Translunar Research Articles

Onboard Burn Targeting and Guidance of NASA Human Flight Vehicles

The mission requirements of crewed space vehicles flown by NASA drove the development of new techniques for burn targeting and guidance for ascent, rendezvous, lunar landing, and deorbit. The Saturn V Iterative Guidance Mode used an approximately optimal steering law that could adjust the trajectory to compensate for performance issues while meeting trajectory constraints at propulsion-system cutoff. Hypersurface targeting provided constraints for the Saturn V Trans-Lunar Injection burn. E Guidance, in quadratic- and linear-acceleration forms, provided closed-loop descent and ascent guidance for the Apollo Lunar Module. The Space Shuttle’s Powered Explicit Guidance algorithm was more flexible than Apollo-era guidance algorithms, and it had better convergence characteristics, enabling it to support challenging abort profiles. The Space Launch System has built on the heritage of the Space Shuttle’s guidance algorithm. The Orion spacecraft’s Two-Level Targeter enables onboard, autonomous targeting of an entire mission profile subject to three-body dynamics in cislunar space. Orion uses Shuttle-derived guidance as the basis for an orbit-guidance package with more capability than guidance algorithms of previous vehicles.

Space tether research at the University of Stuttgart

Space tether research activities at the University date back to the 1990s. First research projects investigated tether-assisted re-entry of payload return capsules from space stations. Tether research was resumed in 2015 focusing on the application of tethered planetary exploration rovers, based on the micro-rover Nanokhod. This includes robust, highly-integrated and miniaturised tethers and tether spooling systems, which are specifically adapted to the challenging lunar environmental and dust conditions. For this, several prototypes were developed and tested and a tether-dust testing facility was setup. In addition, developments have been made in the tether detection by creating a simulation framework, tracking algorithms and low-fidelity test bench for the verification of the algorithms. Based on the experience of the planetary tether applications, the research at the University of Stuttgart was expanded to Tethered Satellite Systems in 2022, utilising the tether spooling technology. In-depth studies on tethered CubeSat missions were developed together with students as part of educational activities, including tethered rendezvous capabilities and electrodynamic tether operation. In addition, breadboard models of optical detection and tracking payloads were developed for tracking a CubeSat sized object at full tether deployment of 100m. Additional subsystem development is currently in progress, consolidating the results of the mission studies, as well as dynamic analyses and simulations of the tethered satellite system. Concurrently, a third tether application research area was established, looking into studies for creating tether-based spaceflight infrastructure for lunar exploration missions. A concept study of a Momentum Exchange Tether system to transfer large payloads from Low Earth Orbit to a lunar transfer orbit was conducted and feasible tether system configurations were drafted. Various technological and operational challenges were identified and are now the focus of ongoing Momentum Exchange Tether research at the University of Stuttgart.

Near-optimal maneuver design for high-accuracy trans-lunar injection with highly elliptical phasing loops

Near-optimal maneuver design for high-accuracy trans-lunar injection with highly elliptical phasing loops

Navigation performance analysis of Earth–Moon spacecraft using GNSS, INS, and star tracker

Global Navigation Satellite System (GNSS) can provide an approach for spacecraft autonomous navigation in earth–moon space to make up for the insufficiency of earth-based tracking, telemetry, and control systems. However, its weak power and poor observation geometry near the moon causes new problems. After the GNSS signal characteristics and satellite visibility were evaluated in Phasing Orbit and Lunar Transfer Orbit, we proposed an adaptive Kalman filter based on the Carrier-to-Noise ratio (C/N0) and innovation vector to weaken the influence of GNSS accuracy attenuation as much as possible. The experimental results show that the spacecraft position and velocity accuracy are better than 10 m and 0.1 m/s near the Earth, and better than 50 m and approximately 0.2 m/s near the moon use GNSS with the proposed adaptive algorithms. Additionally, because of the deterioration of navigation performance based on the orbit filter during orbital maneuvering, we used accelerometer data to compensate for the dynamic model to maintain navigation performance. The results of the experiment provide a reference for subsequent studies.

