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In this paper, an integrated optimal flight plan with a guidance plan in a general transfer orbit is considered. Due to the need to simultaneously reduce energy consumption and flight time in some space missions, the spacecraft trajectory is optimized based on two criteria to minimize fuel consumption and flight time in the orbital transfer process. For this purpose, the total velocity impulse on both sides of the transition orbit and the elapsed time are defined as the criteria of the objective function which includes the spacecraft’s insertion conditions and orbital parameters related to the shape of the trajectory. The optimal transition (coasting) trajectory is then obtained using the multi-objective genetic algorithm (MOGA) search method. Subsequently, the velocity-to-be-gained guidance steering scheme is integrated to track the trajectory onboard and reach the final orbit. The numerical results of the proposed algorithm are extracted in three case studies and compared with other references that show its ability to find the optimal transfer.

The optimization of a solar sail-based orbital transfer amounts to searching for the control law that minimizes the flight time. In this context, the optimal trajectory is usually determined assuming constant solar properties. However, the total solar irradiance undergoes both long-term (solar cycles) and short-term variations, and recent analyses have shown that this may have an impact on solar sailing for missions requiring an accurate thrust modulation. In this regard, the paper discusses a strategy to overcome such an issue by suitably adjusting the thrust vector in order to track a reference, optimal, transfer trajectory. In particular, the sail propulsive acceleration magnitude is modified by means of a set of electrochromic material panels, which change their optical properties on application of a suitable electric voltage. The proposed control law is validated with a set of numerical simulations that involve a classical Earth-Mars, orbit-to-orbit, heliocentric transfer.

This paper presents the mission design for a CubeSat-based active debris removal approach intended for transferring sizable debris objects from low-Earth orbit to a deorbit altitude of 100 km. The mission consists of a mothership spacecraft that carries and deploys several debris-removing nanosatellites, called Deorbiter CubeSats. Each Deorbiter is designed based on the utilization of an eight-unit CubeSat form factor and commercially-available components with significant flight heritage. The mothership spacecraft delivers Deorbiter CubeSats to the vicinity of a predetermined target debris, through performing a long-range rendezvous maneuver. Through a formation flying maneuver, the mothership then performs in-situ measurements of debris shape and orbital state. Upon release from the mothership, each Deorbiter CubeSat proceeds to performing a rendezvous and attachment maneuver with a debris object. Once attached to the debris, the CubeSat performs a detumbling maneuver, by which the residual angular momentum of the CubeSat-debris system is dumped using Deorbiter’s onboard reaction wheels. After stabilizing the attitude motion of the combined Deorbiter-debris system, the CubeSat proceeds to performing a deorbiting maneuver, i.e., reducing system’s altitude so much so that the bodies disintegrate and burn up due to atmospheric drag, typically at around 100 km above the Earth surface. The attitude and orbital maneuvers that are planned for the mission are described, both for the mothership and Deorbiter CubeSat. The performance of each spacecraft during their operations is investigated, using the actual performance specifications of the onboard components. The viability of the proposed debris removal approach is discussed in light of the results.

The right ascension of the ascending node is unobservable if only the inter-satellite ranging is used for autonomous orbit determination (AOD) of an Earth navigation constellation. However, if an Earth-Moon libration point satellite is added to the Earth navigation constellation to construct an extended navigation constellation, all the orbital elements can be determined with only the inter-satellite ranging. Furthermore, the extended navigation constellation can provide navigation information for interplanetary probes. For such an extended navigation constellation, orbital control needs to be considered due to the instability of the libration-point satellite orbit. This study concerns the influence of satellite orbital maneuver on the AOD of the extended navigation constellation. An AOD method under orbital maneuver is proposed. A low thrust controller is designed to achieve libration point satellite autonomous orbit maintenance by using AOD results. A navigation constellation consisting of three GPS satellites and one libration point satellite are designed for simulation. The simulation results show that libration point satellites can achieve autonomous navigation and autonomous orbit maintenance by only using inter-satellite ranging information. The rotation drift error of the Earth navigation constellation is also suppressed.

In spacecraft rendezvous, bearings-only navigation generally suffers from a lack of observability in range direction. Therefore, dedicated orbital maneuvers are essential to improve the observability and meet the navigation requirement. This paper proposes a simple one-step guidance method for improving observability. A new cost that quantifies the observability is defined by exploiting a Fisher information matrix (FIM). The resulting delta-v solution, recursively obtained at every maneuvering instant, enables the mission to fulfill the navigation requirement as well as the safety requirement and the final boundary condition. Thanks to its low computational burden, the proposed guidance method can be easily extended to the closed-loop guidance/navigation system. The closed-loop formulation makes the tracking performance robust against the disturbances and the thruster model errors. Numerical simulations demonstrate the effectiveness of the one-step guidance and the extended closed-loop guidance in a v-bar rendezvous scenario.

