General Mission Analysis Tool Research Articles

Lunar SmallSat Missions with Chemical-Electrospray Multimode Propulsion

Multimode spacecraft propulsion combines two or more propulsive modes into a single system using a single propellant. In this study, a multimode system combining a monopropellant chemical decomposition mode with an electric electrospray mode is considered for specific NASA-relevant lunar small satellite missions. This multimode concept is compared to all-chemical and all-electric approaches for four design reference missions (DRMs) in terms of feasibility, propellant mass consumed, and transfer time. Point solution trajectories are developed using NASA’s General Mission Analysis Tool for each propulsion system. This is the first study to consider this multimode concept for specific missions with high-fidelity force modeling. The results demonstrate the multimode approach can complete three of the four DRMs within the allotted propellant budget, while the all-chemical approach fails to complete two DRMs and the all-electric system fails to complete one DRM. Across the three feasible DRMs, the multimode approach completes the mission in 11–55% less time than the all-electric approach while consuming up to 33% less propellant than the all-chemical approach. The number of switching events and the minimum required mode switching time are quantified for the first time, with the latter having values between nearly instantaneous and 112.5 days, depending on the mission.

Earth-Venus Mission Analysis via Weak Capture and Nonlinear Orbit Control

Exploration of Venus is recently driven by the interest of the scientific community in understanding the evolution of Earth-size planets, and is leading the implementation of missions that can benefit from new design techniques and technology. In this work, we investigate the possibility to implement a microsatellite exploration mission to Venus, taking advantage of (i) weak capture, and (ii) nonlinear orbit control. This research considers the case of a microsatellite, equipped with a high-thrust and a low-thrust propulsion system, and placed in a highly elliptical Earth orbit, not specifically designed for the Earth-Venus mission of interest. In particular, to minimize the propellant mass, phase (i) of the mission was designed to inject the microsatellite into a low-energy capture around Venus, at the end of the interplanetary arc. The low-energy capture is designed in the dynamical framework of the circular restricted 3-body problem associated with the Sun-Venus system. Modeling the problem with the use of the Hamiltonian formalism, capture trajectories can be characterized based on their state while transiting in the equilibrium region about the collinear libration point L1. Low-energy capture orbits are identified that require the minimum velocity change to be established. These results are obtained using the General Mission Analysis Tool, which implements planetary ephemeris. After completing the ballistic capture, phase (ii) of the mission starts, and it is aimed at driving the microsatellite toward the operational orbit about Venus. The transfer maneuver is based on the use of low-thrust propulsion and nonlinear orbit control. Convergence toward the desired operational orbit is investigated and is proven analytically using the Lyapunov stability theory, in conjunction with the LaSalle invariance principle, under certain conditions related to the orbit perturbing accelerations and the low-thrust magnitude. The numerical results prove that the mission profile at hand, combining low-energy capture and low-thrust nonlinear orbit control, represents a viable and effective strategy for microsatellite missions to Venus.

Duality-Based Near-Fuel-Optimal Impulsive Trajectory Computation for Spacecraft Rendezvous Under Perturbations

In this study, a novel impulsive trajectory optimization algorithm for near-fuel-optimal rendezvous under perturbations is presented. The algorithm, called algorithm for impulsive rendezvous trajectory optimization under perturbations (AIRTOP), is designed such that the accuracy of rendezvous constraints is improved as much as possible while retaining the first-order optimality, under high-fidelity dynamics models that encompass various orbital perturbations (e.g., nonspherical gravity, air drag, luni-solar gravity, and solar radiation pressure). To eliminate rendezvous constraint errors, AIRTOP solves the linearized impulsive rendezvous problem recursively using the nonsingular dual-primal optimization algorithm. To improve the computational efficiency, AIRTOP applies the approximate analytical gradient of the constraint error norm during its error elimination process. We present three numerical simulations near circular and elliptical orbits. The simulation results show that i) AIRTOP can successfully solve impulsive rendezvous problems under realistic orbital perturbations with minimal user intervention, and ii) it can generate more fuel-efficient solutions in similar or shorter computation time than two other methods, namely, the differential corrector of the General Mission Analysis Tool and the global optimization approach, which can also take complex perturbations into account.

