In this study, I calculate the past and future dynamical states of the Earth-Moon system by using modified Lambeck’s formulae. I find that the ocean tidal effect must have been smaller in the past compared to its present amount. Even though the Moon is already in the spin-orbit synchronous rotational state, my calculation suggest that it will not be in geostationary rotational state in the next billion years or so. This is due to the associated Earth’s obliquity increase and slow retardation of Earth’s spin and lunar orbital angular velocities. I also attempt to calculate the precessional period of the Earth in the future. To avoid uncertainties in the time scale, the future state is described by using the Earth-Moon distance ratio as independent parameter. Effects due to solar tidal dissipation are included in all calculations.

The ground tracking support is a critical factor for the navigation performance of spacecraft orbiting around the Moon. Because of the tracking limit of antennas, only a small number of facilities can support lunar missions. Therefore, case studies for various ground tracking support conditions are needed for lunar missions on the stage of preliminary mission analysis. This study analyzes the ground supporting condition effect on orbit determination (OD) of Korea Pathfinder Lunar Orbiter (KPLO) in the lunar orbit. For the assumption of ground support conditions, daily tracking frequency, cut-off angle for low elevation, tracking measurement accuracy, and tracking failure situations were considered. Two antennas of deep space network (DSN) and Korea Deep Space Antenna (KDSA) are utilized for various tracking conditions configuration. For the investigation of the daily tracking frequency effect, three cases (full support, DSN 4 pass/day and KDSA 4 pass/day, and DSN 2 pass/day and KDSA 2 pass/day) are prepared. For the elevation cut-off angle effect, two situations, which are 5 deg and 10 deg, are assumed. Three cases (0%, 30%, and 50% of degradation) were considered for the tracking measurement accuracy effect. Three cases such as no missing, 1-day KDSA missing, and 2-day KDSA missing are assumed for tracking failure effect. For OD, a sequential estimation algorithm was used, and for the OD performance evaluation, position uncertainty, position differences between true and estimated orbits, and orbit overlap precision according to various ground supporting conditions were investigated. Orbit prediction accuracy variations due to ground tracking conditions were also demonstrated. This study provides a guideline for selecting ground tracking support levels and preparing a backup plan for the KPLO lunar mission phase.

In this study, the observational arc-length effect on orbit determination (OD) for the Korea Pathfinder Lunar Orbiter (KPLO) in the Earth-Moon Transfer phase was investigated. For the OD, we employed a sequential estimation using the extended Kalman filter and a fixed-point smoother. The mission periods, comprised between the perigee maneuvers (PM) and the lunar orbit insertion (LOI) maneuver in a 3.5 phasing loop of the KPLO, was the primary target. The total period was divided into three phases: launch–PM1, PM1–PM3, and PM3–LOI. The Doppler and range data obtained from three tracking stations [included in the deep space network (DSN) and Korea Deep Space Antenna (KDSA)] were utilized for the OD. Six arc-length cases (24 hrs, 48 hrs, 60 hrs, 3 days, 4 days, and 5 days) were considered for the arc-length effect investigation. In order to evaluate the OD accuracy, we analyzed the position uncertainties, the precision of orbit overlaps, and the position differences between true and estimated trajectories. The maximum performance of 3-day OD approach was observed in the case of stable flight dynamics operations and robust navigation capability. This study provides a guideline for the flight dynamics operations of the KPLO in the trans-lunar phase.

To ensure the successful launch of the Korea pathfinder lunar orbiter (KPLO) mission, the Korea Aerospace Research Institute (KARI) is now performing extensive trajectory design and analysis studies. From the trajectory design perspective, it is crucial to prepare contingency trajectory options for the failure of the first lunar brake or the failure of the first lunar orbit insertion (LOI) maneuver. As part of the early phase trajectory design and analysis activities, the required time of flight (TOF) and associated delta-V magnitudes for each recovery maneuver (RM) to recover the KPLO mission trajectory are analyzed. There are two typical trajectory recovery options, direct recovery and low energy recovery. The current work is focused on the direct recovery option. Results indicate that a quicker execution of the first RM after the failure of the first LOI plays a significant role in saving the magnitudes of the RMs. Under the conditions of the extremely tight delta-V budget that is currently allocated for the KPLO mission, it is found that the recovery of the KPLO without altering the originally planned mission orbit (a 100 km circular orbit) cannot be achieved via direct recovery options. However, feasible recovery options are suggested within the boundaries of the currently planned delta-V budget. By changing the shape and orientation of the recovered final mission orbit, it is expected that the KPLO mission may partially pursue its scientific mission after successful recovery, though it will be limited.

The first Korea lunar orbiter, Korea Pathfinder Lunar Orbiter (KPLO), has been in development since 2016. After launch, the KPLO will execute several maneuvers to enter into the lunar mission orbit, and will then perform lunar science missions for one year. Among these maneuvers, the lunar orbit insertion (LOI) is the most critical maneuver because the KPLO will experience an extreme velocity change in the presence of the Moon’s gravitational pull. However, the lunar orbiter may have a delayed LOI burn during operation due to hardware limitations and telemetry delays. This delayed burn could occur in different captured lunar orbits; in the worst case, the KPLO could fly away from the Moon. Therefore, in this study, the burn delay for the first LOI maneuver is analyzed to successfully enter the desired lunar orbit. Numerical simulations are performed to evaluate the difference between the desired and delayed lunar orbits due to a burn delay in the LOI maneuver. Based on this analysis, critical factors in the LOI maneuver, the periselene altitude and orbit period, are significantly changed and an additional delta-V in the second LOI maneuver is required as the delay burn interval increases to 10 min from the planned maneuver epoch.