This paper proposes a solution for multiple-impulse orbital maneuvers near circular orbits for special cases where orbital observations are not globally available and the spacecraft is being observed through a limited window from a ground or a space-based station. The current study is particularly useful for small private launching companies with limited access to global observations around the Earth and/or for orbital maneuvers around other planets for which the orbital observations are limited to the in situ equipment. An appropriate cost function is introduced for the sake of minimizing the total control/impulse effort as well as the orbital uncertainty. It is subsequently proved that for a circle-to-circle maneuver, the optimization problem is quasi-convex with respect to the design variables. For near circular trajectories the same cost function is minimized via a gradient based optimization algorithm in order to provide a sub-optimal solution that is efficient both with respect to energy effort and orbital uncertainty. As a relevant case study, a four-impulse orbital maneuver between circular orbits under Mars gravitation is simulated and analyzed to demonstrate the effectiveness of the proposed algorithm., Comment: 9 pages, 12 figures, submitted to Advances in Space Research

With the increase in the number of objects orbiting Earth, space situational awareness (SSA) has becoming an important area of research in the space sector (Lemmens and Krag, 2014). This paper outlines approaches to increase the performance of SSA algorithms. Parallel processing is implemented in orbital maneuver detection methods with the goal of increasing the computational speed and accuracy of detection by fusing two well-known detection methods: Two-Line Elements (TLE) analysis and state propagation into a hybrid detection method. Speed is an important component when considering the implementation of real time SSA, as well as, with the increase in the number of objects orbiting Earth the throughput of maneuver detection algorithms needs to increase to stay feasible. The results show that implementing parallel processing increased the computational speed of TLE analysis by approximately eight times and of state propagation by approximately four orders of magnitude. In terms of computational speed, the novel method performed worse than TLE analysis and state propagation. However, the method reduced the number of false maneuver detections.

Tomographic synthetic aperture radar (TomoSAR) is a modern technique that allows retrieving the structural information of detected objects. This paper investigates the problem of optimal orbit design in TomoSAR space missions. Considering the mission requirement of multi-baseline repeated observation, the orbital characteristics of TomoSAR satellites are analysed under the J 2 perturbation effect. By introducing the performance indicators of sampling period and orbital transfer fuel consumption, the orbit design is transformed into a multi-objective optimization problem. A two-step optimization strategy is developed to find the optimal orbits of TomoSAR satellites. In the first step, where some approximations are made, the idea of Pareto optimal solutions is applied under the objectives of time and fuel. A more accurate model is utilized in the second refinement step, and biogeography-based optimization (BBO) is employed to obtain satisfactory revisit accuracy. Numerical simulations are conducted to testify the effectiveness of the suggested design process, providing references for TomoSAR missions in terms of satellite orbit.

To solve the problem of thrust vector misalignment from the Cubesat center of mass during orbital maneuver, spin-stabilized method is applied to eliminate velocity pointing error. Spinning thrusting Cubesat model involves the effects of mass variation and jet damping is established. Analytical solutions for the angular velocity, nutation angle, Euler angle, and inertial velocity with nonzero initial conditions are derived. Simulations show that the analytical solutions closely match numerical simulations. Based on the analytical solutions, the velocity pointing error influencing factors is analyzed. The results show that the velocity pointing error caused by initial transverse velocity, nutation angle and transverse disturbance torque can be reduced by raising the spin rate, but the initial Euler angle need to be limited. Also, the spinning thrusting maneuver can allow for a lower spin rate by increasing the axial moment of inertia.

In this paper, a general new methodology is presented for the orbital reconfiguration of satellite constellations on the basis of Lambert targeting theorem. In view of the cost and risk reduction, it is very important to consider the problem of satellite constellation reconfiguration with the two constraints of overall mission cost minimization and the desired final configuration. Hence, the dependent non-simultaneous deployment approach is proposed to minimize overall fuel cost. Despite the fact that the satellites deploy in a non-simultaneous manner, supplementary phasing maneuvers on the target orbital pattern to achieve the desired orbital configuration are avoided. Moreover, a novel idea is presented to optimize the flight of satellites, which plays an important role in complying with the constraint of overall fuel cost minimization as much as possible. In order to achieve the global optimal solution of the satellite constellation reconfiguration problem, the efficient hybrid Particle Swarm Optimization/Genetic Algorithm (PSO/GA) technique, is implemented. Finally, to indicate the superiority of the presented method, a comparison to the simultaneous maneuver viewpoint is made on a number of representative cases. The obtained results imply significant reduction of reconfiguration costs by employing the proposed method.

