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All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

NASA's Efforts to Pursue Commercial Communications Services for Missions in Near Space

The National Aeronautics and Space Administration (NASA) Space Communications and Navigation (SCaN) Program enables high speed, robust, secure and cost-effective space communications and navigation services to current and future science and exploration missions. Consistent with National Space Policy, NASA is seeking commercial services for all its future near Earth requirements by incorporating additional direct to Earth (DTE) providers and introducing commercial satellite communications (SATCOM) vendors as NASA’s Tracking and Data Relay Satellites (TDRS) begin to decline. Through the progression of these efforts, SCaN is also integrating commercial services in the cislunar domain. The overarching objective is to satisfy the demands from the mission community – both in terms of capacity and capability – in a robust and cost-effective way, leveraging the strong and growing commercial space sector. For near earth space relay, six SATCOM vendors were awarded Funded Space Act Agreements in June of 2022 to demonstrate the ability to serve near-Earth missions, and are working through their committed milestones. The failure of TDRS Flight-9 (F9) in late 2022 prompted an increased tempo of mission engagement to identify driving user needs that commercial SATCOM can meet in the near-term. NASA has set a course to accelerate a decision to terminate commitments for TDRS services to new missions and has developed a plan to execute validation and risk reduction efforts with early adopter “pathfinder” missions to pave the way to earlier operational services. As the Artemis Program matures and builds on the successful Artemis I flight in November/December of 2022, the definition of the supporting communications and navigation architecture has further been refined. Although NASA government assets will continue to play a key role in provision of services, such as through the Deep Space Network, SCaN is pursuing commercial services offerings to expand ground network capability and implement lunar relay services. In February of 2023, SCaN released solicitation for services that include DTE services to missions near-Earth and in cislunar space, as well as lunar relay services. Further, SCaN is seeking opportunities to integrate commercial capability into lunar surface communications infrastructure. NASA is also advocating for standards that promote interoperability and strategic technology investments in the commercial sector. This paper addresses the recent progress and future plans in the near-Earth space and lunar regimes, discusses the unified approach for industry engagement, and highlights both the common and unique challenges of commercialization efforts in the two regimes.

commercialization↗
NASA NTRSDate not supplied

Gateway Autonomy for Enabling Deep Space Exploration

The Gateway spacecraft is an important stepping-stone to exploration of the solar system, integrating commercial and international partners into a tightly coupled system, enabling cislunar activities, and implementing key technologies for missions to Mars. Autonomy is a capability area necessary to handle long communication outages where intervention from Earth is impossible, to prepare to operate with long communication delays that will be common in interplanetary travel, and to make spaceflight more affordable and accessible by reducing sustaining operations costs. The Gateway Concept of Operations states that one of Gateway’s goals is to “focus on infrastructure and systems that will allow autonomous operations aboard the Gateway with robotics, automated systems, advanced communications, and distributed computing.” Gateway’s Vehicle Systems Manager (VSM) and associated Autonomous Spacecraft Management Architecture (ASMA) are key products towards delivering autonomous capability. The primary functions of the control architecture are Mission Management and Timeline Execution, Resource Management, Fault Management, and Vehicle Control and Operation (VCO). In each of these areas, there is an initial level of capability to be delivered at launch, with plans to continue development and grow to greater capability. The initial deployment of VSM will focus on maintaining vehicle safety by focusing on full fault management capabilities and deploying only enough resource and timeline planning functionality to support that. The final deployment of VSM will add significant planning and control optimization functionality to support nominal operations for up to 21 days without ground support, even accommodating fault and failure conditions. While the VSM is the vehicle-level representation of autonomous reasoning, distributed automation is essential to provide the right scope and abstraction of information to process. Module and system support of automation and simplicity of interfaces are two important design paradigms that Gateway is focusing on to garner a systems approach to autonomy. Distribution of reasoning can increase complexity, so Gateway is also taking a strict hierarchical approach to information flow and decision making. VSM is not the only capability necessary to achieve an autonomous spacecraft. Robotics support for maintenance of the spacecraft will be essential to provide continued vehicle functionality even when crew is not present. Technical and programmatic challenges exist when implementing autonomous robotics operations. These challenges include sufficient network flexibility to support data transfer to the rest of the vehicle to coordinate module-to-module robotic walk-offs and finding the proper interfaces to allow sufficient dexterity. Communication system upgrades planned for Gateway include Delay Tolerant Networking to best utilize the complex network of relays that will be part of mature cislunar operations. Distributed computing and management will provide failure tolerance, robustness, and growth of capabilities while still allowing significant reuse of heritage software on heritage systems as well as reuse of common applications across a spacecraft to minimize new development, but this requires adherence to key standards and interfaces. The Gateway program has demonstrated significant progress towards these capabilities and has identified challenges other spacecraft developers should be aware of from the start.