Modelling of Spacecraft Orbit via Neural Networks

In order to have a spacecraft orbital motion model, the developer usually tends to use traditional spacecraft orbital motion models. In order to have a good model, the developer resorts to modelling techniques that are more complex. Increasing model complexity increases algorithm execution time and prevents its usage on-board a spacecraft. This is due to real time constraints and limited computational resources usually imposed by the spacecraft on-board computer. This article develops a new method based on neural networks. The developed method allows the developer of spacecraft orbital motion model to alleviate the problem of increasing execution time with increasing model complexity. The positioning error percent of the proposed algorithm should not be more than 5%. The new method effectiveness evaluation is confirmed by the calculations using three test cases. The first test case has been the exact solution of the two-body problem. The second test case has been the Gamma Ray Observatory (GRO) spacecraft verified simulator. The third test case is a spacecraft simulated on the General Mission Analysis Tool (GMAT), which is developed by NASA and private industries. The maximum obtained error percent of the new method in all the test cases is 0.6%, which is considered a very good performance compared to the predefined 5% bound. The average execution time of traditional spacecraft motion models increases approximately 700% as the disturbance model complexity increases. On the contrary, the developed neural networks algorithm has approximately a constant average execution time regardless of the complexity of the disturbance models utilized. This enables using of the newly developed neural networks algorithm with very complex disturbance models without any increase of the computational load.

Radioprotective effects of induced astronaut torpor and advanced propulsion systems during deep space travel

Background. Human metabolic suppression is not a new concept, with 1950s scientific literature and movies demonstrating its potential use for deep space travel (Hock, 1960). An artificially induced state of metabolic suppression in the form of torpor would improve the amount of supplies required and therefore lessen weight and fuel required for missions to Mars and beyond (Choukèr et al., 2019). Transfer habitats for human stasis to Mars have been conceived (Bradford et al., 2018). Evidence suggests that animals, when hibernating, demonstrate relative radioprotection compared to their awake state. Experiments have also demonstrated relative radioprotection in conditions of hypothermia as well as during sleep (Bellesi et al., 2016 and Andersen et al., 2009). Circadian rhythm disrupted cells also appear to be more susceptible to radiation damage compared to those that are under a rhythmic control (Dakup et al., 2018).An induced torpor state for astronauts on deep space missions may provide a biological radioprotective state due to a decreased metabolism and hypothermic conditions. A regular enforced circadian rhythm might further limit DNA damage from radiation.The As Low As Reasonably Achievable (A.L.A.R.A.) radiation protection concept defines time, distance and shielding as ways to decrease radiation exposure. Whilst distance cannot be altered in space and shielding either passively or actively may be beneficial, time of exposure may be drastically decreased with improved propulsion systems. Whilst chemical propulsion systems have superior thrust to other systems, they lack high changes in velocity and fuel efficiency which can be achieved with nuclear or electric based propulsion systems.Radiation toxicity could be limited by reduced transit times, combined with the radioprotective effects of enforced circadian rhythms during a state of torpor or hibernation.Objectives. 1. Investigate how the circadian clock and body temperature may contribute to radioprotection during human torpor on deep space missions.2. Estimate radiation dose received by astronauts during a transit to Mars with varying propulsion systems.Methods. We simulated three types of conditions to investigate the potential radioprotective effect of the circadian clock and decreased temperature on cells being exposed to radiation such that may be the case during astronaut torpor. These conditions were:- Circadian clock strength: strong vs weak.- Light exposure: dark-dark vs light-dark cycle- Body temperature: 37C vs hypothermia vs torpor.We estimated transit times for a mission to Mars from Earth utilizing chemical, nuclear and electrical propulsion systems. Transit times were generated using the General Mission Analysis Tool (GMAT) and Matlab. These times were then input into the National Aeronautics and Space Administration (NASA) Online Tool for the Assessment of Radiation In Space (OLTARIS) computer simulator to estimate doses received by an astronaut for the three propulsion methods.Results. Our simulation demonstrated an increase in radioprotection with decreasing temperature. The greatest degree of radioprotection was shown in cells that maintained a strong circadian clock during torpor. This was in contrast to relatively lower radioprotection in cells with a weak clock during normothermia. We were also able to demonstrate that if torpor weakened the circadian clock, a protective effect could be partially restored by an external drive such as lighting schedules to aid entrainment i.e.: Blue light exposure for periods of awake and no light for rest timesFor the propulsion simulation, estimated transit times from Earth to Mars were 258 days for chemical propulsion with 165.9mSv received, 209 days for nuclear propulsion with 134.4mSv received and 80 days for electrical propulsion with 51.4mSv received.Conclusion. A state of torpor for astronauts on deep space missions may not only improve weight, fuel and storage requirements but also provide a potential biological radiation protection strategy. Moreover, maintaining a controlled circadian rhythm during torpor conditions may aid radioprotection. In the not too distant future, propulsion techniques will be improved to limit transit time and hence decrease radiation dose to astronauts. Limiting exposure time and enhancing physiological radioprotection during transit could provide superior radioprotection benefits compared with active and passive radiation shielding strategies alone.