The thrust vector control (TVC) scheme is a powerful method in spacecraft attitude control. Since the control of a small spacecraft is being studied here, a solid rocket motor (SRM) should be used instead of a liquid propellant motor. Among the TVC methods, gimbaled-TVC as an efficient method is employed in this paper. The spacecraft structure is composed of a body and a gimbaled-SRM where common attitude control systems such as reaction control system (RCS) and spin-stabilization are not presented. A nonlinear two-body model is considered for the characterization of the gimbaled-thruster spacecraft where, the only control input is provided by a gimbal actuator. The attitude of the spacecraft is affected by a large exogenous disturbance torque which is generated by a thrust vector misalignment from the center of mass (C.M). A linear control law is designed to stabilize the spacecraft attitude while rejecting the mentioned disturbance torque. A semi-analytical formulation of the region of attraction (RoA) is developed to ensure the local stability and fast convergence of the nonlinear closed-loop system. Simulation results of the 3D maneuvers are included to show the applicability of this method for use in a small spacecraft.

This paper introduces a mission concept for active removal of orbital debris based on the utilization of the CubeSat form factor. The CubeSat is deployed from a carrier spacecraft, known as a mothership, and is equipped with orbital and attitude control actuators to attach to the target debris, stabilize its attitude, and subsequently move the debris to a lower orbit where atmospheric drag is high enough for the bodies to burn up. The mass and orbit altitude of debris objects that are within the realms of the CubeSat’s propulsion capabilities are identified. The attitude control schemes for the detumbling and deorbiting phases of the mission are specified. The objective of the deorbiting maneuver is to decrease the semi-major axis of the debris orbit, at the fastest rate, from its initial value to a final value of about 6471 km (i.e., 100 km above Earth considering a circular orbit) via a continuous low-thrust orbital transfer. Two case studies are investigated to verify the performance of the deorbiter CubeSat during the detumbling and deorbiting phases of the mission. The baseline target debris used in the study are the decommissioned KOMPSAT-1 satellite and the Pegasus rocket body. The results show that the deorbiting times for the target debris are reduced significantly, from several decades to one or two years.

An image-based servo controller for the guidance of a spacecraft during non-cooperative rendezvous is presented in this paper. The controller directly utilizes the visual features from image frames of a target spacecraft for computing both attitude and orbital maneuvers concurrently. The utilization of adaptive optics, such as zooming cameras, is also addressed through developing an invariant-image servo controller. The controller allows for performing rendezvous maneuvers independently from the adjustments of the camera focal length, improving the performance and versatility of maneuvers. The stability of the proposed control scheme is proven analytically in the invariant space, and its viability is explored through numerical simulations.

The optimization of an LEO cooperative multi-spacecraft refueling mission considering the J 2 perturbation and target’s surplus propellant constraint is studied in the paper. First, a mission scenario is introduced. One service spacecraft and several target spacecraft run on an LEO near-circular orbit, the service spacecraft rendezvouses with some service positions one by one, and target spacecraft transfer to corresponding service positions respectively. Each target spacecraft returns to its original position after obtaining required propellant and the service spacecraft returns to its original position after refueling all target spacecraft. Next, an optimization model of this mission is built. The service sequence, orbital transfer time, and service position are used as deign variables, whereas the propellant cost is used as the design objective. The J 2 perturbation, time constraint and the target spacecraft’s surplus propellant capability constraint are taken into account. Then, a hybrid two-level optimization approach is presented to solve the formulated mixed integer nonlinear programming (MINLP) problem. A hybrid-encoding genetic algorithm is adopted to seek the near optimal solution in the up-level optimization, while a linear relative dynamic equation considering the J 2 perturbation is used to obtain the impulses of orbital transfer in the low-level optimization. Finally, the effectiveness of the proposed model and method is validated by numerical examples.

In this article, a novel approach is introduced for the satellite constellation reconfiguration based on Lambert’s theorem. Some critical problems are raised in reconfiguration phase, such as overall fuel cost minimization, collision avoidance between the satellites on the final orbital pattern, and necessary maneuvers for the satellites in order to be deployed in the desired position on the target constellation. To implement the reconfiguration phase of the satellite constellation arrangement at minimal cost, the hybrid Invasive Weed Optimization/Particle Swarm Optimization (IWO/PSO) algorithm is used to design sub-optimal transfer orbits for the satellites existing in the constellation. Also, the dynamic model of the problem will be modeled in such a way that, optimal assignment of the satellites to the initial and target orbits and optimal orbital transfer are combined in one step. Finally, we claim that our presented idea i.e. coupled non-simultaneous flight of satellites from the initial orbital pattern will lead to minimal cost. The obtained results show that by employing the presented method, the cost of reconfiguration process is reduced obviously.

The problem of two-tangent-impulse space target flyby is drawn in this paper. Unlike the traditional method, the transfer orbit is divided into two parts, i.e. the phasing orbit and the approaching orbit, considering the temporal and the spatial constraint respectively. The method of the phasing orbit and approaching orbit determination is formulated firstly. Then, the attainable target areas from a given position on the initial elliptic orbit, the feasible impulse position for approaching to a given point in space and the optimal approaching orbit to a given point are analyzed. Based on the optimal approaching orbit, the optimal solution for target flyby is provided in the time free case, and a suboptimal solution for the case of time-constrained. Numerical simulations demonstrate the application of the solutions to space target flyby in different scenarios.

