Free-return Trajectories Research Articles

Bayesian Optimization of crewed lunar free return abort trajectory

Maneuvering to a free return trajectory is a vital abort means for crewed lunar missions. A novel method of solving the fuel optimization of free return abort trajectory for Earth-Moon transfer by two-stage transformation on optimization model and Bayesian optimization is documented. Two new design variables—perilune altitude and transfer time from earth to perilune, instead of the original injection velocity vector, are introduced to transform the general model into a two-dimensional model. Each feasible abort trajectory is determined by a numerical method including initial estimate and exact solution. Then the characteristics of the relationship between the new variables and the fuel objective of impulse maneuver are applied to further transform the model into a one-dimensional model. Based on the Bayesian optimization method, fuel optimization is successfully and efficiently implemented for the free return abort trajectory at multiple abort moments during the Earth-Moon transfer. Furthermore, the influence of the initial Earth-Moon phase on the result of fuel optimization is presented. Numerical simulations are conducted to demonstrate the efficacy of the proposed method.

Business Case Study for the Cycler: A Circumlunar Vehicle for Development of Space Tourism and Lunar Infrastructure by 2030

Cislunar space tourism is still a futuristic concept. However, the thrill and innovation that it offers has the potential to attract the attention of High-Net-Worth Individuals. As a result, developing regular tourist-focused cislunar transportation could be an opportunity for space entrepreneurs. Moreover, once established, cyclic lunar transportation might be a factor that could improve lunar business and infrastructure such as those considered for Moon Village. Today, the commercial development of cislunar vehicles is limited by costs and long duration research and development programs, while, the commercial benefits of a reliable transportation system of crew, tools, materials, and supplies are not fully understood. Consequently, the authors present the commercial viability of a cislunar space tourism vehicle utilizing the cycler concept. This article presents a business case for such a cislunar transportation vehicle and a related portfolio of services that might be realized by 2030. The business case expands previous studies on the Cycler concept proposed by Bombardier, Farr, and Peraldi in 2016. The commercial viability of this cislunar vehicle offers the opportunity for international collaboration as well as the potential for providing access to spaceflights for the space emerging nations. The cislunar space tourism Cycler is envisaged as a modular vehicle that will orbit the Earth and the Moon on a free return trajectory in a 7-day crewed journey (based on a study by Genova and Aldrin). The modular structure provides comfortable to premium travel conditions for 8 paying customers and 3 crew members as well as transporting goods using a cargo unit and a dedicated module to conduct scientific experiments. The article proposes a vehicle architecture using available components with the current Technical Readiness Levels of 6 or higher. This approach identifies technology gaps that need to be addressed to develop cislunar tourism and transportation and demonstrates the limited number of nations that are currently involved in developing these components. Furthermore, the article introduces a risk assessment of the envisaged civil cislunar transportation system, a dedicated financial modeling tool together with potential approach for financing the system through International public–private partnerships.

Trajectories for Flyby Sample Return at Icy Moons

Ballistic trajectories are computed that aim to achieve a sample-return mission to Europa, Enceladus, or Titan without capturing, descending, or landing. The low-cost mission concept uses a free-return trajectory that also involves a close flyby of the icy moon. A broad-search algorithm is developed to construct feasible itineraries, and Venus and Earth gravity-assist sequences are considered. Select solutions from the broad search are then optimized to be continuous using gravity of the full ephemeris. Solution characteristics are examined over a complete 12-year Jupiter period and 30-year Saturn period. For Europa and Titan, the outbound Venus–Earth–Earth gravity assist (VEEGA) option can significantly reduce launch , compared to alternate options. For Europa, various optimized results are computed with as low as , reentry speeds comparable to the Stardust capsule, and flight times of 9–15 years. Unfortunately, an Enceladus mission requires a flight time of 25 years or more and incurs fairly high relative speeds. Optimized direct and VEEGA missions to Titan are presented, with total flight times of 16 and 25 years, respectively.