Geosynchronous transfer orbits as a market for impulse delivered by lunar sourced propellant

Every year around 100 metric tons of commercially addressable geostationary satellites are launched into geosynchronous transfer orbits (GTOs). The orbit raising from GTO to geostationary equatorial orbit (GEO) is an existing market for impulse that could be addressed by a service using propellant sourced from the Moon. We reconstructed the economic model in the recently published Commercial lunar propellant architecture: a collaborative study of lunar propellant production (Kornuta et al., 2019) and used it to investigate the financial viability of providing propulsion as a service in GTOs. We used NASA’s General Mission Analysis Tool to design a GTO service delivery flight plan, which we extend to cover sub and super synchronous delivery. We used economic, astrodynamic, and engineering models to derive the sensitivity of the internal rate of return to GTO launch costs, sale prices, tug inert mass fractions, and delivery orbit. While falling launch prices erode the impulse service returns, they may create other markets for propellant, we explore some higher return products these markets would make available.

State-Transition Matrix for Satellite Relative Motion in the Presence of Gravitational Perturbations

A state-transition matrix (STM) for the relative motion of artificial satellites is presented in this work that is valid in the presence of the gravitational spherical harmonic perturbations. The perturbed relative motion is modeled as a first-order variation of the equinoctial orbital elements describing the reference orbit. A satellite theory is derived for the analytical propagation of the reference orbit that includes the secular and periodic effects due to the zonal, sectorial, and tesseral harmonic perturbations. In case of the relative motion STM, the two main goals achieved are as follows. The analytic expressions for the elements of the STM are derived in a generalized form valid for an arbitrary spherical harmonic, and these expressions are in closed-form without using any series expansion in either the eccentricity or the ratio of the mean motion to the angular velocity of the gravitational body. The STM includes the short-period effects due to all the tesseral harmonics in addition to the secular, long-period, and short-period effects due to all the zonal harmonics. Avoidance of the series expansions in the eccentricity ensures that the accuracy of the STM does not degrade for satellite formations in medium to highly eccentric orbits. Additionally, the STM is nonsingular in case of the reference orbits that are near the resonant region; however, the long-period effects due to the resonant tesseral harmonics are ignored in this work. The proposed relative motion STM is implemented in MATLAB, and its accuracy is validated against numerical propagation with a Earth gravity field in NASA’s General Mission Analysis Tool.

Development of General-Purpose Root-Finding Module for General Mission Analysis Tool

A general-purpose root-finding module for designing spacecraft trajectories is developed to have similar accuracy to that of other well-known root-finding modules, and greater speed. Three quasi-Newton root-finding algorithms are implemented: the Newton–Raphson method, the Broyden’s method and the Generalized Broyden’s method. Based on the proposed root-finding module, General Mission Analysis Tool (GMAT) of National Aeronautics and Space Administration’s Goddard Space Flight Center (NASA/GSFC) is functionally extended by integrating the Broyden’s method and the Generalized Broyden’s method into its differential corrector module. Non-trivial spacecraft trajectory design problems, such as Lambert’s problem for trans-lunar trajectory and minimum-time transfer problem to the Mars are solved to analyze the performance of the proposed module. The numerical performances of each root-finding algorithm are quantitatively analyzed by the total number of function evaluations, the total number of iterations, convergence error, mean convergence rate, and running time. The overall comparative analysis shows that the Broyden’s method and the Generalized Broyden’s method are about 20–40% faster than the Newton–Raphson method and solutions from each algorithm have similar numerical accuracy. We also show that for selected test problems, the Generalized Broyden’s method converges in less running time than others with similar numerical accuracy in GMAT. The updated differential corrector module was released in R2014a version of GMAT.

