Earth Escape Research Articles

Nuclear Thermal Propulsion for Jupiter and Saturn Rendezvous Missions

Highly efficient nuclear thermal propulsion (NTP) can enable a new class of planetary science missions for deep space exploration. This paper presents Jupiter and Saturn rendezvous missions using an NTP system that will focus on end-to-end trajectory analysis. The complexities of Earth escape and planetary orbital insertion using finite burn maneuvers are highlighted. With respect to the mission design problem, NTP-powered missions need to integrate the requirements and constraints of mission objectives, spacecraft design, NTP system design, and launch vehicle limits into a self-consistent model. Using a single high-performance-class commercial launch vehicle with a lift capability to low Earth orbit of 22 metric tons, an NTP-powered mission can deliver NASA’s large strategic science missions in a direct transfer trajectory to Jupiter in 2.1 years and to Saturn in 4.7 years.

Minimum-Time Earth-to-Mars Interplanetary Orbit Transfer Using Adaptive Gaussian Quadrature Collocation

The problem of minimum-time, low-thrust, Earth-to-Mars interplanetary orbital trajectory optimization is considered. The minimum-time orbital transfer problem is modeled as a four-phase optimal control problem where the four phases correspond to planetary alignment, Earth escape, heliocentric transfer, and Mars capture. The four-phase optimal control problem is then solved using a direct collocation adaptive Gaussian quadrature collocation method. The following three models are used in the study: 1) circular planetary motion, 2) elliptic planetary motion, and 3) elliptic planetary motion with gravity perturbations, where the transfer begins in a geostationary orbit and terminates in a Mars-stationary orbit. Results for all three cases are provided, and one particular case is studied in detail to show the key features of the optimal solutions. Using the particular value thrust specific force of , it was found that the minimum times for cases 1, 2, and 3 are, respectively, 215, 196, and 198 d with departure dates, respectively, of 1 July 2020, 30 June 2020, and 28 June 2020. Finally, the problem formulation developed in this study is compared against prior work on an Earth-to-Mars interplanetary orbit transfer where it is found that the results of this research show significant improvement in transfer time relative to the prior work.

ESA F-Class Comet Interceptor: Trajectory design to intercept a yet-to-be-discovered comet

Comet Interceptor (Comet-I) was selected in June 2019 as the first ESA F-Class mission. In 2029+, Comet-I will hitch a ride to a Sun-Earth L2 quasi-halo orbit, as a co-passenger of ESA's M4 ARIEL mission. It will then remain idle at the L2 point until the right departure conditions are met to intercept a yet-to-be-discovered long period comet (or interstellar body). The fact that Comet-I target is thus unidentified becomes a key aspect of the trajectory and mission design. The paper first analyses the long period comet population and concludes that 2 to 3 feasible targets a year should be expected. Yet, Comet-I will only be able to access some of these, depending mostly on the angular distance between the Earth and the closest nodal point to the Earth's orbit radius. A preliminary analysis of the transfer trajectories has been performed to assess the trade-off between the accessible region and the transfer time for a given spacecraft design, including a fully chemical, a fully electric and a hybrid propulsion system. The different Earth escape options also play a paramount role to enhance Comet-I capability to reach possible long period comet targets. Particularly, Earth-leading intercept configurations have the potential to benefit the most from lunar swing-by departures. Finally, a preliminary Monte Carlo analysis shows that Comet-I has a 95–99% likelihood of successfully visit a pristine newly-discovered long period comet in less than 6 years of mission timespan.