Two-segment lunar free-return trajectories design using the pseudostate theory

Accurate initial solutions for two-segment Earth-Moon free-return trajectories, with midcourse transfer opportunities for favorable lunar targeting, are developed analytically by using the pseudostate theory. A constrained flight-path angle quasi-Lambert problem is formulated to determine the lunar-orbiting phase of the free-return trajectory. Gradient and direct-shooting algorithms are used to correct the initial estimates of certain two-body parameters. Numerical simulations with a high-fidelity model are undertaken to verify the accuracy of the pseudostate solutions and to illustrate the efficiency of the proposed algorithm. Perilune altitude errors for the pseudostate method are less than 10% of their corresponding values for the patched conic technique. The differences between the pseudostate and the high-fidelity solutions can be eliminated rapidly.

Mars double-aeroflyby free returns

Mars double-flyby free-return trajectories that pass twice through the Martian atmosphere are documented. This class of trajectories is advantageous for potential Mars atmospheric sample return missions because of its low geocentric energy at departure and arrival, because it would enable two sample collections at unique locations during different Martian seasons, and because of its lack of deterministic maneuvers. Free return opportunities are documented over Earth departure dates ranging from 2015 through 2100, with viable missions available every Earth-Mars synodic period. After constraining the maximum lift-to-drag ratio to be less than one, the minimum observed Earth departure hyperbolic excess speed is 3.23 km/s, the minimum Earth atmospheric entry speed is 11.42 km/s, and the minimum round-trip flight time is 805 days. An algorithm using simplified dynamics is developed along with a method to derive an initial estimate for trajectories in a more realistic dynamic model. Multiple examples are presented, including free returns that pass outside and inside of Mars's appreciable atmosphere.

Theorem of Optimal Image Trajectories in the Restricted Problem of Three Bodies

The restricted three-body problem represents the dynamical framework employed for spacecraft mission analysis, in the presence of two attracting bodies, since the 1950s. In this context, orbital motion is often chaotic, although several special solutions (equilibrium points, periodic orbits, and quasiperiodic trajectories) exist, and can be--or have already been--profitably employed in space missions. The theorem of image trajectories, proven five decades ago by Miele, states that for a given path in the restricted problem of three bodies (with primaries in mutual circular orbits), there exists a mirror trajectory (in two dimensions) and three mirror paths (in three dimensions). This theorem regards feasible trajectories and proved extremely useful for investigating the natural dynamics in the restricted problem of three bodies, by identifying special solutions, such as symmetric periodic orbits and free return trajectories. This work extends the theorem of image trajectories to optimal paths, which minimize either the propellant consumption or the time of flight, by determining the relations between the optimal thrust sequence, magnitude, and direction of an outgoing path and a symmetrical returning trajectory. This means that while the theorem of image paths revealed extremely useful for investigating natural dynamics, the theorem of optimal image trajectories can be profitably employed for powered orbital motion, i.e., in the context of impulsive and finite-thrust orbit transfers and rendezvous, as well as for the purpose of analyzing artificial periodic orbits that use very low thrust propulsion.

A UKF based design method for lunar free-return trajectories

A method based on unscented Kalman filter parameter estimation is proposed for the design of lunar free-return trajectories. The method avoids calculating the Jacobian matrix and obtains large convergence ability compared with the common differential-correction method. Given that the initial estimate of the free-return trajectory is only required to be generated under the two-body Earth–spacecraft model, the difficulty of guessing a good initial estimate is greatly reduced. Through converting the original problem to a parameter estimation representation, the method is used to find the converged final solution that satisfies the constraints at injection, perilune, and Earth-entry interface under a high-fidelity gravitational model. In addition to its deceptively simplicity, the method proves to be quite effective through numerical examples in finding the solution to lunar free-return trajectories within a few iterations with great numerical accuracy.

