Parking Orbit Research Articles

Special Refill Spacecraft Debris Collector, Equipped with Electro Rocket Engine of Low-thrust, Design Parameters Optimization

The problem of near Earth space debris is studied in this article. A special spacecraft debris collector, equipped with electro rocket engine of low-thrust, for large space debris disposal is introduced. The mass model of spacecraft debris collector, one-off or reusable, is obtained. Ballistic scheme, spacecraft debris collector orbital transfer from parking orbit to space debris orbit, its disposal in Earth atmosphere and reusable spacecraft return to the parking orbit are studied. For the introduced criteria of transport transfer efficiency and assumption about consistency of acceleration from thrust, analytical relations for spacecraft design parameters calculation are obtained. The design parameters calculation results are shown in a generalized form.

Conceptual design of the space disposal system for the highly radioactive component of the nuclear waste

A system for space disposal of the most radioactive component of the spent fuel produced by the nuclear reactors is designed conceptually with an intent of ensuring safety. Unlike the earlier design by NASA, this system is to use a commercially available launch vehicle and be launched from the western Pacific Ocean. It will fly low until it acquires Earth-escape velocity, so that the nuclear package will not fall on land in case of system malfunctioning. The package will be parked in one of the lunar libration points L4 or L5, and kept vigilant by a watch-dog orbital transfer vehicle which will push the package away in case an asteroid approaches. The calculation shows that such a safe system will be feasible and relatively cheap. The details of how the nuclear package is made, how the launch vehicle is made and flown, and how the nuclear package is managed in the final parking orbit are described.

On-Board Orbit Propagator and Orbit Data Compression for Lunar Explorer using B-spline

In this paper, an on-board orbit propagator and compressing trajectory method based on B-spline for a lunar explorer are proposed. An explorer should recognize its own orbit for a successful mission operation. Generally, orbit determination is periodically performed at the ground station, and the computed orbit information is subsequently uploaded to the explorer, which would generate a heavy workload for the ground station and the explorer. A high-performance computer at the ground station is employed to determine the orbit required for the explorer in the parking orbit of Earth. The method not only reduces the workload of the ground station and the explorer, but also increases the orbital prediction accuracy. Then, the data was compressed into coefficients within a given tolerance using B-spline. The compressed data is then transmitted to the explorer efficiently. The data compression is maximized using the proposed methods. The methods are compared with a fifth order polynomial regression method. The results show that the proposed method has the potential for expansion to various deep space probes.

Heliocentric phasing performance of electric sail spacecraft

We investigate the heliocentric in-orbit repositioning problem of a spacecraft propelled by an Electric Solar Wind Sail. Given an initial circular parking orbit, we look for the heliocentric trajectory that minimizes the time required for the spacecraft to change its azimuthal position, along the initial orbit, of a (prescribed) phasing angle. The in-orbit repositioning problem can be solved using either a drift ahead or a drift behind maneuver and, in general, the flight times for the two cases are different for a given value of the phasing angle. However, there exists a critical azimuthal position, whose value is numerically found, which univocally establishes whether a drift ahead or behind trajectory is superior in terms of flight time it requires for the maneuver to be completed. We solve the optimization problem using an indirect approach for different values of both the spacecraft maximum propulsive acceleration and the phasing angle, and the solution is then specialized to a repositioning problem along the Earth's heliocentric orbit. Finally, we use the simulation results to obtain a first order estimate of the minimum flight times for a scientific mission towards triangular Lagrangian points of the Sun−[Earth+Moon] system.

Rendezvous missions to temporarily captured near Earth asteroids

Missions to rendezvous with or capture an asteroid present significant interest both from a geophysical and safety point of view. They are key to the understanding of our solar system and are stepping stones for interplanetary human flight. In this paper, we focus on a rendezvous mission with 2006 RH120, an asteroid classified as a Temporarily Captured Orbiter (TCO). TCOs form a new population of near Earth objects presenting many advantages toward that goal. Prior to the mission, we consider the spacecraft hibernating on a Halo orbit around the Earth–Moon׳s L2 libration point. The objective is to design a transfer for the spacecraft from the parking orbit to rendezvous with 2006 RH120 while minimizing the fuel consumption. Our transfers use indirect methods, based on the Pontryagin Maximum Principle, combined with continuation techniques and a direct method to address the sensitivity of the initialization. We demonstrate that a rendezvous mission with 2006 RH120 can be accomplished with low delta-v. This exploratory work can be seen as a first step to identify good candidates for a rendezvous on a given TCO trajectory.

