Lunar transfer trajectory design and the four body problem
This paper presents a review of lunar transfer trajectories that go beyond three-body theory and the Jacobi integral.
lunar↗
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Lunar transfer trajectory design and the four-body problem
The existence of a ballistic trajectory from the Earth to orbit about the Moon was long considered to be impossible based on analysis of the three-body problem. In 1990 a ballistic trajectory from the Earth to lunar orbit was discovered while analyzing a plan to salvage the Muses A (Hiten) spacecraft. This trajectory utilized the Sun's gravity in conjunction with the Earth and Moon's gravity and was thus the first example of a practical four-body trajectory design. This paper presents a review of lunar transfer trajectories that go beyond three-body theory and the Jacobi integral. These include Hiten, Lunar A and the Genesis return trajectory from the vicinity of the Moon to Earth.It is shown that these trajectories may be analyzed by piecing together segments where three-body motion dominates.
Muses↗
A method for the construction of a lunar transfer trajectory using ballistic capture
The weak stability boundary (WSB) method for the design and optimization of lunar transfer trajectories is described. Considerable savings of propellant are shown over classical methods of orbit transfer such as the Hohmann transfer method. The savings in Delta V required of the spacecraft ranges from 100 to 200 m/s, which translates into a 5-10 percent reduction in spacecraft propellant for a science payload. Another advantage of the WSB method involves the utilization of low thrust propellant systems. Since the transfer trajectory is nearly completely ballistic, thrusting propulsive maneuvers may be performed over a long time duration.
Miller, James K.↗
Overview of the Lunar Transfer Trajectory of the Co-Manifested First Elements of NASA’s Gateway
This paper documents the current design reference mission planned for the first two elements of NASA’s Gateway. When launched together, the Power and Pro-pulsion Element and Habitation and Logistics Outpost comprise the Co-Manifested Vehicle (CMV).1The low-thrust transfer between the initial parking orbit and the final insertion into the operational Near Rectilinear Halo Orbit is described. While each specific trajectory depends on launch date, trends are identified in the dynamics and orientation of the CMV as it traverses its spiral orbit. This paper describes the interplay between various assumptions and constraints on the development of the low thrust lunar transfer.
low thrust↗
Comparison of Low-Energy Lunar Transfer Trajectories to Invariant Manifolds
In this study, transfer trajectories from the Earth to the Moon that encounter the Moon at various flight path angles are examined, and lunar approach trajectories are compared to the invariant manifolds of selected unstable orbits in the circular restricted three-body problem. Previous work focused on lunar impact and landing trajectories encountering the Moon normal to the surface, and this research extends the problem with different flight path angles in three dimensions. The lunar landing geometry for a range of Jacobi constants are computed, and approaches to the Moon via invariant manifolds from unstable orbits are analyzed for different energy levels.
inveriant manifolds↗
Overview of the Lunar Transfer Trajectory of the Co-Manifested First Elements of NASA’s Gateway
This paper documents the current design reference mission planned for the first two elements of NASA’s Gateway. When launched together, the Power and Propulsion Element and Habitation and Logistics Outpost comprise the Co-Manifested Vehicle (CMV). The low-thrust transfer between the initial parking orbit and the final insertion into the operational Near Rectilinear Halo Orbit is described. While each specific trajectory depends on launch date, trends are iden-tified in the dynamics and orientation of the CMV as it traverses its spiral orbit. This paper describes the interplay between various assumptions and constraints on the development of the low thrust lunar transfer.
electric propulsion↗
Targeting an Optimal Lunar Transfer Trajectory Using Ballistic Capture
A new method is described for design of an Earth-Moon transfer trajectory with substantial savings of propellant over classical methods.
trajectory earth-moon transfer trajectory ballisti↗
Lunar Cube Transfer Trajectory Options
Numerous Earth-Moon trajectory and lunar orbit options are available for Cubesat missions. Given the limited Cubesat injection infrastructure, transfer trajectories are contingent upon the modification of an initial condition of the injected or deployed orbit. Additionally, these transfers can be restricted by the selection or designs of Cubesat subsystems such as propulsion or communication. Nonetheless, many trajectory options can be considered which have a wide range of transfer durations, fuel requirements, and final destinations. Our investigation of potential trajectories highlights several options including deployment from low Earth orbit (LEO), geostationary transfer orbits (GTO), and higher energy direct lunar transfers and the use of longer duration Earth-Moon dynamical systems. For missions with an intended lunar orbit, much of the design process is spent optimizing a ballistic capture while other science locations such as Sun-Earth libration or heliocentric orbits may simply require a reduced Delta-V imparted at a convenient location along the trajectory.