Fast Free Returns to Mars and Venus with Applications to Inspiration Mars

Mars free-return trajectories are investigated both with and without the use of Venus for gravity assist. Launch dates are searched from 2015 to 2060, and focus is placed on identifying opportunities that have a short total time of flight (that is, that are “fast” among the available free-return opportunities) so that they may be used for a human mission to flyby Mars. Constraints on Earth launch and Earth arrival are based on those used for the nominal Inspiration Mars opportunity in 2018. All attractive Mars free-return candidates found are shown to be rare, with launch opportunities only repeating (approximately) every 15 years, or every 32 years if a Venus flyby is used. A set of near-term candidate trajectories are found using the gravity-assist path Earth–Venus–Mars–Earth, which may be suitable for backup to (or replacement for) the nominal Inspiration Mars free return. One such candidate, with a launch date on 22 November 2021, has an Earth launch of ( of ) and an arrival of (entry speed of ), both of which are lower than the nominal Inspiration Mars trajectory, with a total flight time of 582 days. Venus free-return opportunities are also found, with promising application for a human flyby mission to Venus. An entry analysis is done for select cases (including the 2018 and 2021 opportunities) and shown to be feasible using present-day or near-term technology. An opportunity in 2023 is also found, which may be feasible if aerocapture is available.

High-latitude-landing circumlunar free return trajectory design

Purpose The purpose of this paper is to design free return trajectories launching at lower-latitude launch site Wenchang and landing at relatively high-latitude landing site Siziwang Banner tailored to human lunar missions for China, and in general demonstrate the feasibility of high-latitude landings with acceptable entry range.

Circumlunar free return trajectories design and validation for high-speed moon-to-earth reentry mission

This paper introduces the trajectory design method used in CE-5T1 mission and the flight results. Firstly, the design method and analysis of circumlunar trajectory is studied. Secondly, circumlunar trajectory correction maneuver (TCM) strategy is discussed, including full target strategy, reduced-order target strategy and bias target strategy. In the end, the flight data is compared with predicted value.

Target selection and mass estimation for manned NEO exploration using a baseline mission design

In recent years Near-Earth Objects (NEOs) have received an increased amount of interest as a target for human exploration. NEOs offer scientifically interesting targets, and at the same time function as a stepping stone for achieving future Mars missions. The aim of this research is to identify promising targets from the large number of known NEOs that qualify for a manned sample-return mission with a maximum duration of one year. By developing a baseline mission design and a mass estimation model, mission opportunities are evaluated based on on-orbit mass requirements, safety considerations, and the properties of the potential targets. A selection of promising NEOs is presented and the effects of mission requirements and restrictions are discussed. Regarding safety aspects, the use of free-return trajectories provides the lowest on-orbit mass, when compared to an alternative design that uses system redundancies to ensure return of the spacecraft to Earth. It is discovered that, although a number of targets are accessible within the analysed time frame, no NEO offers both easy access and high incentive for its exploration. Under the discussed aspects a first human exploration mission going beyond the vicinity of Earth will require a trade off between targets that provide easy access and those that are of scientific interest. This lack of optimal mission opportunities can be seen in the small number of only 4 NEOs that meet all requirements for a sample-return mission and remain below an on-orbit mass of 500 metric Tons (mT). All of them require a mass between 315 and 492mT. Even less ideal, smaller asteroids that are better accessible require an on-orbit mass that exceeds the launch capability of future heavy lift vehicles (HLV) such as SLS by at least 30mT. These mass requirements show that additional efforts are necessary to increase the number of available targets and reduce on-orbit mass requirements through advanced mission architectures. The need for on-orbit assembly also becomes apparent, as availability of a HLV alone does not provide sufficient payload capabilities for any manned mission targeting NEOs.

Lunar orbit insertion targeting from the two-segment lunar free-return trajectories

This paper presents a method for designing a lunar orbit insertion (LOI) targeting sequence from a two-segment lunar free-return trajectory. To reduce the fuel consumption for lunar orbit targeting, the algorithm modifies the LOI sequence and simultaneously optimizes the midcourse lunar-targeting maneuver (LTM) time. The circular restricted three-body is used to construct the two-segment lunar free-return trajectories and to observe the trajectory characteristics during the midcourse transfer and lunar encounter. A high-fidelity lunar gravitational model is adopted to modify the initial estimates of the LTM time and LOI sequence. Numerical examples are presented to illustrate the fuel consumption for accomplishing the lunar global targeting from a specified two-segment lunar free-return trajectory. The result indicates the lunar global targeting can be achieved within a LOI budget of 2.6km/s and LTM budget of 0.4km/s. The use of the proposed method provides an accurate initial solution that can be further optimized rapidly on higher-fidelity models. The procedure is well suited for onboard, real-time control of lunar global access missions.