Optimization of low-thrust transfers to libration point orbits

Purpose – The purpose of this paper is to develop a superconvergent trajectory optimization method for the design of low-thrust transfer trajectories from parking orbit to libration point orbits near the collinear libration points. Design/methodology/approach – The optimization method is developed by merging the concept of Lyapunov feedback control law with the manifold dynamics. First, the whole transfer trajectory is divided into two segments, raising segment and coast segment. Then, the trajectories of each segment are described in different coordinate frames, and designed with Lyapunov feedback control law and the manifold dynamics, respectively. The Poincare section is used as an effective tool to search the compatible patching point between these two segments on the manifold. Finally, the transfer trajectory is optimized using sequential quadratic programming. Findings – In the numerical simulation, the proposed optimization method does not have any convergence problem. It is a fast and effective me...

Design of robotic manipulators for orbit removal of spent launchers’ stages

This paper deals with the main drivers for the design of a space manipulator aimed to the removal of the final stages which remain in Low Earth Orbit after releasing their payloads. At the scope, the different phases of a debris removal mission are considered, starting from the parking orbit where the servicing spacecraft equipped with the manipulator (chaser) waits for the call on duty, encompassing the approach to the target and its grasping and finally dealing with the dismissal of the captured object. The characteristics and requirements of each phase, in terms of torques to be applied to the joints of the manipulator(s) and to the forces to be generated via thrusters at the system level, are analysed. The number of robotic arms, the number of joints of each arm, and the torque level that each joint motor should supply are mainly defined by the grasping phase and the de-orbit phase. During the grasping, the tumbling target must be tracked with a large degree of robustness, and, to this aim, a redundant manipulator must be designed, so that its workspace can be as large as possible. On the other hand, increasing the degrees of freedom of a robotic arm means higher complexity and manufacturing costs. The number of arms depends also on the final de-orbit phase, in which the powerful apogee motor of the chaser satellite is ignited to change the composite system (chaser+target) orbit. The thrust, applied on the chaser, is transferred to the target by means of the manipulator(s): it is shown that a single robotic arm could not be sufficient to withstand the high stress acting during this phase. The torques at the joints required to maintain the arms in the desired configuration end up to be very high too, and the motors – as well as in general the structural elements of the arms – should be sized according to this phase of the mission.

Exploring the Moon gravity to escape from the Earth–Moon system

Escape trajectories from the Earth–Moon system can be obtained through a single gravity assist maneuver of a spacecraft with the Moon. This paper presents a semi-analytical study of variations in the semi-major axis and the eccentricity of a spacecraft for a geocentric frame—before and after a close encounter of the spacecraft with the Moon. Studies on the swing-by dynamics between a spacecraft and the Moon were performed in order to establish a set of initial conditions in terms of eccentricities and semi-major axes of geocentric initial orbits. This way, it was possible identify which orbits, launched from Earth parking orbits, accomplish swing-bys with the Moon and generate escape trajectories.

Precise halo orbit design and optimal transfer to halo orbits from earth using differential evolution

The mission design to a halo orbit around the libration points from Earth involves two important steps. In the first step, we design a halo orbit for a specified size and in the second step, we obtain an optimal transfer trajectory design to the halo orbit from an Earth parking orbit. Conventionally, the preliminary design for these steps is obtained using higher order analytical solution and the dynamical systems theory respectively. Refinements of the design are carried out using gradient based methods such as differential correction and pseudo arc length continuation method under the of circular restricted three body model. In this paper, alternative single level schemes are developed for both of these steps based on differential evolution, an evolutionary optimization technique. The differential evolution based scheme for halo orbit design produces precise halo orbit design avoiding the refinement steps. Further, in this approach, prior knowledge of higher order analytical solutions for the halo orbit design is not needed. The differential evolution based scheme for the transfer trajectory, identifies the precise location on the halo orbit that needs minimum energy for insertion and avoids exploration of multiple points. The need of a close guess is removed because the present scheme operates on a set of bounds for the unknowns. The constraint on the closest approach altitude from Earth is handled through objective function. The use of these schemes as the design and analysis tools within the of circular restricted three body model is demonstrated through case studies for missions to the first libration point of Sun–Earth system.