Made available in DSpace on 2018-12-11T17:27:20Z (GMT). No. of bitstreams: 0 Previous issue date: 2016-02-15 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Space missions to visit small bodies of the Solar System are important steps to improve our knowledge of the Solar System. Usually those bodies do not have well known characteristics, as their gravity field, which make the mission planning a difficult task. The present paper has the goal of studying orbits around the triple asteroid 2001SN263, a Near-Earth Asteroid (NEA). A mission to this system allows the exploration of three bodies in the same trip. The distances reached by the spacecraft from those three bodies have fundamental importance in the quality of their observations. Therefore, the present research has two main goals: (i) to develop a semi-analytical mathematical model, which is simple, but able to represent the main characteristics of that system; (ii) to use this model to find orbits for a spacecraft with the goal of remaining the maximum possible time near the three bodies of the system, without the need of space maneuvers. This model is called Precessing Inclined Bi-Elliptical Problem with Radiation Pressure (PIBEPRP). The use of this model allow us to find important natural orbits for the exploration of one, two or even the three bodies of the system. These trajectories can be used individually or combined in two or more parts using orbital maneuvers. National Institute for Space Research São Paulo State University FEG/UNESP São Paulo State University FEG/UNESP CNPq: 2011/08171-3 CNPq: 2011/13101-4 CNPq: 2012/21023-6 CNPq: 2014/06688-7

The scheduling problem of multiple geosynchronous satellites refueling mission with a servicing satellite and a fuel station is studied in this paper. In the proposed mission scenario, a number of geosynchronous satellites require a specified weight of fuel to be delivered. The servicing satellite and the fuel station are initially parked in the geosynchronous Earth orbit (GEO). The capacitated servicing satellite is expected to visit and refuel these fuel-deficient GEO targets with the fuel received from the fuel station. In general, the fuel station will refuel the servicing satellite more than once. The refueling order and binary decision variable are used as design variables, whereas the total fuel consumed by orbital maneuvers is used as a design objective. A one-level optimization model and a two-level optimization model are formulated to find the optimal refueling order and decision variable. Genetic algorithm (GA) is employed to address the one-level optimization problem. For the two-level optimization problem, the up-level GA that optimizes the refueling order is combined with the low-level random search that can quickly locate the near-optimal binary decision variable. Finally, the proposed methods are applied to numerical test cases to demonstrate that they are valid for mission planning optimization for multiple GEO targets refueling.

Several possibilities of launching a space vehicle from the orbital station are considered and compared. Orbital maneuvers discussed in the paper can be useful in designing a trajectory for a specific space mission. The relative motion of orbiting bodies is investigated on examples of spacecraft rendezvous with the space station that stays in a circular orbit around the Earth. An elementary approach is illustrated by an accompanying simulation computer program and supported by a mathematical treatment based on fundamental laws of physics and conservation laws. Material is appropriate for engineers and other personnel involved in space exploration, undergraduate and graduate students studying classical physics and orbital mechanics.

The present research studies Swing-By maneuvers combined with the application of an impulse at the spacecraft periapsis passage. The studies were made for different values of r p (periapsis distance), δ V (magnitude of the impulse), Ψ (angle of approach) and α (angle that defines the direction of the impulse). The results show the best direction to apply the impulse for each specific geometry of the passage, maximizing the gains or energy losses. The results show, as an example, that an angle α near 20° gives the best solution to maximize the energy gains for the situation where the periapsis distance is 1.1 Moon’s radius and Ψ = 90 ° . This value goes to near - 20 ° when Ψ = 270 ° . In the case of maximizing the energy losses, two families with impulses against the direction of the spacecraft motion are found to be the best solutions. Conditions where the impulse generates a capture around the Moon or a collision are also mapped. For values larger than 1.1 Moon’s radius for the periapsis distance, the angle that maximizes the energy variation increases. Empirical analytical equations are obtained that express the energy variation as a function of the angle of approach, which replaces well-known equations obtained from the two-body approximation.

The scheduling of multispacecraft refueling based on cooperative maneuver in a circular orbit is studied in this paper. In the proposed scheme, both of the single service vehicle (SSV) and the target satellite (TS) perform the orbital transfer to complete the rendezvous at the service places. When a TS is refueled by the SSV, it returns to its original working slot to continue its normal function. In this way, the SSV refuels the TS one by one. A MINLP model for the mission is first built, then a two-level hybrid optimization approach is proposed for determining the strategy, and the optimal solution is successfully obtained by using an algorithm which is a combination of Multi-island Genetic Algorithm and Sequential Quadratic Programming. Results show the cooperative strategy can save around 27.31% in fuel, compared with the non-cooperative strategy in which only the SSV would maneuver in the example considered. Three conclusions can be drawn based on the numerical simulations for the evenly distributed constellations. Firstly, in the cooperative strategy one of the service positions is the initial location of the SSV, other service positions are also target slots, i.e. not all targets need to maneuver, and there may be more than one TS serviced in a given service position. Secondly, the efficiency gains for the cooperative strategy are higher for larger transferred fuel mass. Thirdly, the cooperative strategy is less efficient for targets with larger spacecraft mass.