Analysis of Two-Segment Lunar Free-Return Trajectories

A precise and convenient procedure for designing the two-segment lunar free-return trajectory is presented in this paper. The trajectory characteristics are analyzed to support the lunar mission design associated with the higher inclination lunar approaches and safer returns from the moon. The concise procedure is established based on the matched conic model. An analytical algorithm is developed to compute the spacecraft state at the lunar sphere of influence to complete the conic matching. An iteration process is then adopted to generate favorable initial solutions that satisfy the constraints at injection, perilune, and Earth-entry interface. Orbital launch windows for departure from Earth, lunar encounter, and returns to Earth are established in the years 2024 and 2034. These years are chosen due to the moon’s inclination reaching a maximum in 2024 and it reaching a minimum in 2034 during a Metonic cycle. This novel trajectory enables greater lunar surface coverage than standard free-return trajectories. The trajectory can be used to lower the fuel consumption for high-latitude lunar orbiting and landing. In case a mission should be aborted in the lunar approach stage, the spacecraft can safely return without additional maneuvering. The initial trajectory is modified in a high-fidelity gravitational model and the results indicate that the difference is small and convergence is rapid.

Free return trajectories or enmeshment? Some psychodynamic factors and thoughts on the role of social capital in the use of substituted cathinones (M-cats)

Purpose – The purpose of this paper is to suggest that the emergence of substituted cathinones or M-cat drugs (notably mephedrone and methylone) and their rapid proliferation of use, amongst drug users in the UK from 2009 onwards, signals changes in the habits, preferences and lifestyle choices made by certain drug users, whilst also indicating a pronounced increase in the levels of co-morbid mental health conditions experienced by another, yet often distinct, group of users. Design/methodology/approach – This latter group of users, it is suggested, tend to initiate use of psychoactive substances (including tobacco and alcohol) at a younger age. In addition, it is suggested, they often present to treatment and criminal justice services with a history of chronic childhood relational trauma, as a background against which severe patterns of drug abuse has evolved. In this light the lack of significant supplies of social capital, as a protective factor against the development of chronic drug use, is further considered in the paper that follows though a brief literature review and qualitative clinical case reports. Findings – Novel psychoactive substances ( Newcombe, 2013) appear so seductive, for a certain group of users, because they seem to provide a temporary form of cognitive and emotional anaesthesia, enabling users to self-medicate, often against experiences of profound psychological trauma and contemporary lives that are typically experienced as boring, hopeless and pointless. The euphoric effects of psycho-stimulants such as mephedrone are particularly appealing to individuals attempting to escape a subjective sense of daily dysphoria and may on this basis lead to, rather than recreational use, more persistent patterns of drug use. However, in contradistinction to this group of users, another recreational – mainly weekend leisure – group of users continues to evidence a voracious appetite for psycho-stimulant substances. Originality/value – It is suggested that this second group of users has been particularly influential in substitute displacement towards the emergence of legal highs, due to the poor quality and illegal status of street drugs such as cocaine, amphetamine sulphate and MDMA (ecstasy).

Optimal Free-Return Trajectories to Near-Earth Asteroids

A method is presented to calculate optimal trajectories to near-Earth asteroids that incorporate free-return trajectory segments. These trajectories are useful because they return to Earth with no fuel penalty, which is useful for risk mitigation on manned missions. The algorithm minimizes total velocity change over an entire nominal mission, encompassing a single impulsive maneuver each for Earth departure, leaving the free-return trajectory, rendezvous with and departure from the asteroid, culminating with unpowered reentry into Earth’s atmosphere. Two example cases are presented in the circular restricted three-body model: a mission to 2000 SG344 from 23 August 2028 to 9 October 2029 with a cost of , and a mission to 2006 BZ147 from 9 February 2033 to 21 December 2033 with a cost of . The results presented here showcase the usage of the algorithm, which may be applied to free-return trajectories to a wide variety of near-Earth objects.