Feasibility of Synchronized CubeSat Missions from Low Earth Orbit to Near-Earth Asteroids

The present study investigates the feasibility of deploying multiple CubeSats from low Earth orbit to near-Earth asteroids for an increased scientific return and reduced mission costs. It is found that for an escape time of 300 days, solar cell and battery degradation are 11 and 28%, respectively. The escape orbital plane inclination of 51.6 deg reduces the overall radiation dosage and requires 2.51 kg of propellant. Interplanetary mission values fall between 0 and , and low-thrust propellant requirements fall between 2.51 and 3.11 kg, for a dry spacecraft mass of 4.5 kg. The deployment strategy reduces mission costs by allowing the CubeSats to perform the Earth escape maneuver independently once deployed from the International Space Station. Time series regression neural networks were constructed to predict future space-station orbital states, whose uncertainty limits fall within CubeSat mass constraints. Synchronization of missions is performed by selecting the deployment sequence, which minimizes the overall time between consecutive CubeSat orbital injections. Optimal interplanetary, low-thrust trajectories were obtained using differential evolution, with a corrective high-thrust maneuver required at the start of the interplanetary phase. Propellant requirements for the corrective maneuver range between 1.3 and 3.3 kg of propellant using chemical propulsion.

Water Electrolysis for Propulsion of a Crewed Mars Mission

NASA’s Mars Design Reference Architecture 5.0 presents architecture options for a crewed Mars mission. This paper compares the cryogenic chemical-propulsion option in that study with an alternative: water-electrolysis propulsion. Propellant is stored as liquid water instead of cryogenic hydrogen and oxygen, and then electrolyzed on demand into gaseous hydrogen and oxygen for combustion. This addresses a technology gap in the reference architecture: cryogenic propellant storage life. Water is inert and stable, allowing indefinite storage. The mission refuels from pre-positioned tanks at a lunar libration point and Mars orbit, significantly reducing vehicle mass. Low-thrust transfers between Earth escape, Mars encounter, and vice versa reduce the need to store gas for impulsive maneuvers. Only relatively small impulsive maneuvers are used for orbit injection, escape, and plane changes. The proposed architecture achieves the same mission with at most the same number of launch vehicles and without cryogenic propellant storage. Both architectures use five superheavy lift launch vehicles; however, the reference architecture demands all five within 120 days. The alternative is more flexible. Pre-positioning propellant ahead of time allows a less demanding launch cadence. Potential utilization of water from the moon or elsewhere reduces the number of launches from five to as few as two.

Mission design for multi-target and multi-mode rendezvous missions to small bodies

Multi-target exploration to small bodies has the advantages of reducing mission cost and increasing scientific return. It will be widely used in the future small body exploration missions. This paper investigates the problem of perturbation sensitivity, complicated constraints and changeable thrust, which may be faced in the multi-target exploration mission. The Earth quasi-satellite sampling return and main-belt comet rendezvous missions are studied. First, based on the mission constraints, the mission design schedule and relevant constraints are given. Then, the multi-impulse asteroid sampling return trajectory is investigated in the elliptical three body model. Considering the gravitational perturbation of Earth, the integral trajectory design consist of Earth escape phase, interplanetary transfer phase, and Earth reentry phase is proposed. The trajectory design is divided into two parts. The optimal preliminary transfer opportunity is firstly searched in two-body problem and is transferred to the elliptical three body model. The differential correction scheme is applied to correct the error caused by Earth gravity perturbation. The trajectory for the Earth quasi-satellite 2016HO3 is designed. Finally, considering the engineering constraints, the first-order necessary condition of the changeable low-thrust trajectory are derived, where both the thrust and special impulse change with the distance to Sun. By introducing the B-plane parameters, the initial states determination under the constraint of the gravity assist is developed. Based on the homotopy method, the low-thrust optimal trajectory after Mars gravity assist to the main belt comet 133P are designed and compared with constant low thrust trajectory. The proposed multi-target exploration scheme and the orbit design method can provide a reference for future small bodies exploration missions in China.

Double Asteroid Redirection Test Mission: Heliocentric Phase Trajectory Analysis

Double Asteroid Redirection Test will be the first mission to demonstrate and characterize the concept of a kinetic impactor for planetary defense, by impacting the smaller member of a binary asteroid system Didymos. The results of this mission will have implications for planetary defense, near-Earth object science, and resource utilization. This research focuses on the heliocentric transfer phase of the mission. The heliocentric trajectory is evaluated using various objective functions, including a search for the latest possible Earth escape date, the shortest time of flight, and the maximum impact energy. Also included in the search is the potential to use Earth gravitational assists, which proves not to offer any useful advantages. A new way to assess the trajectory’s margin for missed thrust is used, which quantifies the ability of the spacecraft to recover its mission following unplanned nonthrusting events, such as safe mode. The baseline trajectory is shown to be capable of recovering from missed-thrust events lasting 14 days using only 1% of its propellant as margin. Finally, contingency trajectories that attempt to impact Didymos at a subsequent perihelion are considered.