An interval programming method of earth-moon trajectory for manned lunar exploration mission under interval uncertainty

There are always uncertainties in practical engineering, and the design of the optimal Earth-Moon trajectory under uncertainties significantly reduces flight risk for the manned lunar exploration mission (MLEM). This paper proposes an interval programming method to optimize the trans-lunar trajectory under interval uncertainties. Firstly, the influence of the trans-lunar injection uncertainties (TLI) is investigated, finding that the reached orbit at the perilune is very sensitive to the impulse errors at TLI. Then, the design methods of the Earth-Moon trajectory and the trajectory correction maneuver (TCM) are presented. Based on the mathematical tool of the interval possibility degree, the interval programming model is built to transform the uncertain optimization problem into a deterministic one, and then a multi-layer optimization scheme is proposed to solve it. The uncertain objectives and constraints’ interval bounds are calculated in the inner loop, and the design variables are searched and optimized in the outer loop. The proposed method is used to design the Earth-Moon trajectories of both manned and unmanned spacecraft. The designed trajectories are insensitive to the uncertainties and are validated by the Monte Carlo simulations.

Korea Pathfinder Lunar Orbiter (KPLO) Operation: From Design to Initial Results

Korea Pathfinder Lunar Orbiter (KPLO) is South Korea’s first space exploration mission, developed by the Korea Aerospace Research Institute. It aims to develop technologies for lunar exploration, explore lunar science, and test new technologies. KPLO was launched on August 5, 2022, by a Falcon-9 launch vehicle from cape canaveral space force station (CCSFS) in the United States and placed on a ballistic lunar transfer (BLT) trajectory. A total of four trajectory correction maneuvers were performed during the approximately 4.5-month trans-lunar cruise phase to reach the Moon. Starting with the first lunar orbit insertion (LOI) maneuver on December 16, the spacecraft performed a total of three maneuvers before arriving at the lunar mission orbit, at an altitude of 100 kilometers, on December 27, 2022. After entering lunar orbit, the commissioning phase validated the operation of the mission mode, in which the payload is oriented toward the center of the Moon. After completing about one month of commissioning, normal mission operations began, and each payload successfully performed its planned mission. All of the spacecraft operations that KPLO performs from launch to normal operations were designed through the system operations design process. This includes operations that are automatically initiated post-separation from the launch vehicle, as well as those in lunar transfer orbit and lunar mission orbit. Key operational procedures such as the spacecraft’s initial checkout, trajectory correction maneuvers, LOI, and commissioning were developed during the early operation preparation phase. These procedures were executed effectively during both the early and normal operation phases. The successful execution of these operations confirms the robust verification of the system operation.

Post Trajectory Insertion Performance Analysis of Korea Pathfinder Lunar Orbiter Using SpaceX Falcon 9

This paper presents an analysis of the trans-lunar trajectory insertion performance of the Korea Pathfinder Lunar Orbiter (KPLO), the first lunar exploration spacecraft of the Republic of Korea. The successful launch conducted on August 4, 2022 (UTC), utilized the SpaceX Falcon 9 rocket from Cape Canaveral Space Force Station. The trans-lunar trajectory insertion performance plays a crucial role in ensuring the overall mission success by directly influencing the spacecraft’s onboard fuel consumption. Following separation from the launch vehicle (LV), a comprehensive analysis of the trajectory insertion performance was performed by the KPLO flight dynamics (FD) team. Both orbit parameter message (OPM) and orbit determination (OD) solutions were employed using deep space network (DSN) tracking measurements. As a result, the KPLO was accurately inserted into the ballistic lunar transfer (BLT) trajectory, satisfying all separation requirements at the target interface point (TIP), including launch injection energy per unit mass (C3), right ascension of the injection orbit apoapsis vector (RAV), and declination of the injection orbit apoapsis vector (DAV). The precise BLT trajectory insertion facilitated the smoother operation of the KPLO’s remainder mission phase and enabled the utilization of reserved fuel, consequently significantly enhancing the possibilities of an extended mission.