Molly Anderson↗
NASA NTRSDate not supplied

Defining a Global Lunar Position, Navigation, and Timing System

As NASA seeks to fulfill its mission of extending humanity’s reach through exploration as delineated in the Moon to Mars Strategy and Objectives Development and the Moon to Mars Architecture Definition Document, accurate and timely position, navigation, and timing (PNT) services are critical in the architecture, identifying a need to expand a PNT capability to the full lunar proximity service volume. This is echoed in the White House Office of Science, Technology, and Policy Cislunar Science and Technology Strategy, which pinpoints the fundamental need for PNT infrastructure to enable and sustain a vibrant cislunar ecosystem. While the Human Lunar Return segment seeks commercial services to provide a PNT service over a South Pole service volume for a limited period per Earth day, meeting the Sustained Lunar Evolution segment requires a Lunar Navigation System (LNS) focused on delivery of precise and resilient PNT services across the lunar globe and near-Moon space. This presentation describes the pre-Phase A system concept for an orbital constellation, the requisite lunar surface-based in-situ monitor and control segment, and an Earth control segment to provide lunar PNT services out to 200km altitude above the surface. The LNS leverages the foundational efforts on lunar reference system components such as the Lunar Geodetic System, Lunar Time System, and lunar ephemeris and orientation critical to safe, accurate, and seamless navigation.

navigation↗
NASA NTRSDate not supplied

Jettison and Disposal from Near Rectilinear Halo Orbits, Part 1: Theory

The proposed Gateway spacecraft in a Near Rectilinear Halo Orbit (NRHO) will be a human outpost in cislunar space. The baseline mission may experience the deployment of visiting vehicles, cubesats, and on-orbit debris. Departure from the NRHO and cislunar space is nontrivial due to the complex gravitational environment that persists in and around Gateway. Long-term disposal orbits in heliocentric space offer safe destinations for deployed objects. To mitigate risks associated with conjunctions between Gateway and deployed objects, strategies to identify risk-avoidant paths to heliocentric space are necessary for Gateway mission operations.

Stephen T. Scheuerle↗
NASA NTRSDate not supplied

NASA’s Efforts to Pursue Commercial Communications Services for Missions in Near Space

The National Aeronautics and Space Administration (NASA) Space Communications and Navigation (SCaN) Program enables high speed, robust, secure, and cost-effective space communications and navigation services to current and future science and exploration missions. Consistent with National Space Policy, NASA is seeking commercial services for all its future near-Earth requirements by incorporating additional direct to Earth (DTE) providers and introducing commercial satellite relay communications (SATCOM) vendors as NASA’s Tracking and Data Relay Satellites (TDRS) begin to decline. Through the progression of these efforts, SCaN is also integrating commercial services in the cislunar domain. The overarching objective is to satisfy the demands from the mission community – both in terms of capacity and capability – in a robust, reliable, and cost-effective way, leveraging the strong and growing commercial space sector. For near earth space relay, six SATCOM vendors were awarded Funded Space Act Agreements in June of 2022 to demonstrate the ability to serve near-Earth missions with space-based communication relay services. All six vendors are working through their committed milestones with end-to-end service demonstrations tacking place throughout the mid-2020’s. The failure of TDRS Flight-9 (F9) in late 2022 prompted an increased tempo of mission engagement to identify driving user needs that commercial SATCOM can meet in the near-term. NASA has set a course to accelerate a decision to terminate offering TDRS services to new missions and is developing a plan to execute validation and risk reduction efforts with early adopter “pathfinder” missions, paving the way to operational services. As the Artemis Program matures and builds on the successful Artemis I flight in November-December of 2022, the definition of the supporting communications and navigation architecture has further been refined. Although NASA government assets will continue to play a key role in provision of services, such as through the Deep Space Network, SCaN is pursuing commercial services offerings to expand ground network capability and implement lunar relay services. In February of 2023, SCaN released solicitation for services that include DTE services to missions near-Earth and in cislunar space, as well as lunar relay services. Further, SCaN is seeking opportunities to integrate commercial capability into lunar surface communications infrastructure. NASA is also advocating for standards that promote interoperability and strategic technology investments in the commercial sector. This paper addresses the recent progress and future plans in the near-Earth space and lunar regimes, discusses the unified approach for industry engagement, and highlights both the common and unique challenges of commercialization efforts in the two regimes.