Electron density profiles probed by radio occultation of FORMOSAT-7/COSMIC-2 at 520 and 800 km altitude

Abstract. The FORMOSAT-7/COSMIC-2 (F7/C2) will ultimately place 12 satellites in orbit with two launches with 24–28.5° inclination and 520–550 km altitude in 2016 and with 72° inclination and 720–750 km altitude in 2018. It would be very useful for the community to construct the global three-dimensional electron density structure by simultaneously combining the two launch observations for studying ionospheric structure and dynamics. However, to properly construct the global electron density structure, it is essential to know and evaluate differences between the ionospheric electron densities probed by the two launches. To mimic the F7/C2 observations, we examine the electron density probed at the two satellite altitudes 500 and 800 km by means of FORMOSAT-3/COSMIC (F3/C) observations at the parking orbit 500 km altitude and mission orbit 800 km altitude, as well as a corresponding observing system simulation experiment (OSSE). Observation and OSSE results show that the sounding geometries by satellite orbiting at 500 and 800 km altitudes can cause the overall differences in the electron density, the F2 peak electron density, and the F2 peak height of about 18–24, 12–28 %, and 7–19 km, respectively. Results confirm that the discrepancies mainly result from the sounding geometry and the grid (contour) bias of the electron density.

A realistic concept of a manned Mars mission with nuclear–electric propulsion

Based on state-of-the-art technique and recent developments, it would be feasible to send some cosmonauts to Mars around 2035. The key to this enterprise is the nuclear–electric in-space propulsion (NEP). In 2010, the development of the 1MWe nuclear space power plant as well as of the ion thrusters with the ion beam diameter of 50cm and specific impulse of 7000s was started at the Keldysh Research Center in Moscow. With regard to thrusters, the Keldysh Research Center cooperated with the Moscow Aviation Institute. According to our analysis, a cluster of ion thrusters (each of 50kW in power) with three 1MW reactors could propel a 250-tons vehicle with four cosmonauts on board to Mars and back.The mission architecture would be quite straightforward: the still unmanned spaceship will be assembled in the 800km LEO and then spiraled up by NEP into the 200,000km launch orbit. There, the chemical crew transport vehicle will arrive and dock. The interplanetary journey to Mars will require 337 days. On its arrival to Mars, the spaceship will spiral down into the 500km parking orbit. Then, a 65ton descent/ascent vehicle with three or four cosmonauts will leave the NEP vehicle and land. After 218 days, the excursion team will return to the mothership for the homebound trip. At the Earth approach, the cosmonauts will change to the crew transport vehicle, descend and land, whereas the burnt-out ship will be lost in space.It is true that one single spaceship is able to accomplish the mission. However, an international fleet of two or three manned ships together with a cargo ship would be recommendable, not only with regard to the volume of scientific results and a risk reduction, but also to demonstrate solidarity of mankind.

Interplanetary parking method and its applications

In this study, we propose a flexible orbit design method that enables anytime launch of a deep-space explorer. Based on the Electric Delta-V Earth Gravity Assist (EDV-EGA) scheme, (Kawaguchi, 2001, 2002) [1,2] the proposed interplanetary parking method enables the explorer to make an Earth return orbit at an arbitrary time-of-flight by connecting to the minimum energy transfer orbit to destination. While the time-of-flight of the transfer orbit is fixed, the Earth return orbit with the arbitrary time-of-flight significantly alleviates the severe launch window constraint in interplanetary missions. We offer two case examples of applications of this method. The first is the dual launch of a Mars explorer with a geostationary transfer orbit (GTO) mission payload. The second is a dual launch of Mars and Venus explorers by a single launch vehicle. In the first case, we assume that a small Mars explorer is dual launched into a GTO for a secondary payload. With this assumption, the secondary payload cannot choose a desirable launch epoch for itself because the launch window to Mars is very narrow and opens only every 2 years. Moreover, the GTO, whose orbital period is approximately 10h, repeatedly passes through the Van Allen belt wherein the radiation level is very high. Hence, the explorer has to escape from the GTO as soon as possible. However, our proposed interplanetary parking method enables the explorer to reach the destination within the limits of a practical mass resource, regardless of the Earth departure epoch. In the second case, the explorers traveling to different destinations, i.e., Mars and Venus, are dual launched by a single launch vehicle, and they fly to each destination via an interplanetary parking orbit. Our proposed method will widen the scope of opportunity for interplanetary missions.