Reachable set analysis of practical trans-lunar orbit via a retrograde semi-analytic model

Different from the Apollo flight mode, a safer trans-lunar flight mode for the crews is preferred. The previous-arrived lunar module rendezvouses with the crew exploration vehicle at a low lunar destination orbit, and then the crews ride the lunar module to descend the lunar surface sampling destination. The lunar module, which includes the descent and ascent stages, flies from a low Earth orbit to the low lunar destination orbit with two tangential impulses. The low lunar destination orbital reachable set of the practical trans-lunar orbit limits the feasible lunar surface sampling region. Therefore, this paper addresses the low lunar destination orbital reachable set of the practical trans-lunar orbit. A retrograde semi-analytic model is proposed for rapidly computing the practical two-impulse trans-lunar orbit firstly, which refers the ephemeris table twice for more precision perilune orbital elements. The reachable set is generated using the multiple-level traversal searching approach with this retrograde semi-analytic mode. Its envelope is re-checked by the continuation theory with the high-precision orbital model. Besides, some factors that affect the reachable set are also measured. The results show that neither the Earth–Moon distance nor the trans-lunar duration affects the reachable set. However, if the trans-lunar injection inclination is smaller than the inclination of the moon’s path, the reachable set becomes smaller or even reduces into an empty set. In brief, the proposed retrograde semi-analytic model for computing the reachable set provides a helpful and fast tool for selecting an applicable lunar surface sampling site for the manned lunar mission overall design.Graphical

Design and Analysis of the Cis-Lunar Navigation for the ArgoMoon CubeSat Mission

In the framework of the Artemis-1 mission, 10 CubeSats will be released, including the 6U CubeSat ArgoMoon, built by the Italian company Argotec and coordinated by the Italian Space Agency. The primary goal of ArgoMoon is to capture images of the Interim Cryogenic Propulsion Stage. Then, ArgoMoon will be placed into a highly elliptical orbit around the Earth with several encounters with the Moon. In this phase, the navigation process will require a precise Orbit Determination (OD) and a Flight Path Control (FPC) to satisfy the navigation requirements. The OD will estimate the spacecraft trajectory using ground-based radiometric observables. The FPC is based on an optimal control strategy designed to reduce the dispersion with respect to the reference trajectory and minimize the total ΔV. A linear approach was used to determine the optimal targets and the number and location of the orbital maneuvers. A covariance analysis was performed to assess the expected OD performance and its robustness. The analysis results show that the reference translunar trajectory can be successfully flown and the navigation performance is strongly dependent on the uncertainties of the ArgoMoon’s Propulsion Subsystem and of the orbit injection.

Global Sensitivity Analysis of Earth-Moon Transfer Orbit Parameters Based on Sobol Method

In the process of Earth-Moon transfer orbit, many parameters are involved and the degree of influence varies among the parameters. How to accurately distinguish the influence relationship between different parameters is of great significance to engineering missions. Based on Sobol sequence sampling method and Sobol global sensitivity analysis method, a calculation process of global sensitivity analysis is proposed in this paper for high-fidelity Earth-Moon transfer orbit. A numerical simulation method is used to verify that the Sobol sequence sampling method has better convergence and higher precision than other sampling methods and has better adaptability in global sensitivity analysis. The effects of different state parameters and the combination of different parameters on the perilune parameters of Earth-Moon transfer orbit are given by simulation examples, which verifies the effectiveness and feasibility of the calculation process proposed in this paper. Simulation results show that the radial position and tangential velocity at the trans-lunar injection point are the main sensitivity parameters, and the other parameters have little effect on the results. The sensitivity of the orbital elements at the trans-lunar injection point to the perilune parameters is different and needs to be determined according to the specific parameters. The results of this study can provide important reference for future Earth-Moon transfer orbit design and related engineering missions.