commercial services↗
NASA NTRSDate not supplied

Gateway Autonomy for Enabling Deep Space Exploration

The Gateway spacecraft is an important stepping-stone to exploration of the solar system, integrating commercial and international partners into a tightly coupled system, enabling cislunar activities, and implementing key technologies for missions to Mars. Autonomy is a capability area necessary to handle long communication outages where intervention from Earth is impossible, to prepare to operate with long communication delays that will be common in interplanetary travel, and to make spaceflight more affordable and accessible by reducing sustaining operations costs. The Gateway Concept of Operations states that one of Gateway’s goals is to “focus on infrastructure and systems that will allow autonomous operations aboard the Gateway with robotics, automated systems, advanced communications, and distributed computing.” Gateway’s Vehicle Systems Manager (VSM) and associated Autonomous Spacecraft Management Architecture (ASMA) are key products towards delivering autonomous capability. The primary functions of the control architecture are Mission Management and Timeline Execution, Resource Management, Fault Management, and Vehicle Control and Operation (VCO). In each of these areas, there is an initial level of capability to be delivered at launch, with plans to continue development and grow to greater capability. The initial deployment of VSM will focus on maintaining vehicle safety by focusing on full fault management capabilities and deploying only enough resource and timeline planning functionality to support that. The final deployment of VSM will add significant planning and control optimization functionality to support nominal operations for up to 21 days without ground support, even accommodating fault and failure conditions. While the VSM is the vehicle-level representation of autonomous reasoning, distributed automation is essential to provide the right scope and abstraction of information to process. Module and system support of automation and simplicity of interfaces are two important design paradigms that Gateway is focusing on to garner a systems approach to autonomy. Distribution of reasoning can increase complexity, so Gateway is also taking a strict hierarchical approach to information flow and decision making. VSM is not the only capability necessary to achieve an autonomous spacecraft. Robotics support for maintenance of the spacecraft will be essential to provide continued vehicle functionality even when crew is not present. Technical and programmatic challenges exist when implementing autonomous robotics operations. These challenges include sufficient network flexibility to support data transfer to the rest of the vehicle to coordinate module-to-module robotic walk-offs and finding the proper interfaces to allow sufficient dexterity. Communication system upgrades planned for Gateway include Delay Tolerant Networking to best utilize the complex network of relays that will be part of mature cislunar operations. Distributed computing and management will provide failure tolerance, robustness, and growth of capabilities while still allowing significant reuse of heritage software on heritage systems as well as reuse of common applications across a spacecraft to minimize new development, but this requires adherence to key standards and interfaces. The Gateway program has demonstrated significant progress towards these capabilities and has identified challenges other spacecraft developers should be aware of from the start.