Libration Orbits↗
Lunar Cube Transfer Trajectory Options
Numerous Earth-Moon trajectory and lunar orbit options are available for Cubesat missions. Given the limited Cubesat injection infrastructure, transfer trajectories are contingent upon the modification of an initial condition of the injected or deployed orbit. Additionally, these transfers can be restricted by the selection or designs of Cubesat subsystems such as propulsion or communication. Nonetheless, many trajectory options can b e considered which have a wide range of transfer duration, fuel requirements, and final destinations. Our investigation of potential trajectories highlights several options including deployment from low Earth orbit (LEO) geostationary transfer orbits (GTO) and higher energy direct lunar transfer and the use of longer duration Earth-Moon dynamical systems. For missions with an intended lunar orbit, much of the design process is spent optimizing a ballistic capture while other science locations such as Sun-Earth libration or heliocentric orbits may simply require a reduced Delta-V imparted at a convenient location along the trajectory.
Libration Orbits↗
Lunar Browser trajectory tool
The Lunar Browser is a tool developed at NASA Ames Research Center for building, processing, and analyzing a database of lunar transfer trajectory solutions. Examples of intended uses include design trades for lunar missions and preliminary assessments of key parameters such as launch opportunities, delta-v and propulsion budgets, communication windows, eclipse durations, and lunar landing windows. The Lunar Browser tool is in the development phase and it is already producing results in its current form to address various NASA program requirements, proposals, and mission trajectories. The tool has also been used for research analysis in trajectory design, including a first publication regarding its application to the CLPS and Artemis programs. In particular, the results included transfers to lunar frozen orbits. Future work include the generation of more trajectories to expand the existing database and the optimization of the results.
Lunar Browser trajectory tool↗
Transfers from TLI to Lunar Frozen Orbits with Applications to NASA’s CLPS & Artemis Programs
This paper will focus on trajectory transfers from trans-lunar injection (TLI) to lunar frozen orbits with applications to NASA’s Commercial Lunar Payload Services (CLPS) and Artemis Human Landing System (HLS) programs. For a CLPS application, the CS-3 mission is explored, which will deploy a communications relay satellite in lunar elliptical frozen orbit followed by landing a payload on the lunar farside during dawn. Given HLS will land a crew near the lunar south pole with lighting and timing requirements, the effect of varying the Earth-Moon transit duration to influence the approach direction upon landing will be explored.
lunar frozen orbits↗
Lunar Cube Transfer Trajectory Options
Contingent upon the modification of an initial condition of the injected or deployed orbit. Additionally, these designs can be restricted by the selection of the Cubesat subsystem design such as propulsion or communication. Nonetheless, many trajectory options can be designed with have a wide range of transfer durations, fuel requirements, and final destinations. Our investigation of potential trajectories highlights several design options including deployment into low Earth orbit (LEO), geostationary transfer orbits (GTO), and higher energy direct lunar transfer orbits. In addition to direct transfer options from these initial orbits, we also investigate the use of longer duration Earth-Moon dynamical systems. For missions with an intended lunar orbit, much of the design process is spent optimizing a ballistic capture while other science locations such as Sun-Earth libration or heliocentric orbits may simply require a reduced Delta-V imparted at a convenient location along the trajectory. In this article we examine several design options that meet the above limited deployment and subsystem drivers. We study ways that both impulsive and low-thrust Solar Electric Propulsion (SEP) engines can be used to place the Cubesat first into a highly eccentric Earth orbit, enter the Moon's Sphere of Influence, and finally achieve a highly eccentric lunar orbit. We show that such low-thrust transfers are feasible with a realistic micro-thruster model, assuming that the Cubesat can generate sufficient power for the SEP. Two examples are shown here: (1) A Cubestat injected by Exploration Mission 1 (EM-1) then employing low thrust; and (2) a CubSat deployed in a GTO, then employing impulsive maneuvers. For the EM-1 injected initial design, we increase the EM-1 targeted lunar flyby distance to reduce the energy of the lunar flyby to match that of a typical lMoon system heteroclinic manifold. Figure 1 presents an option that encompasses the similar dynamics as that of the ARTEMIS mission design. Low-thrust maneuvers are used along the manifold trajectory to raise perigee to that of a lunar orbit, adjust the timing with respect to the Moon, rotate the line of apsides, and target a ballistic lunar encounter. In this design a second flyby decreases the orbital energy with respect to the Moon, so that C3 -0.1 km2s2. Another design, shown in Figure 2 emanates from a GTO then uses impulsive maneuvers to phase onto a local Earth-Moon manifold, which then transfers the CubeSat to a lunar encounter.