Active Learning in Physics, Astronomy and Engineering with NASA’s General Mission Analysis Tool

Astrodynamics is the study of the motion of artificial satellites and spacecraft, subject to both natural and artificially induced forces. It combines celestial mechanics, attitude dynamics and aspects of positional astronomy to describe spacecraft motion and enable the planning and analysis of missions. It is of significant interdisciplinary interest with relevance to physics, astronomy and spaceflight engineering, but can be challenging to deliver in an effective, engaging manner because of the often abstract nature of some concepts, the four-dimensional nature of the problems, and the computation required to explore realistic astrodynamics behaviour. The University of Leicester has adopted NASA’s General Mission Analysis Tool as a core resource to support active learning in this subject for students at Level 6 (BSc) and Level 7 (MSc). This paper describes our approach to the implementation of GMAT as an essential element of teaching and learning in the subject.

Unified Lambert Tool for Massively Parallel Applications in Space Situational Awareness

This paper introduces a parallel-compiled tool that combines several of our recently developed methods for solving the perturbed Lambert problem using modified Chebyshev-Picard iteration. This tool (unified Lambert tool) consists of four individual algorithms, each of which is unique and better suited for solving a particular type of orbit transfer. The first is a Keplerian Lambert solver, which is used to provide a good initial guess (warm start) for solving the perturbed problem. It is also used to determine the appropriate algorithm to call for solving the perturbed problem. The arc length or true anomaly angle spanned by the transfer trajectory is the parameter that governs the automated selection of the appropriate perturbed algorithm, and is based on the respective algorithm convergence characteristics. The second algorithm solves the perturbed Lambert problem using the modified Chebyshev-Picard iteration two-point boundary value solver. This algorithm does not require a Newton-like shooting method and is the most efficient of the perturbed solvers presented herein, however the domain of convergence is limited to about a third of an orbit and is dependent on eccentricity. The third algorithm extends the domain of convergence of the modified Chebyshev-Picard iteration two-point boundary value solver to about 90% of an orbit, through regularization with the Kustaanheimo-Stiefel transformation. This is the second most efficient of the perturbed set of algorithms. The fourth algorithm uses the method of particular solutions and the modified Chebyshev-Picard iteration initial value solver for solving multiple revolution perturbed transfers. This method does require “shooting” but differs from Newton-like shooting methods in that it does not require propagation of a state transition matrix. The unified Lambert tool makes use of the General Mission Analysis Tool and we use it to compute thousands of perturbed Lambert trajectories in parallel on the Space Situational Awareness computer cluster at the LASR Lab, Texas A&M University. We demonstrate the power of our tool by solving a highly parallel example problem, that is the generation of extremal field maps for optimal spacecraft rendezvous (and eventual orbit debris removal). In addition we demonstrate the need for including perturbative effects in simulations for satellite tracking or data association. The unified Lambert tool is ideal for but not limited to space situational awareness applications.

A Deep Space Orbit Determination Software: Overview and Event Prediction Capability

This paper presents an overview of deep space orbit determination software (DSODS), as well as validation and verification results on its event prediction capabilities. DSODS was developed in the MATLAB object-oriented programming environment to support the Korea Pathfinder Lunar Orbiter (KPLO) mission. DSODS has three major capabilities: celestial event prediction for spacecraft, orbit determination with deep space network (DSN) tracking data, and DSN tracking data simulation. To achieve its functionality requirements, DSODS consists of four modules: orbit propagation (OP), event prediction (EP), data simulation (DS), and orbit determination (OD) modules. This paper explains the highest-level data flows between modules in event prediction, orbit determination, and tracking data simulation processes. Furthermore, to address the event prediction capability of DSODS, this paper introduces OP and EP modules. The role of the OP module is to handle time and coordinate system conversions, to propagate spacecraft trajectories, and to handle the ephemerides of spacecraft and celestial bodies. Currently, the OP module utilizes the General Mission Analysis Tool (GMAT) as a third-party software component for highfidelity deep space propagation, as well as time and coordinate system conversions. The role of the EP module is to predict celestial events, including eclipses, and ground station visibilities, and this paper presents the functionality requirements of the EP module. The validation and verification results show that, for most cases, event prediction errors were less than 10 millisec when compared with flight proven mission analysis tools such as GMAT and Systems Tool Kit (STK). Thus, we conclude that DSODS is capable of predicting events for the KPLO in real mission applications.

Orbit Design and Simulation for Kufasat Nanosatellite

Abstract Orbit design for KufaSat Nano-satellites is presented. Polar orbit is selected for the KufaSat mission. The orbit was designed with an Inclination which enables the satellite to see every part of the earth. KufaSat has a payload for imaging purposes which require a large amount of power, so the orbit is determined to be sun synchronous in order to provide the power through solar panels. The KufaSat mission is designed for the low earth orbit. The six initial Keplerian Elements of KufaSat are calculated. The orbit design of KufaSat according to the calculated Keplerian elements has been simulated and analyzed by using MATLAB first and then by using General Mission Analysis Tool.