In order to maintain optimal signal coverage, GNSS satellites have to experience orbital maneuvers. For China’s COMPASS system, precise orbit determination (POD) as well as rapid orbit recovery after maneuvers contribute to the overall Positioning, Navigation and Timing (PNT) service performance in terms of accuracy and availability. However, strong statistical correlations between clock offsets and the radial component of a satellite’s positions require long data arcs for POD to converge. We propose here a new strategy which relies on time synchronization between ground tracking stations and in-orbit satellites. By fixing satellite clock offsets measured by the satellite station two-way synchronization (SSTS) systems and receiver clock offsets, POD and orbital recovery performance can be improved significantly. Using the Satellite Laser Ranging (SLR) as orbital accuracy evaluation, we find the 4-hr recovered orbit achieves about 0.71 m residual root mean square (RMS) error of fit SLR data, the recovery time is improved from 24-hr to 4-hr compared with the conventional POD without time synchronization support. In addition, SLR evaluation shows that for 1-hr prediction, about 1.47 m accuracy is achieved with the new proposed POD strategy.

A new approach of formation initialization called separation initialization method was presented, using spring separation mechanism to release payload satellites one by one and enable them formation flying without any orbital maneuver. Firstly, the effect of relative motion caused by on-orbit separation was analyzed ideally by Hill–Clohessy–Wiltshire equations, while considering each separation as a velocity increment for payload satellite. Based on this analysis, the initial formation configuration was described in a series of closed relative motion ellipses by separation parameters, including the direction and size of ΔV for each payload satellite, and the time interval between two separations. Then, typical schemes of separation initialization were designed for the incompact formation and the combined incompact CartWheel formation. For separation ΔV of 1–3 m/s, the short semi axis of the formed relative motion ellipses are about 1–10 km in Low Earth Orbit, and 15–40 km in Geostationary Earth Orbit. At last, the stability of formed initial configurations was analyzed considering J2 perturbation. In order to prevent their along-track secular drifts, the constraints of separation ΔV based on linearized equations of relative motion were also improved by the constraint of J2-invariant. A few examples were developed to verify the theoretical analysis and to evaluate application schemes. Results show that the separation initialization method could provide stable formations in two weeks or more in Low Earth Orbit for small satellites cooperation without propulsion systems, and the formations could be kept even longer for a higher reference orbit.

This paper is concerned with two-impulse transfers from Earth to Earth–Moon L 3 halo orbits. After an orbit injection maneuver from an Earth orbit, a spacecraft travels on a ballistic accelerated manifold trajectory to a position intersection with a halo orbit where an orbit injection maneuver is executed. Although many types of transfers are located, our primary concern is transfers that require either a low transfer time of flight or a small orbit injection maneuver. Several families of transfers lie along the edge of a time of flight/injection maneuver Pareto Front. These families share similar characteristics and are shown to be an extension of a transfer that utilizes a stable invariant manifold. The quickest family of transfers to L 3 can be completed in 28.5–33 days with an injection maneuver of 61.75–130 m/s, with shorter duration transfers requiring a larger injection maneuver. The family of transfers with the smallest injection maneuvers given a duration limit of 140 days required 13.45 m/s.

An extensive analysis of the gravitational capture of a spacecraft by Jupiter is performed for the main regions of interest around this planet. Four different dynamical models are used to study the problem. Our methodology is analogous to the one used to study the gravitational capture maneuvers in the Earth-Moon system. However, here the motion of the spacecraft is free to occupy the three-dimensional space rather than been limited to the orbital plane of the primaries, that is the most usual approach available in the literature. Similarly to what was done in the Earth-Moon system, the two-body energy Jupiter-spacecraft is monitored all the time and an impulsive maneuver should be applied to complete the capture when the spacecraft reaches the periapsis of the close approach trajectory. Our results show that the presence of the oblateness of Jupiter in the dynamical model is essential to obtain lower values for the two-body energy in times that are not too long for practical missions. The Galilean satellites are also very important, and despite their contribution in the gravitational capture maneuver itself, they can be used as a source of swing-bys that decrease the two-body energy Jupiter-spacecraft.