Hayabusa 2 extension plan: Asteroid selection and trajectory design

The Hayabusa 2 mission is targeted to explore the asteroid (162173) 1999 JU3 and return surface as well as sub-surface samples through a novel impactor. Upon its return, at the end of 2020, the spacecraft will release the capsule for Earth re-entry and drift away from the planet. Based on the current mission profile, the spacecraft is expected to retain 30 kg of xenon propellant for trajectory maneuvers after the capsule is released. This remaining fuel can be used to extend the mission and improve its scientific return by exploring a new target. Work herein outlines an extension plan for Hayabusa 2, detailing the target selection process and its subsequent trajectory design. Due to final Earth escape trajectory, considering the excess velocity and orbital geometry, the only available extension option is an asteroid flyby. One of the most important trajectory characteristic is to maximize the spacecraft's optical detection capabilities. As a result the asteroid 2001 WR1 is identified as the most promising target candidate. The resulting trajectory uses all the available xenon with 100% duty cycle. Furthermore, the extension lasts for 932 days and offers 1.57 days of optical navigation time for a flyby on June 27, 2023.

An analytical description of three-dimensional heliocentric solar sail orbits

This paper introduces a simple analytical approximation to three-dimensional heliocentric solar sail orbits where the only forces considered are solar gravity and solar radiation. The approximation is based upon the previously studied hodograph transformation and provides a description of the inclination, longitude of ascending node and true latitude for a specific set of initial conditions. It is shown that the rotational symmetry of a heliocentric orbit allows this specific solution to be mapped onto a solution with arbitrary initial conditions. The approximation is then compared to the numerical results for a solar sail on an Earth escape trajectory with an area to mass ratio up to twice as high as current technology allows.

Mechanical Limitations of Motorised Tethers for Payload Orbital Transfer

In recent decades much research has focused on the use of space tether systems for payload orbital transfers. Orbit raising through the exchange of momentum using hanging tether systems in addition to enhanced momentum exchange resulting from motorised torque-driven systems have both been considered. In this paper the fo- cus is on the performance of symmetrically laden motorised momentum exchange tethers with the aim of conducting orbital transfers. These consist of two propulsion tethers symmetrically attached to a motor shaft with payloads, to be later trans- ferred, attached to their free ends. Rotation is achieved through reaction against two further tethers and masses attached to the motor stator with an estimated mass of this system, minus the propulsion tethers and payloads, of 1.5 tonnes. By deriv- ing the maximum tension acting on a system orbiting an oblate Earth expressions are obtained for the maximum rotational velocity that the tether systems are capa- ble of withstanding, based upon the material properties of the tethers themselves. Having obtained these expressions the performance of both hanging and motorised tether systems for conducting orbital transfers is analysed in terms of the gain in energy when the orbital geometry and tether length are varied. From this analysis the material-specifc tether length which gives the greatest gain in rotational kinetic energy to the payloads is established for a motorised system. Finally, by utilising this material-specific length, the minimum semi-major axis which is capable of per- forming lunar transfers and Earth escape trajectories is obtained.