Design and optimization of low-energy transfer orbit to Mars with multi-body environment

This paper discusses the problem of design and optimization of low-energy transfer orbit with multi-body environment. A new integrative method is proposed to effectively solve the problem, in which the parameterized patched manifolds in CR3BP (circular restricted three-body problems), the shape-based method with multi-body environment, the homotopic method with multi-body environment, and the low-thrust capturing and descending algorithm with multi-body environment are all included. Firstly, the parameters describing the patched manifolds in CR3BP are optimized until the least total absolute velocity increment has been got, including the employment of the shape-based method with multi-body environment. Secondly, the low-thrust control laws of the transfer orbit are optimized employing the homotopic method with multi-body environment that transfers the fuel optimization problem to an easier energy optimization problem. Thirdly, the low-thrust descending orbit around Mars is computed using the laws proposed in this paper. As a typical example, the Earth-Mars transfer orbit design is discussed. The results showed that the parameters describing the patched manifolds could be optimized by the DE (differential evolution) algorithm effectively; the homotopic method with multi-body environment could get the optimal value that meets the first order optimality conditions; and the low-thrust descending orbit could effectively be captured by Mars and finally become a circular parking orbit around it by the hypothesis control laws proposed in this paper. It shows that the final fuel cost is much less than the optimal transfer in the patched two-body problems. In conclusion, the method proposed in this paper could effectively solve the low-energy low-thrust optimal control problem in multi-body environment for the future deep space explorations.

Generation of launch windows for high-accuracy lunar trajectories

The purpose of this paper is to systematically establish in arbitrary timespan a full set of instantaneous ground launch windows for certain accurate three-dimensional asymmetric free return circumlunar trajectories tailored to human lunar missions for China, and in general propose a novel methodology useful for determining ground launch windows for other Earth-to-Moon trajectories.Using time-varying spherical trigonometry, an analytical design method for finding ground launch windows is developed with two-body model assumption. Windows appear when the Moon at arrival time and the Earth parking orbit nodes on lunar orbit plane have similar right ascensions. The numerical first guesses obtained almost instantly are within minutes of accurate solutions and refined to highly accurate trajectories by differential corrections of only one phase. A translunar launch window plot visualizing all monthly and daily launch windows differentiating two types of translunar injections is created.The method proposed can be used for automated generation of complete trajectory sets, and provide the basis for the preparation of launch timetables satisfying lunar mission requirements.

On equatorial inclination of parking orbits in transfers to lunar halo orbits

This paper presents a detailed analysis on the equatorial inclination of Earth parking orbits associated with transfer trajectories to lunar libration point orbits. Orbital inclination in this work is defined with respect to the Earth’s equator other than the lunar orbital plane as commonly adopted in previous works. This definition connects to the convention widely adopted in current aerospace industry, and therefore has practical meanings. By introducing a number of intermediate reference frames, an algorithm to compute the parking orbit’s equatorial inclination is presented. Numerical results show that, for the same transfer trajectory designed in the autonomous framework of CR3BP (circular restricted three-body problem), the value of the equatorial inclination of the departure LEO largely depends on the choice of departure time at which the spacecraft is injected into the transfer trajectory. Two types of major periodicity, both due to the natural motion of the Moon and the Earth, are discovered to play a role in this time dependency. It is concluded that the equatorial inclination of the departure LEO can be varied by as much as 57° through changing the departure times within half a month. Extensive results obtained in this work should provide good reference for the selections of both launch sites and launch windows in all missions involving Earth–Moon libration point orbits.

Autonomous Rendezvous Architecture Design for Lunar Lander

A precise and convenient targeting architecture for accomplishing the rendezvous of a lunar lander with an orbiter in a near-circular lunar parking orbit is proposed in this paper. This procedure enables a systematic design and refinement of the number of thrust impulses, their application times, and the mission duration. The simplicity and accuracy of this targeting procedure makes it well suited for onboard use during real-time control and strategy reconstruction operations. A concise and revealing form of the linearized rendezvous equations is derived based on the Clohessy–Wiltshire model, as adopted to generate feasible initial solutions to satisfy the demands of rapid mission analysis and design. A three-step iterative procedure is adopted to determine the minimum-impulse control strategies for autonomous rendezvous, involving the progress of the solution from a linear model to a nonlinear, two-body model and finally to a high-fidelity model. The two-body model is introduced as an intermediary to enable a smooth transition from the linear to the high-fidelity lunar gravitational model. Numerical simulations are undertaken to verify the control strategies calculated and to illustrate the efficiency and convergence of the proposed iteration algorithm.