Restricted Kinematic Alignment in Total Knee Arthroplasty: Scientific Exploration Involving Detailed Planning, Precise execution, and Knowledge of When to Abort.

Not long ago, we were all transfixed by 50th anniversary tributes to humankind’s most daring achievement to date, the Apollo 11 moon landing. At 2 hours 44 minutes and 19 seconds after launch, the crew performed another jaw-dropping procedure. Translunar injection, a 6-minute burst of Saturn V engines, thrust Apollo 11 out of a low, circular parking orbit around Earth and catapulted it at 25,000 mph toward its precise target: the Moon.

Performance evaluation of multi-GNSSs navigation in super synchronous transfer orbit and geostationary earth orbit

The autonomous navigation of the spacecrafts in High Elliptic Orbit (HEO), Geostationary Earth Orbit (GEO) and Geostationary Transfer Orbit (GTO) based on Global Navigation Satellite System (GNSS) are considered feasible in many studies. With the completion of BeiDou Navigation Satellite System with Global Coverage (BDS-3) in 2020, there are at least 130 satellites providing Position, Navigation, and Timing (PNT) services. In this paper, considering the latest CZ-5(Y3) launch scenario of Shijian-20 GEO spacecraft via Super-Synchronous Transfer Orbit (SSTO) in December 2019, the navigation performance based on the latest BeiDou Navigation Satellite System (BDS), Global Positioning System (GPS), Galileo Navigation Satellite System (Galileo) and GLObal NAvigation Satellite System (GLONASS) satellites in 2020 is evaluated, including the number of visible satellites, carrier to noise ratio, Doppler, and Position Dilution of Precision (PDOP). The simulation results show that the GEO/Inclined Geo-Synchronous Orbit (IGSO) navigation satellites of BDS-3 can effectively increase the number of visible satellites and improve the PDOP in the whole launch process of a typical GEO spacecraft, including SSTO and GEO, especially for the GEO spacecraft on the opposite side of Asia-Pacific region. The navigation performance of high orbit spacecrafts based on multi-GNSSs can be significantly improved by the employment of BDS-3. This provides a feasible solution for autonomous navigation of various high orbit spacecrafts, such as SSTO, MEO, GEO, and even Lunar Transfer Orbit (LTO) for the lunar exploration mission.

Exploration of Low-Energy Earth-Moon Transfer Orbit Based on Crossing Orbit of Double Three-Body System

The design of low energy lunar transfer orbit and orbit optimization method based on crossing orbit is studied in this paper. The four-body problem of Sun-Earth-Moon-satellite is decoupled into two three-body problems of Sun-Earth-satellite and Earth-Moon-satellite. Low-energy lunar exploration orbit is designed by changing orbit at a certain intersection field through manifold of two Halo orbit of three-body system. A serial optimization design method for global initial value search and local gradient optimization are designed. When a motion state variable is partially modified, the differential correction method combined with adaptive regression algorithm is adopted. For the splicing points of manifolds of different systems, the velocity vector is modified to make the spacecraft get into the target berthing track, and to obtain the splicing points that can form crossing track of the two three-body systems. An example of orbit design is given to show that the Earth-Moon transfer orbit based on invariant manifold splicing has the characteristics of energy saving and long-time consumption, which can be used for the tasks with large loads and low time requirements. This research provides a method for the design of low energy lunar transfer orbit. It will benefit the energy consuming, material design of spacecraft, and so on.