Defining the Optimal Requirements for the Liquid Indium Microelectric Propulsion System

Recent technology advancements in microelectric propulsion will enable the next generation of small spacecraft to perform trajectory and attitude maneuvers with significant requirements, provide thrust over long mission durations, and replace reaction wheels for attitude control. These advancements will open up the class of mission architectures achievable by small spacecraft to include formation flying, proximity operations, and precision pointing missions in both low Earth orbit and interplanetary destinations. The goal of this study is to establish the optimal performance parameters for future microelectric propulsion technology that are applicable to a broad range of flight demonstration platforms (for example, dedicated 3- to 12-unit CubeSats to evolved expendable launch vehicle secondary payload adaptor-class spacecraft) for a variety of applications, including low Earth orbit and Earth escape orbit transfers, travel to interplanetary destinations, hover and drag makeup missions, and performing reaction-wheel-free attitude control. An integrated systems-level model for propulsion, spacecraft (power, data, telecommunication, thermal management), and orbit and attitude maneuvers is developed to support solution space exploration. Microelectric propulsion system performance parameters are derived that maximize the performance capability subject to realistic system-level constraints in the context of upcoming mission opportunities where microelectric propulsion is enabling or advantageous relative to other technologies.

Optimization of CubeSat System-Level Design and Propulsion Systems for Earth-Escape Missions

Small spacecraft can now perform trajectory maneuvers resulting in significant orbit changes that were once only feasible with larger spacecraft due to the development of miniaturized propulsion technology. This paper addresses the feasibility of using CubeSat Ambipolar Thruster, a large miniaturized propulsion system for constellation control, Earth escape, and planetary flybys, to enable Earth-escape maneuvers on a CubeSat form factor. Operational and trajectory variables include the power setting during thrust maneuvers, when to thrust, and the attitude control inputs. The dynamic energy available through the maneuvers, which is constrained by the power available from the sun depending on the orbit and is consumed in propulsion, is modeled as well as attitude control maneuvers and realistic battery degradation. To explore the design space of this capability, the sensitivity of solutions to spacecraft mass, fuel quantity, initial orbit, solar power collection, and battery size is demonstrated. Optimal orbit-raising techniques are compared and the optimal approach depending on the goals is discussed (i.e., minimize time, minimize fuel, minimize batteries, minimize propulsion system volume, and minimize accumulated radiation). The models and results presented lay the groundwork for future work in integrated vehicle and operational design optimization problems with both interplanetary and constellation architectures.

Small satellite survey mission to the second Earth moon

This paper presents an innovative space mission devoted to the survey of the small Earth companion asteroid by means of nano platforms. Also known as the second Earth moon, Cruithne, is the target identified for the mission. Both the trajectory to reach the target and a preliminary spacecraft budget are here detailed. The idea is to exploit high efficient ion thrusters to reduce the propellant mass fraction in such a high total impulse mission (of the order of 1e6 Ns). This approach allows for a 100kg class spacecraft with a very small Earth escape energy (5km2/s2) to reach the destination in about 320days. The 31% propellant mass fraction allows for a payload mass fraction of the order of 8% and this is sufficient to embark on such a small spacecraft a couple of nano-satellites deployed once at the target to carry out a complete survey of the asteroid. Two 2U Cubesats are here considered as representative payload, but also other scientific payloads or different platforms might be considered according with the specific mission needs. The small spacecraft used to transfer these to the target guarantees the manoeuvre capabilities during the interplanetary journey, the protection against radiations along the path and the telecommunication relay functions for the data transmission with Earth stations. The approach outlined in the paper offers reliable solutions to the main issues associated with a deep space nano-satellite mission thus allowing the exploitation of distant targets by means of these tiny spacecraft. The study presents an innovative general strategy for the NEO observation and Cruithne is chosen as test bench. This target, however, mainly for its relevant inclination, requires a relatively large propellant mass fraction that can be reduced if low inclination asteroids are of interest. This might increase the payload mass fraction (e.g. additional Cubesats and/or additional scientific payloads on the main bus) for the same 100kg class mission.