Molly Anderson↗
NASA NTRSDate not supplied

Future Homes in Space: Development of Concepts for Exploration Space Habitats

NASA’s Artemis campaign seeks to return humans to the moon and establish a sustained presence on the lunar surface. This session will emphasize how habitation capabilities on the moon and in cislunar space can potentially contribute to the sustainability objectives of Artemis. Habitable elements represent opportunities to enable longer duration stays, increase the number of crew members present, enhance science and utilization activities, drive technology development for future Mars exploration, perform analog missions, and fuel economic opportunities for US industry. Panelists include Paul Kessler (NASA Marshall Space Flight Center, deputy lead for lunar surface habitation); Andrew Choate (NASA Marshall Space Flight Center, Mars habitation lead); Krystofer Dudzinski (NASA Marshall Space Flight Center, a space architect within the MSFC Advanced Concepts Office); and Larry Toups (retired from NASA Johnson Space Center, currently an adjunct professor at University of Houston in space architecture). The panel is moderated by Tracie Prater (NASA Marshall Space Flight Center, Habitation Systems Development Office). The panel will begin with an overview of the history of habitation concepts and an academic perspective on general considerations in space habitat design (Larry Toups). Paul Kessler and Andrew Choate will introduce NASA’s principle of “architecting from the right” to help define objectives for Artemis missions, needs/characteristics, use cases, and functions (as published in the agency’s Architecture Definition Document) and provide perspective on how this principle informs habitation concept development work. NASA panelists will discuss key engineering challenges identified for developing, deploying, and operating habitable assets on the lunar surface and/or in deep space. These may include dust mitigation, outfitting of inflatable softgoods (for concepts which may use softgoods as a primary structural material), survival in lunar darkness, human health and performance considerations, maintenance/repair/sparing, and autonomy. These identified challenges represent risks for habitation systems development and relate closely to capability gaps identified by the agency. While the work of NASA Marshall Space Flight Center’s habitation development office is primarily focused on habitats which are launched from earth pre-integrated (referred to as Class I in the framework previously developed by NASA space architects Kennedy/Cohen) or launched from earth and deployed at the point of use (Class II), there is also extensive work in NASA, academia, and companies on constructed habitats, which would be built on a planetary surface using indigenous resources (Class III habitats). Panelist Krystopher Dudzinski will discuss potential evolutionary pathways from Class I and Class II habitats to Class III habitats, unique and common architectural challenges within each habitat class, and key gaps in implementing Class III habitats from an architectural perspective. NASA panelists and the moderator will also provide an overview of partnership opportunities and avenues for further engagement to advance habitation systems for the SpaceCom audience. NASA is currently developing notional concepts for a lunar surface habitat and Mars transit habitat, which will be discussed during this panel session and used as examples. These concepts represent options for habitation system design and are a point of departure. They do not represent a final plan or formal recommendation on the part of the agency. Based on the most recent analysis cycle, NASA’s lunar surface habitat (SH) concept nominally supports two crew members for 30 days, with the capacity to support four crew during a surge period where crew will swap between the SH and another surface asset, such as a pressurized rover. This example design has a metallic airlock for ingress/egress and the upper portion is an inflatable material system which serves as the habitation module. The notional interior of the habitat is a three-deck layout/configuration which supports all crew mission functions, including exercise, stowage, extravehicular activity (EVA), sleep, hygiene waste collection, maintenance and repair, and meal preparation. Under analysis assumptions for habitation, the Mars Transit Habitat (TH) concept would support four crew on an up to 1,200 day Mars mission. One option for the concept is to initially dock Transit Habitat at Gateway, where it can be used to increase the duration of crew stays in cislunar space and perform shakedown and analog missions prior to a Mars departure. One challenge in longer duration missions which involve both surface exploration and transit is understanding crew adaptation when transitioning between partial gravity and microgravity environments. TH at Gateway offers an opportunity to study this transition and in doing so reduce risks associated with future Mars exploration. Like lunar SH, the most recent analysis cycle concept of a Mars TH is a hybrid structure design, with a metallic section supporting EVAs, axial/radial docking, and Safe Haven capabilities, and an inflatable softgoods structure for the primary habitation function. Interior layouts to optimize crew usability and livability are currently under trade. The panel will include presentation material, but also seeks to engage the audience in a highly interactive conversation regarding the potential role for habitation in future exploration initiatives. Potential topics for discussion include the influence of the crew experience on habitation systems design and livability/usability considerations, the benefits of space habitation development in terrestrial applications, and challenges and opportunities in “feeding forward” lunar surface habitation systems development to Mars exploration.

