass Budget Estimation 52
• 3.4.2. SmallSat Mission Capabilities 60
• 3.4.3. Example of Transfer Trajectory 63
• 3.5. Discussion 67
• Chapter 4. Point Return Orbit Design 69
• 4.1. PRO Design Method and Three-step Approach 69
• 4.1.1. Problem Definition 69
• 4.1.2. The Three-step Approach 75
• 4.1.2.1. Step 1: Feasible Trans-Earth-Injection (TEI) Condition search 75
• 4.1.2.2. Step 2: Initial M–E Trajectory Generation 79
• 4.1.2.3. Step3: PRO Optimization 81
• 4.2. Simulation Setup and Assumptions 84
• 4.3. Simulation Results 86
• 4.3.1. Feasible Ranges of TEI Conditions (results from Step 1) 86
• 4.3.2. Initial M–E Trajectory Generation and Analysis (results from Step 2) 91
• 4.3.2.1. TEI Condition Characteristics 91
• 4.3.2.1.1. , , and Characteristics 91
• 4.3.2.1.2. and Expressed in the Moon-to-Earth Rotating (MER) Frame 99
• 4.3.2.2. and Characteristics 102
• 4.3.3. Opimized PRO and Example Trajectory (results from step 3) 104
• 4.3.3.1. Optimization of Test Cases 104
• 4.3.3.2. Extended Analysis 113
• 4.4. Discussion 119
• Chapter 5. Conclusion 121
• Chapter 6. Future Work 123
• References 124
• 국문초록 133
• Appendix 136