Free Return Trajectories in Lunar Missions

Four types of symmetric free return trajectories in the planar circular restricted three-body problem are computed and compared with each other. One of these four types is most applicable in practice. Concentrating ourselves on this special type of free return trajectory, the corresponding planar asymmetric cases are studied. Then the studies are generalized to the three-dimensional case. The restrictions on the inclination angle of the probe at the perilune are discussed. It is found that the maximum inclination at the perilune between the probe's orbit plane and the Moon's orbit plane is restricted by the heights of the perigee and the perilune of the free return trajectory. However, the inclination at the perigee is nearly not affected by them. At last, a strategy to design free return trajectories in the real Earth-Moon system is proposed. Some numerical simulations are done to show the feasibility of this orbit design strategy. The discussions from the planar case to the spatial case and then to the real force model can also be applied to the other three types of planar free return trajectories.

Generation of Multisegment Lunar Free-Return Trajectories

To support the mission and trajectory design problems associated with the Earth-to-moon trajectories for a crewed vehicle, a multisegment lunar free-return trajectory is proposed. The multisegment free return differs from hybrid profiles in that it consists of free-return sections only; however, it maintains the advantages of hybrid returns. The analysis presented here is limited to a two-segment class of trajectories. In this profile, the translunar injection puts the spacecraft onto a free-return trajectory with a high perilune altitude; then, the spacecraft performs a transfer maneuver onto a new translunar coast trajectory that has an approximate perilune altitude of 100 km. This new translunar coast trajectory is also designed as a free-return trajectory that can perform a safe return. With a finite sphere of influence model, an analytical model of the multisegment free-return trajectories is developed by the matched-conic technique. Characteristics of the injection velocity, flight time, and lunar approach inclinations of the multisegment lunar free returns have been extensively investigated. The results indicate that multisegment free returns allow a wider range of lunar approach inclinations and freer launch window than free-return profiles.

Design of Earth—Moon Free-Return Trajectories

A new algorithm for designing free-return lunar flyby trajectories between the Earth and the moon is developed. The pseudostate theory is adopted to get the initial solution of the free-return trajectory. Using this initial solution, an improved differential-correction method is employed to find the final solution with a more complicated dynamic model. Compared with the original differential-correction method, the improved one can extend the convergence domain and have a fast convergence speed. A large number of numerical examples are carried out to test the reliability and efficiency of the algorithm, and also study the global features of free-return lunar flyby trajectories. The features are mainly affected by the geometric relationship between the Earth and the moon, the altitude of perilune, and the transfer time from perigee to perilune.

Optimal Lunar Orbit Insertion from a Variable Symmetric Free-Return Trajectory

A method for the optimization of a multiple-impulse lunar orbit insertion sequence from a symmetric free-return trajectory is presented. Both the inclination and altitude at lunar periapsis along the free return are variable. The algorithm systematically optimizes the orbit insertion sequence while simultaneously generating a free-return outbound trajectory. With a direct multiple-shooting method, optimization is performed in the circular restricted three-body model with a constrained sequential quadratic programming algorithm. The necessary gradients are derived with linear perturbation theory, and a closed-form expression is derived for computing gradients along a general n-impulse trajectory. Examples are presented for two classes of symmetric free returns, and a range of lunar orbit orientations is examined to assess the impact on velocity impulse requirements.

Automated Generation of Symmetric Lunar Free-Return Trajectories

A procedure for free-return trajectory generation in a simplified Earth-moon system is presented. With two-body and circular restricted three-body models, the algorithm constructs an initial guess of the translunar injection state and time of flight. Once the initial trajectory is found, the Jacobian of the constraints is derived analytically using linear perturbation theory, and a square system of nonlinear equations is solved numerically to target Earth entry interface conditions leading to feasible free-return trajectories. No trial and error is required to generate the initial guess. Possible free returns include departures from both posigrade and retrograde Earth orbits coupled with circumlunar or cislunar flight, in and out of the Earth-moon plane.