Dynamical System↗
Postflight Evaluation of Atlas-Centaur AC-6 (Launched August 11, 1965)
The sixth Atlas Centaur vehicle (AC-6) was successfully launched from the Eastern T e s t Range, Complex 36B, on August 11, 1965, at 0931:04.430 EST. A 2084-pound dynamic model of the Surveyor payload was placed in a simulated lunar transfer trajectory. Vehicle systems operated satisfactorily and all the flight objectives were accomplished. Lift-off within 4 seconds of the window opening demonstrated the launch-on-time capability of the vehicle were accurately compensated for by the Centaur guidance system. the Surveyor model into a near-perfect lunar transfer trajectory would have resulted in an impact of the moon without a midcourse correction. To hit the precise target area on the lunar surface, the required correction would have been 4.25 meters per second, which is well within the spacecraft capability. Normal thrust and impulse levels were obtained with both the A t l a s and Centaur propulsion systems. However, a sizeable thrust overshoot on startup of the Centaur engines has not been resolved. A propellant-utilization system used for the first time on the Centaur, accurately controlled the fuel and oxidant consumption. The turnaround and retrothrust maneuver were performed without incident. Relatively high longitudinal modal excitations and lateral payload excitations were obtained at lift-off; these high perturbations are believed t o be related t o the launcher holddown arms. Nominal temperatures were recorded for both the external vehicle skin and the payload compartment; however, abnormally low temperatures were measured in the forward equipment area, which may have resulted from leakage of cold helium purge gas. All vehicle electrical systems performed satisfactorily; the only difficulty with the RF systems was obtained with the C-band transponder. of the vehicle instrumentation yielded valid data. The AC-6 vehicle was constructed with several new lightweight designs including the forward bulkhead, thrust barrel, interstage adapter and tank skin thickness reduction from 0.016 t o 0.014 inch. No deficiencies were observed in any of these new structural elements.
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Low-Thrust Transfer to Interplanetary Trajectories from Lunar Trajectories with Rideshare
Accessing interplanetary space is challenging when using low thrust systems. Injecting spacecraft onto interplanetary trajectories is difficult with small launch vehicles, but it is possible to instead transfer to an interplanetary trajectory from a lunar flyby. Such cases are useful, for example, in rideshares between lunar and interplanetary missions. This work examines the problem of rideshare for small satellites onto lunar flyby trajectories, with transfers to an interplanetary trajectory. Low thrust interplanetary trajectories are examined starting from a rideshare mission on a lunar trajectory using delivery systems based on a modified Rocket Lab USA Electron vehicle and Photon stage.
Darcey R Graham↗
Powered flight trajectory optimization for lunar and interplanetary transfer.
Steepest descent method of trajectory optimization for computing lunar and interplanetary transfer missions, noting terminal constraints
LUNAR EXPLORATION↗
Flight performance of Atlas-Agena launch vehicles in support of the Lunar Orbiter missions 3, 4, and 5
Atlas-Agena launch vehicles successfully boosted a series of five Lunar Orbiters into proper lunar transfer trajectories. This report discusses the flight performance of the last three Atlas-Agenda launch vehicles (for Lunar Orbiters 111, IV, and V) from lift-off through the Agenda retromaneuver. The objective of these flights was to perform seleno- graphic investigations including photography of the lunar surface. Lunar Orbiter V, launched in August 1967, concluded the Lunar Orbiter missions
Source record↗
Analysis of the Radio Astronomy Explorer lunar orbit mission.
The second Radio Astronomy Explorer spacecraft (RAE-B) is planned to be inserted into lunar orbit in 1973. The transfer trajectory design, lunar orbit selection and launch opportunities are developed in relation to the spacecraft mass properties, propulsion capability and the scientific, environmental and engineering constraints. Alternative midcourse guidance and lunar orbit trim strategies are analyzed and compared. A means of achieving a launch window without varying launch azimuth and park orbit coast time is described. The resulting mission design is characterized by near-minimum energy lunar transfer trajectories and low eccentricity, retrograde critical inclination lunar orbits. Acceptable launch periods are shown to exist for six consecutive months and for two to four consecutive days per month.
Groves, R. T.↗
Postflight Evaluation of Atlas-Centaur AC-5 (Launched 2 March 1965)
The Atlas-Centaur AC-5 vehicle was launched from ETR Complex 36A on March 2., 1965 at 8:25.04 a.m. EST. Within about 1 second after launch the thrust of the Atlas booster engine decayed rapidly; the vehicle settled back on the launch pad and was quickly destroyed by fire and explosion. Considerable damage was sustained by the launch complex and its associated equipment. Loss of booster engine thrust was due to fuel depletion at the turbopump inlets, which is attributed to closure of the fuel prevalve or the staging valve. To preclude the recurrence of either of these fuel valving malfunctions, the following corrective action has been taken: The remote control actuator has been replaced by manual operation of the Atlas fuel prevalve; the internal passage dimensions in the staging valve have been increased to lessen the hydraulic load on the valve poppet. In addition to the Atlas fuel system malfunction, a failure in the power control circuitry of the Centaur guidance computer resulted in partial removal of power at umbilical ejection. To prevent such a guidance system failure on future flights some redundant circuitry has been eliminated and more rigorous checkout procedures have been adopted. No further anomalies were discovered in the telemetered data prior to the Atlas booster thrust decay. A prime objective of the AC-5 flight was to place a dynamic model of the Surveyor spacecraft in a simulated lunar transfer trajectory. An important facet of this problem is the demonstration of a launch-on-time capability in accordance with the proper Earth-moon relation. The window opening time was established at 8:25 a.m. EST; thus the actual launch occurred within 4 seconds of the planned time.
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