Impact experiments with a new technique for acceleration of projectiles to velocities higher than Earth's escape velocity of 11.2 km/s

The impact velocities of asteroids on Earth and other terrestrial planets can be greater than 10 km/s, and impacts at these high velocities can produce significant effects on the planetary surfaces. However, since macroscopic (>∼0.1 mm) projectiles with an aspect ratio of ∼1 are not easily accelerated to more than 10 km/s in laboratories, there are few detailed experimental studies. In this paper, we demonstrate that impact velocities greater than 10 km/s can be achieved with glass and aluminum projectiles of 0.1–0.3 mm in diameter using a high‐power laser, GEKKO XII‐HIPER at Institute of Laser Engineering, Osaka University. The velocity of the projectiles is estimated based on the images taken by high‐speed X‐ray streak and framing cameras. Projectiles collide into copper or LiF plate targets. The copper plates are recovered for analysis. The sizes of craters on the copper plates are not far from the extrapolations from previous work with lower velocities. A tantalum witness plate placed near the copper plates records a large number of secondary craters from each impact. In the case of the impacts of the LiF plates, we observe two emission lines of Li gas using a spectrometer with a streak camera. Thus, we can simulate the hypervelocity impacts with velocities higher than 10 km/s in laboratories.

Optimal interplanetary rendezvous combining electric sail and high thrust propulsion system

The aim of this paper is to study, from a mission analysis point of view, the performance of a hybrid propulsion concept for a two-dimensional transfer towards a planet of the Solar System. The propulsion system is obtained by combining a chemical thruster, used for the phases of Earth escape and/or target planet capture, with an electric sail, which provides a continuous thrust during the heliocentric transfer. Two possible mission scenarios are investigated: in the first case the sailcraft reaches the target planet with zero hyperbolic excess velocity, thus performing a classical rendezvous mission in a heliocentric framework. In the second mission scenario, a given final hyperbolic excess velocity relative to the planet is tolerated in order to decrease the mission flight time. The amount of final hyperbolic excess velocity is used as a simulation parameter for a tradeoff study in which the minimum flight time is related to the total velocity variation required by the chemical thruster to accomplish the mission, that is, for Earth escape and planetary capture.

Very high delta-V missions to the edge of the solar system and beyond enabled by the dual-stage 4-grid ion thruster concept

A new and innovative type of gridded ion thruster, the “Dual-Stage 4-Grid” or DS4G concept, has been proposed and its predicted high performance validated under an ESA research, development and test programme. The DS4G concept is able to operate at very high specific impulse and thrust density values well in excess of conventional 3-grid ion thrusters at the expense of a higher power-to-thrust ratio. This makes it a possible candidate for ambitious missions requiring very high delta-V capability and high power. Such missions include 100 kW-level multi-ton probes based on nuclear and solar electric propulsion (SEP) to distant Kuiper Belt Object and inner Oort cloud objects, and to the Local Interstellar medium. In this paper, the DS4G concept is introduced and its application to this mission class is investigated. Benefits of using the DS4G over conventional thrusters include reduced transfer time and increased payload mass, if suitably advanced lightweight power system technologies are developed. A mission-level optimisation is performed (launch, spacecraft system design and low-thrust trajectory combined) in order to find design solutions with minimum transfer time, maximum scientific payload mass, and to explore the influence of power system specific mass. It is found that the DS4G enables an 8-ton spacecraft with a payload mass of 400 kg, equipped with a 65 kW nuclear reactor with specific mass 25 kg/kW (e.g. Topaz-type with Brayton cycle conversion) to reach 200 AU in 23 years after an Earth escape launch by Ariane 5. In this scenario, the optimum specific impulse for the mission is over 10,000 s, which is well within the capabilities of a single 65 kW DS4G thruster. It is also found that an interstellar probe mission to 200 AU could be accomplished in 25 years using a “medium-term” SEP system with a lightweight 155 kW solar array (2 kg/kW specific mass) and thruster PPU (3.7 kg/kW) and an Earth escape launch on Ariane 5. In this case, the optimum specific impulse is lower at 3500 s which is well within conventional gridded ion thruster capability.