Lunar close encounters compete with the circumterrestrial Lidov–Kozai effect

Luna 3 (or Lunik 3 in Russian sources) was the first spacecraft to perform a flyby of the Moon. Launched in October 1959 on a translunar trajectory with large semi-major axis and eccentricity, it collided with the Earth in late March 1960. The short, 6-month dynamical lifetime has often been explained through an increase in eccentricity due to the Lidov-Kozai effect. However, the classical Lidov-Kozai solution is only valid in the limit of small semi-major axis ratio, a condition that is satisfied only for solar (but not for lunar) perturbations. We undertook a study of the dynamics of Luna 3 with the aim of assessing the principal mechanisms affecting its evolution. We analyze the Luna 3 trajectory by generating accurate osculating solutions, and by comparing them to integrations of singly- and doubly-averaged equations of motion in vectorial form. Lunar close encounters, which cannot be reproduced in an averaging approach, decisively affect the trajectory and break the doubly-averaged dynamics. Solar perturbations induce oscillations of intermediate period that affect the geometry of the close encounters and cause the singly-averaged and osculating inclinations to change quadrants (the orbital plane ``flips''). We find that the peculiar evolution of Luna 3 can only be explained by taking into account lunar close encounters and intermediate-period terms; such terms are averaged out in the Lidov-Kozai solution, which is not adequate to describe translunar or cislunar trajectories. Understanding the limits of the Lidov-Kozai solution is of particular significance for the motion of objects in the Earth-Moon environment and of exoplanetary systems.

Solution set calculation of the Sun-perturbed optimal two-impulse trans-lunar orbits using continuation theory

The solution set of the Sun-perturbed optimal two-impulse trans-lunar orbit is helpful for overall optimization of the lunar exploration mission. A model for computing the two-impulse trans-lunar orbit, which strictly satisfies the boundary constraints, is established. The solution set is computed first with a circular restricted three-body model using a generalized local gradient optimization algorithm and the strategy of design variable initial continuation. By taking the solution set of a circular restricted three-body model as the initial values of the design variables, the Sun-perturbed solution set is calculated based on the dynamic model continuation theory and traversal search methodology. A comparative analysis shows that the fuel cost may be reduced to some extent by considering the Sun’s perturbation and choosing an appropriate transfer window. Moreover, there are several optimal two-impulse trans-lunar methods for supporting a lunar mission to select a scenario with a certain ground measurement and to control the time cost. A fitted linear dependence relationship between the Sun’s befitting phase and the trans-lunar duration could thus provide a reference to select a low-fuel-cost trans-lunar injection window in an engineering project.

Adaptive LEO-Phase Free-Return Orbit Design Method for Manned Lunar Mission Based on LEO Rendezvous

To design a free-return orbit for manned lunar mission based on low earth orbit (LEO) rendezvous, an adaptive LEO-phase free-return orbit design method based on high-precision dynamics model is proposed. First, the radius of perilune and the absolute value of perilune velocity are decoupled using a coordinate system rotation, which is derived from moon-centric local vertical and local horizontal instantaneous coordinate system at the time of perilune. The two Euler rotation angles and the absolute value of perilune velocity are used as independent design variables because their initial values are easy to guess. Next, a two-segment numerical integration strategy is proposed to calculate orbital elements at the moments of trans-lunar injection and free-return vacuum perigee. Subsequently, an optimization algorithm software package for solving large-scale nonlinear sequential quadratic programming problems (SQP_snopt) is employed to search the objective free-return orbit with a fixed trans-lunar injection inclination and the other two constraints on radiuses of perigee at the times of trans-lunar injection and vacuum perigee. After that, an iteration algorithm is devised to adjust trans-lunar injection window for adaptive LEO-phase. Finally, numerical results show a fast and accurate performance of the direct optimization method, which can provide valuable references to manned lunar missions based on LEO rendezvous.

Development of General-Purpose Root-Finding Module for General Mission Analysis Tool