The deep space orbit determination software (DSODS) is a part of a flight dynamic subsystem (FDS) for the Korean Pathfinder Lunar Orbiter (KPLO), a lunar exploration mission expected to launch after 2018. The DSODS consists of several sub modules, of which the orbit determination (OD) module employs a weighted least squares algorithm for estimating the parameters related to the motion and the tracking system of the spacecraft, and subroutines for performance improvement and detailed analysis of the orbit solution. In this research, DSODS is demonstrated and validated at lunar orbit at an altitude of 100 km using actual Lunar Prospector tracking data. A set of a priori states are generated, and the robustness of DSODS to the a priori error is confirmed by the NASA planetary data system (PDS) orbit solutions. Furthermore, the accuracy of the orbit solutions is determined by solution comparison and overlap analysis as about tens of meters. Through these analyses, the ability of the DSODS to provide proper orbit solutions for the KPLO are proved.

The current study designs the mission orbit of the lunar CubeSat spacecraft to measure the lunar local magnetic anomaly. To perform this mission, the CubeSat will impact the lunar surface over the Reiner Gamma swirl on the Moon. Orbit analyses are conducted comprising ΔV and error propagation analysis for the CubeSat mission orbit. First, three possible orbit scenarios are presented in terms of the CubeSat’s impacting trajectories. For each scenario, it is important to achieve mission objectives with a minimum ΔV since the CubeSat is limited in size and cost. Therefore, the ΔV needed for the CubeSat to maneuver from the initial orbit toward the impacting trajectory is analyzed for each orbit scenario. In addition, error propagation analysis is performed for each scenario to evaluate how initial errors, such as position error, velocity error, and maneuver error, that occur when the CubeSat is separated from the lunar orbiter, eventually affect the final impact position. As a result, the current study adopts a CubeSat release from the circular orbit at 100 km altitude and an impact slope of 15°, among the possible impacting scenarios. For this scenario, the required ΔV is calculated as the result of the ΔV analysis. It can be used to practically make an estimate of this specific mission’s fuel budget. In addition, the current study suggests error constraints for ΔV for the mission.

In this study, the uncertainty requirements for orbit, attitude, and burn performance were estimated and analyzed for the execution of the 1st lunar orbit insertion (LOI) maneuver of the Korea Pathfinder Lunar Orbiter (KPLO) mission. During the early design phase of the system, associate analysis is an essential design factor as the 1st LOI maneuver is the largest burn that utilizes the onboard propulsion system; the success of the lunar capture is directly affected by the performance achieved. For the analysis, the spacecraft is assumed to have already approached the periselene with a hyperbolic arrival trajectory around the moon. In addition, diverse arrival conditions and mission constraints were considered, such as varying periselene approach velocity, altitude, and orbital period of the capture orbit after execution of the 1st LOI maneuver. The current analysis assumed an impulsive LOI maneuver, and two-body equations of motion were adapted to simplify the problem for a preliminary analysis. Monte Carlo simulations were performed for the statistical analysis to analyze diverse uncertainties that might arise at the moment when the maneuver is executed. As a result, three major requirements were analyzed and estimated for the early design phase. First, the minimum requirements were estimated for the burn performance to be captured around the moon. Second, the requirements for orbit, attitude, and maneuver burn performances were simultaneously estimated and analyzed to maintain the 1st elliptical orbit achieved around the moon within the specified orbital period. Finally, the dispersion requirements on the B-plane aiming at target points to meet the target insertion goal were analyzed and can be utilized as reference target guidelines for a mid-course correction (MCC) maneuver during the transfer. More detailed system requirements for the KPLO mission, particularly for the spacecraft bus itself and for the flight dynamics subsystem at the ground control center, are expected to be prepared and established based on the current results, including a contingency trajectory design plan.

In this paper, a brief but essential development strategy for the lunar orbit determination system is discussed to prepare for the future Korea’s lunar missions. Prior to the discussion of this preliminary development strategy, technical models of foreign agencies for the lunar orbit determination system, tracking networks to measure the orbit, and collaborative efforts to verify system performance are reviewed in detail with a short summary of their lunar mission history. Covered foreign agencies are European Space Agency, Japan Aerospace Exploration Agency, Indian Space Research Organization and China National Space Administration. Based on the lessons from their experiences, the preliminary development strategy for Korea’s future lunar orbit determination system is discussed with regard to the core technical issues of dynamic modeling, numerical integration, measurement modeling, estimation method, measurement system as well as appropriate data formatting for the interoperability among foreign agencies. Although only the preliminary development strategy has been discussed through this work, the proposed strategy will aid the Korean astronautical society while on the development phase of the future Korea’s own lunar orbit determination system. Also, it is expected that further detailed system requirements or technical development strategies could be designed or established based on the current discussions.