The present paper has the goal of mapping orbits, with respect to the perturbations, for a spacecraft traveling around the asteroid 2001SN 263 . This asteroid is a triple system, which center of mass is in an elliptic orbit around the Sun. The perturbations considered in the present model are the ones due to the oblateness of the central body, the gravity field of the two satellite bodies (Beta and Gamma), the Sun, the Moon, the asteroids Vesta, Pallas and Ceres and all the planets of the Solar System. This mapping is important, because it shows the relative importance of each force for a given orbit for the spacecraft, helping to make a decision about which forces need to be included in the model for a given accuracy and nominal orbit. Another important application of this type of mapping is to find orbits that are less perturbed, since it is expected that those orbits have good potential to require a smaller number of station-keeping maneuvers. Simulations under different conditions are made to find those orbits. The main reason to study those trajectories is that, currently, there are several institutions in Brazil studying the possibility to make a mission to send a spacecraft to this asteroid (the so-called ASTER mission), because there are many important scientific studies that can be performed in that system. The results showed that Gamma is the main perturbing body, followed by Beta (10 times smaller) and the group Sun–Mars-oblateness of Alpha, with perturbations 1000 times weaker than the effects of Gamma. The other bodies have perturbations 10 7 times smaller. The results also showed that circular and polar orbits are less perturbed, when compared to elliptical and equatorial orbits. Regarding the semi-major axis, an internal orbit is the best choice, followed by a larger external orbit. The inclination of the orbit plays an important role, and there are values for the inclination where the perturbations show minimum and maximum values, so it is important to make a good decision on those values.

By developing approximate analytical models considering the J2 perturbation, the effects of an in-track maneuver on the orbital Sun illumination conditions of near-circular low Earth orbits are analyzed. First, two approximate models for the variations in orbital sunshine angles are developed, one for variations at a given time and the other for variations at a given argument of latitude. Next, two approximate models for variations in orbital arc in Earth shadow are developed, one considers the small eccentricity and the other uses the zero eccentricity. Finally, the developed approximate models are applied to analyzing the Sun illumination conditions of a typical in-track maneuver mission on a near-circular low Earth orbit. From the results obtained, three major conclusions can be drawn. First, the variations in orbital sunshine angles at a given time may reach tens of degrees when the drifting time reaches hundreds of orbital periods, and the approximate model for that situation cannot effectively approach the numerical results. Second, the variations in orbital sunshine angles for any given argument of latitude are only a couple of degrees even when the drifting time reaches 500 orbital periods, and the approximation model developed can effectively approach the numerical results. Third, for variations in orbital arc in Earth shadow, the approximate model considering the small eccentricity has simple expressions and can effectively approach the numerical results; in contrast, the approximate model using the zero eccentricity has relatively worse precision.

To achieve hovering, a spacecraft thrusts continuously to induce an equilibrium state at a desired position. Due to the constraints on the quantity of propellant onboard, long-time hovering around low-Earth orbits (LEO) is hardly achievable using traditional chemical propulsion. The Lorentz force, acting on an electrostatically charged spacecraft as it moves through a planetary magnetic field, provides a new propellantless method for orbital maneuvers. This paper investigates the feasibility of using the induced Lorentz force as an auxiliary means of propulsion for spacecraft hovering. Assuming that the Earth’s magnetic field is a dipole that rotates with the Earth, a dynamical model that characterizes the relative motion of Lorentz spacecraft is derived to analyze the required open-loop control acceleration for hovering. Based on this dynamical model, we first present the hovering configurations that could achieve propellantless hovering and the corresponding required specific charge of a Lorentz spacecraft. For other configurations, optimal open-loop control laws that minimize the control energy consumption are designed. Likewise, the optimal trajectories of required specific charge and control acceleration are both presented. The effect of orbital inclination on the expenditure of control energy is also analyzed. Further, we also develop a closed-loop control approach for propellantless hovering. Numerical results prove the validity of proposed control methods for hovering and show that hovering around low-Earth orbits would be achievable if the required specific charge of a Lorentz spacecraft becomes feasible in the future. Typically, hovering radially several kilometers above a target in LEO requires specific charges on the order of 0.1 C/kg.

Three major features make Europa a unique scientific target for a lander-oriented interplanetary mission: (1) the knowledge of the composition of the surface of Europa is limited to interpretations of the spectral data, (2) a lander could provide unique new information about outer parts of the solar system, and (3) Europa may have a subsurface ocean that potentially may harbor life, the traces of which may occur on the surface and could be sampled directly by a lander. These characteristics of Europa bring the requirement of safe landing to the highest priority level because any successful landing on the surface of this moon will yield scientific results of fundamental importance. The safety requirements include four major components. (1) A landing site should preferentially be on the anti-Jovian hemisphere of Europa in order to facilitate the orbital maneuvers of the spacecraft. (2) A landing site should be on the leading hemisphere of Europa in order to extend the lifetime of a lander and sample pristine material of the planet. (3) Images with the highest possible resolution must be available for the selection of landing sites. (4) The terrain for landing must have morphology (relief) that minimizes the risk of landing and represents a target that is important from a scientific point of view. These components severely restrict the selection of regions for landing on the surface of Europa. After the photogeologic analysis of all Galileo images with a resolution of better than about 70 m/pixel taken for the leading hemisphere of Europa, we propose one primary and two secondary (backup) landing sites. The primary site (51.8°S, 177.2°W) is within a pull-apart zone affected by a small chaos. The first backup site (68.1°S, 196.7°W) is also inside of a pull-apart zone and is covered by images of the lower resolution (51.4 m/pixel). The second backup site (2.4°N, 181.1°W) is imaged by relatively low-resolution images (∼70 m/pixel) and corresponds to a cluster of small patches of dark and probably smooth plains that may represent landing targets of the highest scientific priority from the scientific point of view. The lack of the high-resolution images for this region prevents, however, its selection as the primary landing target.