Third-Body Perturbation Effects on Satellite Formations

The effects of third-body perturbations on satellite formations are investigated using differential orbital elements to describe the relative motion. Absolute and differential effects of the lunar perturbation on satellite formations are derived analytically based on the simplified model of the circular restricted three-body problem. This analytical description includes averaged long-term effects on the orbital elements, including the full transformation between the osculating elements and the lunar-averaged elements, which is absent from previous research. A simplified Earth-Moon system model is used, but the results are applicable to any formation reference orbit about the Earth. Simulations are performed to determine the effects of the lunar perturbation on example formations in upper MEO, highly eccentric orbits by using the formation design criteria of Phases I and II of the NASA Magnetospheric Multiscale mission. The changes in angular differential orbital elements (δ ω, δΩ, and δ M 0) and in science return quality due to this perturbation are compared to changes due to J 2. The method is then expanded to include the inclination of the Moon’s orbit and results are compared to simulation using the NASA General Mission Analysis Tool.

Satellite formation design in orbits of high eccentricity with performance constraints specified over a region of interest: MMS phase II

The formation design problem for Phase II of the Magnetospheric Multiscale (MMS) mission is addressed using differential mean orbital elements as design variables and the Gim–Alfriend state transition matrix for relative motion propagation. The MMS mission requires a formation of four satellites in a nearly regular tetrahedron throughout a Region of Interest (RoI), defined near apogee of a highly eccentric orbit. Previous papers have addressed the problem of formation design with performance constraints specified over a RoI, and these methods are now applied to the present problem. In addition, the use of a modified along-track drift condition as a constraint to ensure long-term formation stability is investigated. The performance of the designed formations in the presence of differential semimajor axis errors is also examined. Finally, the results are verified using the NASA General Mission Analysis Tool.

Design of Satellite Formations in Orbits of High Eccentricity withPerformance Constraints Specified over a Region of Interest

The Magnetospheric Multiscale (MMS) mission requires a formation of four satellites in a nearly regular tetrahedron throughout a Region of Interest (RoI), defined near the apogee of a highly eccentric reference orbit. In this paper, an approach for determining the differential mean orbital element initial conditions for formations in highly eccentric orbits to maximize a Quality Factor (QF) in a RoI is presented. Previous works on the design of formations in high- eccentricity orbits have used numerical integration-based approaches for orbit propagation. We present a fast optimization scheme by using the Gim-Alfriend state transition matrix. Two optimization approaches are presented for the long-term MMS formation design: a single-orbit constrained (SOC) optimization, subject to an along-track drift condition, and a multi-orbit unconstrained (MOU) optimization. A new along-track drift condition is proposed to minimize the along-track drift only in certain portions of the orbit and is shown to produce much more stable long-term behavior of the QF than the previous condition. A verification of the results sing the NASA General Mission Analysis Tool is provided. Under ideal conditions, i.e., without errors in the establishment of the initial conditions, the best formation can satisfy the MMS mission QF requirements for over 80 days without corrective action.

Optimal Formation Design for Magnetospheric Multiscale Mission Using Differential Orbital Elements

The Magnetospheric Multiscale Mission requires a formation of four satellites in a nearly regular tetrahedron throughout a region of interest defined near the apogee of a highly eccentric reference orbit. Previous papers have addressed the design of formations in orbits of high eccentricity to maximize a quality factor in a region of interest, including the use of differential mean orbital elements as design variables. In this paper, a robust optimization method is presented to improve formation performance in the presence of formation initialization errors. Several design methods are analyzed by applying differential semimajor axis errors, which have a strong effect on the long-term stability of spacecraft formations. It is shown that large formations can satisfy mission requirements for a longer time than smaller formations, when the same magnitude of errors are considered, and generally exhibit less variation in quality factors due to these errors. The robust optimization method is applied to these smaller formations and produces results that are much more stable when semimajor axis errors are included, at a cost of some performance in the nominal error-free case. The results are verified using the NASA General Mission Analysis Tool and are shown to be reasonably accurate, except in predicting very long-term behavior. A physical analysis of the geometry of several magnetospheric multiscale formation designs is provided, and eight distinct optimal tetrahedron orientations are identified (two configurations, in which the chief satellite can be placed at any of the four vertices).