space habitats↗
NASA NTRSDate not supplied

Autonomous Navigation of a Lunar Relay Using GNSS and Other Measurements

Many of the highest priority destinations at the Moon lack a continuous view of Earth, such as the lunar poles or lunar far side. Exploration of these sites will require spacecraft in cislunar space to relay communications and provide position, navigation, and timing (PNT) services. Accurate knowledge of relay position, velocity, and time is essential to these services. This paper describes a concept for a PNT Instrument being developed for the Lunar Communications Relay and Navigation Systems (LCRNS) Project. The instrument is intended as a payload that would enable autonomous, on-board, real-time navigation and timing using Global Navigation Satellite System (GNSS), optical navigation, and one-way measurements from Earth-based ground stations. Hardware-in-the-loop simulations using flight software are used to realistically characterize performance on hardware platforms with a path to flight. These results provide preliminary validation of the proposed PNT Instrument, demonstrate the benefits of augmenting GNSS with other measurements, and serve as an insightful reference for the design of future lunar missions, including those that will operate within the LunaNet framework of standards. This instrument concept relies on several technologies developed at NASA Goddard Space Flight Center (GSFC). For GNSS observables, the instrument relies on the high-altitude NavCube 3 mini (NC3m) GNSS receiver specifically designed for cislunar applications. The autoNGC system, which consists of flight software and a hardware platform, is responsible for fusing the observables using its extended Kalman filter, the Goddard Enhanced Onboard Navigation System (GEONS). Optical navigation observables are processed within autoNGC (“autonomous Navigation, Guidance, and Control”) using the Goddard Image Analysis & Navigation Tool (GIANT) which is also responsible for simulating high-fidelity images for test and analysis. In addition to describing the PNT Instrument and its components, the paper will present predicted performance based on simulation results. As a baseline, it will present GNSS-only hardware-in-the loop results using a NC3m test unit to process Spirent-simulated GPS signals in a potential lunar relay trajectory: a 12-hour elliptical frozen lunar orbit (ELFO). GEONS then processes the GPS pseudorange and time differenced carrier phase measurements to estimate and propagate the relay state (position, velocity, and time). These results extend previously published work that showed preliminary ELFO performance. Previous work has shown the importance of other measurement types, so additional simulations are performed which augment GNSS with ground station observables and several methods of optical navigation, including celestial navigation, limb-finding (e.g., observations of the lunar horizon), and terrain relative navigation (TRN). TRN involves correlating simulated predicted images of the lunar surface with actual imagery; misalignments of landmarks identified in each image are translated into relay state updates. TRN is valuable as a measurement of the relay’s state relative to the Moon, especially during GNSS outages or after maneuvers. One-way Pseudorange and Doppler measurements from Earth-based ground stations are also simulated. The full set of observables is processed using autoNGC. These simulations make use of autoNGC and NC3m test units, a lab atomic clock, and a pulse-per-second (PPS) generation and distribution system. This combination of subsystems, and the hardware platforms used in this analysis, represents a PNT Instrument that could be flown on a lunar relay. Results from the hardware-in-the-loop simulations presented in this paper provide a preliminary assessment of the achievable navigation performance of this instrument concept. PNT Instrument performance is compared to the GPS-only performance, and a discussion is provided on the apparent merits and challenges of each measurement type.

Ben Ashman↗
NASA NTRSDate not supplied

International Coordination and Cooperation on LunaNet Spectrum

LunaNet is planned to be the network of networks operated by a set of cooperating organizations to provide interoperable Communications, networking, Position, Navigation, and Timing (CPNT) services to users on and around the Moon based on a framework of mutually agreed-upon standards, protocols, frequency bands and interface requirements. LunaNet follows a service-oriented architecture that is agnostic about the types of organizations that provide services, e.g., government, industry, or academia. LunaNet is open, scalable, resilient, secure, and extensible. To achieve these goals, LunaNet Service Providers (LNSP) must coordinate with each other to define and develop the architecture, to plan initial and evolved capabilities, and to operate their networks. One of the central LunaNet tenets is the use of shared spectrum. For example, the Lunar Augmented Navigation Service (LANS) acts like a Global Navigation Satellite System (GNSS) such as the US Global Positioning System (GPS) or European Galileo but the LNSPs’ contributions to LunaNet must use the same frequency band (2483.5 MHz-2500.0 MHz) and transmit the same waveform synchronized by highly accurate clocks so that Users ‘see’ one virtual network and use the same multilateration algorithm to determine their positions. This necessitates a high degree of spectrum coordination. NASA’s Lunar and Human Spaceflight Spectrum Management Team has been actively supporting development of the LunaNet Interoperability Specification (LNIS), soliciting inputs from spectrum policy and planning experts across NASA, ESA and JAXA. Cislunar spectrum use considerations have been studied and adjudicated within the Space Frequency Coordination Group (SFCG) and inform the ongoing discussion of a lunar communication and navigation architecture within the existing radio regulatory framework of the International Telecommunication Union, leading to the 2027 World Radiocommunication Conference (WRC-27). The frequency plan contained in the publicly released draft of the LunaNet Interoperability Specification reflects the initial phase of exploration (roughly to 2030) defining an optimal set of radio frequencies in appropriately allocated services consistent with WRC-23 decisions for use by known or planned CPNT applications, while striving to maximize coexistence and compatibility amongst cislunar systems and other systems within the near-Earth regime (< 2 million km from Earth). Important considerations include: protection of extremely sensitive receive-only radio astronomy systems on the lunar far side, known as the Shielded Zone of the Moon (SZM); compatibility between Direct with Earth (DWE) communications links and links needed to support relay satellites in lunar orbit with their customer systems on orbit or on the lunar surface; compatibility between multiple lunar surface communications systems and capabilities over varied and challenging terrain and distances; as well as ensuring compatibility and interoperability between navigation systems which either leverage Earth-based or in-situ lunar systems. In addition, the lunar CPNT architecture is envisioned to be the basis – with adjustments – of the future Mars CPNT architecture as we expand into the solar system using Interplanetary Networking (IPN). The second phase of lunar spectrum definition will address planned international capabilities for the next decade that will require action at WRC-27 and beyond. This paper will discuss each of these considerations in more depth and how the current LunaNet frequency plan addresses them.