The dynamics of the restricted three-body Earth–Moon-particle problem predicts the existence of direct periodic orbits around the Lagrangian equilibrium point L1. From these orbits, we derive a set of trajectories that form links between the Earth and the Moon and are capable of performing transfers between terrestrial and lunar orbits, in addition to defining an escape route from the Earth–Moon system. When we consider a more complex and realistic dynamical system – the four-body Sun–Earth–Moon-particle (probe) problem – the trajectories have an expressive gain of inclination when they penetrate in the lunar influence sphere, thus allowing the insertion of probes into low-altitude lunar orbits with high inclinations, including polar orbits. In this study, we present these links and investigate some possibilities for performing an Earth–Moon transfer based on these trajectories.

The lunar sphere of influence, whose radius is some 66,300 km, has regions of stable orbits around the Moon and also regions that contain trajectories which, after spending some time around the Moon, escape and are later recaptured by lunar gravity. Both the escape and the capture occur along the Lagrangian equilibrium points L1 and L2. In this study, we mapped out the region of lunar influence considering the restricted three-body Earth–Moon–particle problem and the four-body Sun–Earth–Moon–particle (probe) problem. We identified the stable trajectories, and the escape and capture trajectories through the L1 and L2 in plots of the eccentricity versus the semi-major axis as a function of the time that the energy of the osculating lunar trajectory in the two-body Moon–particle problem remains negative. We also investigated the properties of these routes, giving special attention to the fact that they supply a natural mechanism for performing low-energy transfers between the Earth and the Moon, and can thus be useful on a great number of future missions.

A gravitational capture occurs when a spacecraft (or any particle with negligible mass) changes from a hyperbolic orbit with a small positive energy around a celestial body into an elliptic orbit with a small negative energy without the use of any propulsive system. The force responsible for this modification in the orbit of the spacecraft is the gravitational force of the third and the fourth bodies involved in the dynamics. In this way, those forces are used as a zero cost control, equivalent to a continuous thrust applied in the spacecraft. One of the most important applications of this property is the construction of trajectories to the Moon to minimize fuel consumption. The concept of gravitational capture is used, together with the basic ideas of the gravity-assisted maneuver and the bi-elliptic transfer orbit, to generate a trajectory that requires fuel consumption smaller than the one required by the Hohmann transfer. The objective of the present paper is to study the time required for the ballistic gravitational capture in a dynamical model that has the presence of four bodies. In particular, the Earth–Moon–Sun–Spacecraft system is considered.

Collinear libration points of the restricted three body problem (RTBP) play a key role in deep space exploration, due to the fact that they are ideal locations for the spacecraft (such as SOHO) with special purposes. The nominal orbit of the spacecraft is conditionally stable but virtually unstable, and will exponentially diverge from the nominal orbit under small perturbations. If the spacecraft is inserted to the stable manifold associated with the collinear libration points, it will approach the nominal orbit without any more maneuvers, and the total fuel consumption will be reduced. For the nominal orbit of small amplitude, the manifold can not approach the Earth. In this case a direct transfer from the parking orbit, such as low earth orbit (LEO) around the vicinity of the Earth to the manifold will be impossible. Nevertheless, in the real solar system, the Moon bends some of the manifolds to approach the Earth. Based on this consideration, this paper takes the transfer of a spacecraft around L2 of the Sun–Earth system as an example and study the Lunar effect in the transfer of the spacecraft. With the help of the Moon, in the case the transfer could be still not achieved with only one maneuver, but the total fuel consumption is saved by around 100 m/s.

In the present paper, we present an analytical description of the powered swing-by maneuver in the three-dimensional space. To perform this task, new analytical equations are derived for the three-dimensional unpowered swing-by, including the variation in velocity, angular momentum, energy and inclination of the spacecraft due to the maneuver. This is done based on the patched-conics approximation. From those general three-dimensional equations, it is possible to confirm some well-known analytical results for the planar case. The equations developed here are verified by numerical integrations, using the restricted problem of three bodies, showing an agreement better than 1%. After that, based on those equations, some new analytical results are obtained for the situation when an impulse is applied to the spacecraft during the close approach. Those new equations are based in the assumption that the impulse applied is small compared to the velocity of the spacecraft, and they allow the calculation of the same variations cited above. Those equations can be simplified for specific cases, and it can generate some conclusions about the direction to apply the impulse to attend specific goals. A study is also executed to investigate in which cases the impulse is more efficient when applied at the periapsis of the swing-by hyperbola or at points far way from the swing-by body.