A general-purpose root-finding module for designing spacecraft trajectories is developed to have similar accuracy to that of other well-known root-finding modules, and greater speed. Three quasi-Newton root-finding algorithms are implemented: the Newton–Raphson method, the Broyden’s method and the Generalized Broyden’s method. Based on the proposed root-finding module, General Mission Analysis Tool (GMAT) of National Aeronautics and Space Administration’s Goddard Space Flight Center (NASA/GSFC) is functionally extended by integrating the Broyden’s method and the Generalized Broyden’s method into its differential corrector module. Non-trivial spacecraft trajectory design problems, such as Lambert’s problem for trans-lunar trajectory and minimum-time transfer problem to the Mars are solved to analyze the performance of the proposed module. The numerical performances of each root-finding algorithm are quantitatively analyzed by the total number of function evaluations, the total number of iterations, convergence error, mean convergence rate, and running time. The overall comparative analysis shows that the Broyden’s method and the Generalized Broyden’s method are about 20–40% faster than the Newton–Raphson method and solutions from each algorithm have similar numerical accuracy. We also show that for selected test problems, the Generalized Broyden’s method converges in less running time than others with similar numerical accuracy in GMAT. The updated differential corrector module was released in R2014a version of GMAT.

Initial Error Dispersion and Midcourse Correction Maneuver Analysis of the Lunar Orbiter

The preliminary error analysis is performed to design the midcourse correction (MCC) maneuver of the lunar orbiter. During the trans-lunar trajectory, the lunar orbiter will perform several MCC maneuvers using the on-board propulsion system. The objectives of these maneuvers are to remove the deviation from the nominal trajectory by the injection error of the launch vehicle and to achieve the high accuracy for the lunar orbit insertion (LOI). To design the MCC maneuver, it is required to analyze the dispersion of the trans-lunar injection (TLI) error from the launch vehicle. In addition, the MCC maneuver epoch is also considered to design the MCC maneuver, which is an essential factor to analyze the MCC maneuver. To investigate the effects of the TLI uncertainty and the MCC maneuver epoch on the MCC maneuver, the Monte Carlo simulation is performed for the statistical analysis. The numerical simulation results and analysis provide a guideline to design the trans-lunar trajectory using the MCC maneuver in the presence of various error sources in the preliminary design phase.

Physical characterization of the deep-space debris WT1190F: A testbed for advanced SSA techniques

We report on extensive BVRcIc photometry and low-resolution (λ/Δλ∼250) spectroscopy of the deep-space debris WT1190F, which impacted Earth offshore from Sri Lanka, on 2015 November 13. In spite of its likely artificial origin (as a relic of some past lunar mission), the case offered important points of discussion for its suggestive connection with the envisaged scenario for a (potentially far more dangerous) natural impactor, like an asteroid or a comet.Our observations indicate for WT1190F an absolute magnitude Rc=32.45±0.31, with a flat dependence of reflectance on the phase angle, such as dRc/dϕ∼0.007±2 mag deg−1. The detected short-timescale variability suggests that the body was likely spinning with a period twice the nominal figure of Pflash=1.4547±0.0005s, as from the observed lightcurve. In the BVRcIc color domain, WT1190F closely resembled the Planck deep-space probe. This match, together with a depressed reflectance around 4000 and 8500 Å may be suggestive of a “grey” (aluminized) surface texture.The spinning pattern remained in place also along the object fiery entry in the atmosphere, a feature that may have partly shielded the body along its fireball phase perhaps leading a large fraction of its mass to survive intact, now lying underwater along a tight (∼1×80 km) strip of sea, at a depth of 1500 m or less.Under the assumption of Lambertian scatter, an inferred size of 216±30/α/0.1 cm is obtained for WT1190F. By accounting for non-gravitational dynamical perturbations, the Area-to-Mass ratio of the body was in the range (0.006⩽AMR⩽0.011) m2 kg−1.Both these figures resulted compatible with the two prevailing candidates to WT1190F’s identity, namely the Athena II Trans-Lunar Injection Stage of the Lunar Prospector mission, and the ascent stage of the Apollo 10 lunar module, callsign “Snoopy”. Both candidates have been analyzed in some detail here through accurate 3D CAD design mockup modelling and BRDF reflectance rendering to derive the inherent photometric properties to be compared with the observations.

ロケットの近地点引数制約を考慮した実数値遺伝的アルゴリズムによる3インパルス月遷移軌道設計

ロケットの近地点引数制約を考慮した実数値遺伝的アルゴリズムによる3インパルス月遷移軌道設計