Optimal trajectory design to Halo orbits via pseudo-invariant manifolds using a nonlinear four body formulation

This paper investigates the problem of optimal transfer trajectory design towards the L2 centered Halo orbit of the Sun–Earth three body system, where the initial launch is to start from a low Earth parking orbit (LEO). The proposed optimal transfer trajectory consists of an active part with low-thrust propulsion and a passive coasting part with no thrust or fuel consumption. In this respect a pseudo-stable manifold (SM) is initially determined through backward time integration of the bicircular four body (BCFB) equations of motion, whose initial states are obtained via stable manifolds of the restricted three body problem (R3BP). The optimal transfer trajectories are extracted via a hybrid direct–indirect optimization formulation applied on both R3BP as well as the BCFB models for comparative purposes. The optimal transfer trajectories are designed and analyzed for different Halo injection points (HOI), different Moon׳s final anomaly (FMA) and also for different locations of the burn-out conditions.

Choice of design characteristics of «garbage collector» spacecraft with a low-thrust electrojet engine

The paper is devoted to the problem of debris in the near-Earth space. We investigate a method of cleaning the space of large fragments of space debris using a garbage collector spacecraft with a low- thrust electrojet engine. A mass model of one-shot and shuttle spacecraft has been constructed. A mission trajectory plan is presented that includes the spacecraft flight from the parking orbit to that of debris location, its descent to the surface of the Earth and the return of reusable spacecraft to the parking orbit. Analytical relationships for the calculation of the spacecraft design parameters have been obtained for the proposed criterion for evaluating the effectiveness of the logistic space mission and the assumption about constant thrust acceleration. The results of calculation of the design parameters are summarized.

Analytical design methods for determining Moon-to-Earth trajectories

To support China's lunar exploration mission requirements of high-latitude landing and anytime return, i.e., the capability of safely returning the crew exploration vehicle at any time from any lunar parking orbit, an analytical model for determining a transearth trajectory is presented. With a finite sphere of influence model, families of analytical Moon-to-Earth return trajectories are generated and analyzed to observe the characteristics in their Moon departures and Earth encounters. The requirement of high-latitude landing for the return phase trajectory is considered in the modified analytical model. No initial guess is required to generate the analytical solution. The results presented here are limited to a single impulsive maneuver. The difference between the results of the analytical model and a high-fidelity model is compared. This difference is relatively small and can be easily eliminated by a simple differential correction procedure. The solution can be used to establish the orbital launch window for Moon-to-Earth return and to serve as an initial estimate for future optimization procedures.

Optimal interior Earth–Moon Lagrange point transfer trajectories using mixed impulsive and continuous thrust

Optimal interior Earth–Moon Lagrange point transfer trajectories results with fixed flight time using mixed impulsive and continuous thrust propulsion in the framework of the planar Circular Restricted Three-Body Problem are presented. A virtual spacecraft departs geosynchronous or low-Earth orbit and enters a specified Lyapunov orbit around the interior Earth–Moon Lagrange point. For these transfer trajectory designs, a direct transcription and collocation method is employed to reformulate the continuous dynamic optimization problem into a discrete optimization problem, which then is solved using nonlinear programming software. As the design parameters, flight time and relative weighting factor between impulsive and continuous thrust are adjusted in the transfer trajectory design procedure. For practically implementable transfer trajectory designs, the constraints for coast arc and bounded control thrust are applied in the problem formulation as equality and inequality constraints, respectively. In addition, both quadratic performance index and minimum fuel performance index are used to show the relative comparison and analysis in the transfer trajectory design results. According to the relative weighting factor, the transfer trajectories are classified into direct and spiral departure trajectories whose virtual spacecraft directly departs the Earth parking orbit and departs after generating spirals around the Earth, respectively. The convergence of these transfer trajectory design methods are numerically verified by generating varying numbers of nodes and comparing their design results. Especially, the primer vector theory is utilized to analyze the transfer trajectory design results using minimum fuel performance index. Finally, the progressive homotopy continuation method is applied to design low-Earth departure transfer trajectories. These transfer trajectories show that they are numerically and theoretically valid results with the benefit of mixed impulsive and continuous thrust.