LunaNet↗
NASA NTRSDate not supplied

Evolution of Astrodynamics for Multibody Environments, Numerical Precision and Dynamical Understanding

The innovative nature of dynamical systems theory and its applications in trajectory design enabled many recent missions by opening up new transfer and capture opportunities to meet mission requirements, reduce fuel costs, and address various launch constraints and contingencies. With a combination of proven numerical methods and an advanced understanding of the dynamics, an ‘experienced’ user can rapidly design multibody and cislunar missions such as Lunar IceCube and Artemis/Themis and relatively quickly conceive trajectory concepts for Sun-Earth mission orbits, such as the Space Weather Follow On-L1 Lissajous orbit—one that can be achieved and maintained.

Dynamical Systems↗
NASA NTRSDate not supplied

NASA Space Nuclear Propulsion (SNP) MBSE Initiatives

NASA’s Space Nuclear Propulsion (SNP) program is developing several MagicDraw SysML models to support the development of high performance Nuclear Thermal Rocket Engines (NTRE). Currently, the Demonstration Rocket for Agile Cislunar Operations (DRACO) project is aiming to perform the first ever flight demonstration of an NTRE, and NASA is developing a DRACO Insight Project Model Based Systems Engineering (MBSE) model to capture, define, analyze, and report on the flight and ground test system architecture, functional behavior, requirements, risks, and lessons learned. Additional models are in work for engine component trade trees, fault detection sensor coverage analysis using a Goal Function Tree (GFT) plugin, stakeholder engagement, and technology maturation projects. The GFT plugin is the Galois, Inc. Failure Recovery Instruction Generation using Automata derived from Traditional Engineering models (FRIGATE) tool. A new capability for Jira to MagicDraw data sharing using the OpenPDM collaboration platform is under development with partner Victory Solutions, Inc. to enhance risk impact analysis.

Space Nuclear Propulsion (SNP)↗
DOE OSTI2025

SSAPy - Space Situational Awareness for Python

SSAPy is a fast and flexible orbit modeling and analysis tool for orbits spanning from low-Earth into the cislunar regime. Orbits can be flexibly specified from common input formats such as Keplerian elements or two-line element (TLE) data files. SSAPy allows users to model satellites and specify parameters such as satellite area, mass, and drag coefficients. SSAPy includes a customizable force-propagation with a range of Earth, Lunar, radiation, atmospheric, and maneuvering models. SSAPy makes use of various community integration methods and can calculate time-evolved orbital quantities, including satellite magnitudes and state vectors. Users can specify various space- and ground-based observation models with support for multiple coordinate and reference frames. SSAPy also supports orbit analysis and propagation methods such as multiple hypothesis tracking and has built-in uncertainty quantification. The majority of SSAPy’s methods are vectorized and parallelizable, allowing for effective use of high-performance computer (HPC) systems. Finally, SSAPy has plotting functionality, allowing users to visualize orbits and trajectories. Examples are shown in Figure 1 and Figure 2.

97 MATHEMATICS AND COMPUTING↗