The objective of the present paper is to study the ballistic gravitational capture performed by the first primary in a system formed by three bodies: a large central mass, the primary, a second small body that is in orbit of the primary, the secondary, and a massless particle that is moving around the two primaries. The forces involved in this system are explained and analytical equations for their effects are derived, based on the integral of their effects with respect to time from the entrance of the massless body in the sphere of influence of the primary until the periapsis of its trajectory. Then, closed form approximate equations are obtained to estimate the magnitude of its effects and to show the best directions of approach for the maneuver.

In this research, we study trajectories that make a close approach with the planet Jupiter. The main goal is to obtain the velocity increments required to start or to stop the spacecraft at the Earth and the flight path angle at the meeting point for trajectories that cross the Earth’s orbit around the Sun before or after the passage by Jupiter. The regularized planar restricted circular three-body problem is used as the mathematical model. Several trajectories are found and shown in detail, including the impulses required for those maneuvers.

The interplanetary orbits of three pairs of spacecraft, forming three laser interferometers, are designed such that their separations, i.e. the lengths of the interferometer arms, remain nearly constant. Each spacecraft pair is located near the vertex of a rotating equilateral triangle formed by the individual orbits of the spacecraft about the Sun. Feasible spacecraft masses are computed for a scenario with an Ariane 5 launch into a Geostationary Transfer Orbit (GTO) and a three-burn transfer from the GTO to the triangular configuration. The relative motion is perturbed by planetary gravity. However, the arm rate differences degrading the interferometer accuracy can be kept below certain limits by choosing optimum initial conditions and/or by controlling them by occasional orbit adjustment manoeuvres. The achievable orbit determination accuracy is given for systems processing two-way range and Doppler data collected on ground and/or laser interferometer measurements of the rate of change of distance between spacecraft.

Artificial satellites around the Earth can be temporarily captured by the Moon via gravitational mechanisms. How long the capture remains depends on the phase space region where the trajectory is located. This interval of time (capture time) ranges from less than one day (a single passage), up to 500 days, or even more. Orbits of longer times might be very useful for certain types of missions. The advantage of the ballistic capture is to save fuel consumption in an orbit transference from around the Earth to around the Moon. Some of the impulse needed in the transference is saved by the use of the gravitational forces involved. However, the time needed for the transference is elongated from days to months. In the present work we have mapped a significant part of the phase space of the Earth-Moon system, determining the length of the capture times and the origin of the trajectory, if it comes from the Earth direction, or from the opposite direction. Using such map we present a set of missions considering the utilization of the long capture times.

A non-singular analytical theory for the contraction of high eccentricity orbits (eccentricity e > 0.5) under the influence of air drag is developed in terms of the KS elements, using an oblate exponential atmospheric model. With the help of MACSYMA software, the series expansions include up to the sixth power in terms of an independent variable λ, introduced by Sterne as cos E =1 − H λ2a e, where E and a are the eccentric anomaly and semi-major axis of the orbit and H, the density scale height, is assumed constant. The solution is tested numerically over a wide range of orbital parameters: perigee height (Hp), e and inclination (i) up to 100 revolutions and is found to be quite accurate. The % error in the semi-major axis computation when compared with numerically integrated values, for test cases whose perigee heights vary from 150 to 300 km and eccentricities increase from 0.6 to 0.8, is found to be less than one. The decay rates of a and e are found to be lower than those obtained with spherically symmetrical atmospheric models and increasing with increase in inclination. The theory can be effectively used for the orbital decay of Molniya type of communication satellites, decay of geostationary transfer orbits and during mission planning of aeroassisted orbital transfer orbits.

The probability of collision between a spacecraft and another object is calculated for various altitude and orbit conditions, and factors affecting the probability are discussed. It is shown that a collision can only occur when the spacecraft is located at an altitude which is between the perigee and apogee altitudes of the object and that the probability per unit time is largest when the orbit of the object is nearly circular. However, at low altitudes, the atmospheric drag causes changes with time of the perigee and the apogee, such that circular orbits have a much shorter lifetime than many of the elliptical orbits. Thus, when the collision probability is integrated over the lifetime of the orbiting object, some elliptical orbits are found to have much higher total collision probability than circular orbits. Rocket bodies used to boost payloads from low earth orbit to geosynchronous orbit are an example of objects in these elliptical orbits.

An international research laboratory can be established on the Moon in the early years of the 21st Century. It can be built using the transportation system now envisioned by NASA, which includes a space station for Earth orbital logistics and orbital transfer vehicles for Earth-Moon transportation. A scientific laboratory on the Moon would permit extended surface and subsurface geological exploration; long-duration experiments defining the lunar environment and its modification by surface activity; new classes of observations in astronomy; space plasma and fundamental physics experiments; and lunar resource development. The discovery of a lunar source for propellants may reduce the cost of constructing large permanent facilities in space and enhance other space programs such as Mars exploration.