Accretion of the Earth

The origin of the Earth and its Moon has been the focus of an enormous body of research. In this paper I review some of the current models of terrestrial planet accretion, and discuss assumptions common to most works that may require re-examination. Density-wave interactions between growing planets and the gas nebula may help to explain the current near-circular orbits of the Earth and Venus, and may result in large-scale radial migration of proto-planetary embryos. Migration would weaken the link between the present locations of the planets and the original provenance of the material that formed them. Fragmentation can potentially lead to faster accretion and could also damp final planet orbital eccentricities. The Moon-forming impact is believed to be the final major event in the Earth's accretion. Successful simulations of lunar-forming impacts involve a differentiated impactor containing between 0.1 and 0.2 Earth masses, an impact angle near 45 degrees and an impact speed within 10 per cent of the Earth's escape velocity. All successful impacts-with or without pre-impact rotation-imply that the Moon formed primarily from material originating from the impactor rather than from the proto-Earth. This must ultimately be reconciled with compositional similarities between the Earth and the Moon.

Lunar-forming collisions with pre-impact rotation

Abstract Prior models of lunar-forming impacts assume that both the impactor and the target protoearth were not rotating prior to the Moon-forming event. However, planet formation models suggest that such objects would have been rotating rapidly during the late stages of terrestrial accretion. In this paper I explore the effects of pre-impact rotation on impact outcomes through more than 100 hydrodynamical simulations that consider a range of impactor masses, impact angles and impact speeds. Pre-impact rotation, particularly in the target protoearth, can substantially alter collisional outcomes and leads to a more diverse set of final planet–disk systems than seen previously. However, the subset of these impacts that are also lunar-forming candidates—i.e. that produce a sufficiently massive and iron-depleted protolunar disk—have properties similar to those determined for collisions of non-rotating objects [Canup, R.M., Asphaug, E., 2001. Nature 412, 708–712; Canup, R.M., 2004a. Icarus 168, 433–456]. With or without pre-impact rotation, a lunar-forming impact requires an impact angle near 45 degrees, together with a low impact velocity that is not more than 10% larger than the Earth's escape velocity, and produces a disk containing up to about two lunar masses that is composed predominantly of material originating from the impactor. The most significant differences in the successful cases involving pre-impact spin occur for impacts into a retrograde rotating protoearth, which allow for larger impactors (containing up to 20% of Earth's mass) and provide an improved match with the current Earth–Moon system angular momentum compared to prior results. The most difficult state to reconcile with the Moon is that of a rapidly spinning, low-obliquity protoearth before the giant impact, as these cases produce disks that are not massive enough to yield the Moon.

저추력기를 이용한 연료 최적의 지구탈출 궤적 설계 연구

A Discrete continuation Method/homotopy approaches are studied for energy/fuel optimal low thrust Earth escape trajectory by solving a two point boundary value problem(TPBVP). Recently, maneuvers using low thrust propulsion system have been identified as emerging technologies. The low thruster is considered as the main actuator for orbit maneuvers. The cost function consists of a energy/fuel consumption function, and constraints are position and velocity vectors at the terminal escape point. Solving the minimum energy/fuel problem directly is not an easy task, so we adopt the homotopy analysis. Using a solution of the minimum energy, which is solved by discrete continuation method, we obtain the solution of the minimum fuel problem.က€

Near-Optimal Low-Thrust Earth-Mars Trajectories via a Genetic Algorithm

A genetic algorithm is used to determine several types of Earth‐Mars trajectories, with the objective of maximizing payload delivered to Mars. The trajectories have three phases: Earth escape, heliocentric flight, and arrival into low Martian orbit. The actual planetary orbits are used with one approximation: Mars’s very small orbit inclination to the ecliptic plane is ignored. Impulses provided by chemical rockets are used for Earth departure and capture into orbit about Mars. The optimizer chooses the magnitude and direction of the impulse explicitly for the departure from Earth and implicitly, by choosing the hyperbolic excess velocity vector, for the arrival at Mars. The heliocentric flight uses low-thrust nuclear‐electric propulsion; cases with continuous thrust and cases in which a coasting, that is, a no-thrust phase, is allowed are both considered. The continuous time history of the thrust pointing angle is modeled using a sequence of cubic polynomials whose coefficients become parameters of the genetic algorithm’s chromosome. The fitness function of the genetic algorithm is dynamic; it first forces the spacecraft to arrive within the Martian sphere of influence. With that accomplished, it then emphasizes optimizing final mass.