The Role of Computers in Calculating Spacecraft Trajectory

Published on 24 April 2024

The Role of Computers in Calculating Spacecraft Trajectory

When the Soviet Union launched Sputnik-1 in 1957, the first man-made object to orbit the Earth, outer space became the new theatre of rivalry between the United States (US) and the Soviet Union. Suborbital flight of supersonic jets, rockets capable of carrying humans into Earth's orbit, and surveillance satellites suddenly became a new reality. Eventually, the rivalry ended and the competing nations moved over to jointly establish a permanent human presence in outer space onboard the International Space Station (Hansen, 2018). Today, every known planet in the Solar System has been visited by a probe (Butrica, 2001), asteroid sample return missions are on the way and robotic interplanetary missions set the path for future human space exploration (The Planetary Society, 2021). However, sending the spacecraft and scientific instruments into and beyond the Earth’s orbit requires innovation and finding solutions to complex mathematical problems. This paper aims to discuss the role of digital computers in calculating trajectories for orbital and deep space missions. The focus is on the historical perspective in the US and Europe, major motivators, and challenges that have been solved using Computer Science. This paper also discusses the current state of thinking and offers opportunities for potential future development. Additionally, this paper measures the benefits of calculating spacecraft trajectories with digital computers against traditional methods and demonstrates the impact of space exploration and satellite networks on society. Finally, a discussion of major legal, ethical and professional issues surrounding robotic and human space exploration enabled by computer generated trajectories, followed by a conclusion and final remarks, finalising with opportunities for future research.

How Computer Science can be Used to Solve the Problem

One of the more challenging problems that have been solved using Computer Science can be seen in the robotic and human space exploration and satellite services, where calculating the trajectory, for instance, to another planet or object in the Solar System, could determine whether the mission is feasible or not. Agrawal and Maini (2014) define a trajectory as a path taken by a moving object between the origin, i.e., launch pad, and the destination, i.e., Geosynchronous Earth Orbit (GEO) or another planet. In calculating trajectories to escape the Earth’s gravity, several laws of physics need to be considered, i.e., Newton’s Law of Gravitation, Second Law of Motion, and Kepler’s Laws of planetary motion that computers enable quickly to solve. Moreover, combined with signals received by the ground antennas, computers provide efficient satellite tracking system that also is utilised in deep space missions (Agrawal and Maini, 2014). The spacecraft trajectory is divided into mission, journey, and phases, each consisting of its own set of events determined by evolutionary algorithms (Englander et al., 2017). Whilst celestial bodies are in constant motion, missions need to be planned years in advance to find the best time to launch the spacecraft. The Voyager missions demonstrated the benefits of knowing the position of the planets in the Solar System ahead of time to enable the mission planners to take advantage of the planets’ gravitational assist to either accelerate or deflect the spacecraft towards the next destination, consequently saving the fuel and reducing the duration of the interplanetary journey (Butrica, 2001). According to Englander et al. (2017) and Shirazi et al. (2018), knowing the trajectory beforehand help scientists and engineers to define the mission parameters, i.e., launch time, fuel type, flight time, necessary manoeuvres, planetary flybys, power requirements, propulsion system and the choice of the launch vehicle and scientific instruments. Butrica (2001) emphasised that the approval of the instruments carried by spacecraft strongly depends on the predefined spacecraft trajectory. Additionally, knowing the preliminary requirements derived from calculations of the trajectory, makes it easier to predict the lifespan of the mission and secure the necessary funding for the duration of the mission.

In the early days of US space exploration, Katherine Johnson and other mathematicians and engineers at the National Aeronautics and Space Administration (NASA) would workout trajectories for the first spaceflight of the American astronaut Alan Shepard by hand or with the help of slide rules, data cards and early calculators. However, those activities were time- consuming, expensive, and vulnerable to human error (NASA, 2020). Consequently, it was desirable to automate the task of finding solutions to mathematical problems in order to increase the quality of the data for future mission planning activities (Englander et al, 2017). As a result, digital computers provided an opportunity to solve this and other problems faced by the researchers at NASA, and to this day, their ubiquitous presence in mission planning, spacecraft design, and mission control benefits the space exploration (NASA, 2020). However, computers also introduced problems that have been discussed later in this paper.

When Alan Turing described a general-purpose device in the 1930s, unlike its predecessors, for instance, Pascal’s device capable of calculating simple arithmetic equations, the advantage of Turing’s machine was its ability to be programmed by a human programmer to serve many different purposes (Davis, 2018). Previous research has emphasised that the first digital computers invented in the 1940s were slow and could take only a few inputs and outputs at the same time (Ceruzzi, 2009; Davis, 2018). However, the invention of the transistor in the 1940s and the integrated circuit in 1959 gave a rise to the phenomenon known as Moore’s Law, where computer power has been predicted to double every two years (Ceruzzi, 2009; Primiero, 2020). Since the formation of NASA in 1958, the agency was actively investing in the research and development of electronics and computer software (Butrica, 2001; Ceruzzi, 2009). NASA’s administration recognised the value of digital computers in solving intricate mathematical problems encountered in calculating trajectories for deep space missions and the challenges of keeping the spacecraft in control at high speeds and in the vacuum of space (NASA, 2020). As a result, the invention of the ARPANET computer network and the appearance of the first general- purpose object-based programming languages such as FORTRAN (Hatfield, 2003; Ceruzzi, 2009) provided an opportunity to develop a special-purpose computer architecture that has been programmed to solve problems in the first human spaceflight missions at NASA in the mid-1960s. While Russian mathematicians were transitioning to use of digital computers in their space program (Ceruzzi, 2009), computer algorithms enabled NASA to develop computer programs capable of taking different mission parameters to produce multiple trajectories and what-if scenarios in seconds instead of months (Hatfield, 2003). However, due to the experimental nature of the research, computer hardware was often the cause of costly and unacceptable vehicle failures. Therefore, in the 1950s, the US Air Force introduced a “high-reliability” program that outlined a methodologies for rigorous statistical quality control and documentation of computer hardware manufacturing (Ceruzzi, 2009). Similarities can be found to this day across different codes of conduct introduced by professional computer and engineering associations, such as the Association for Computing and Machinery that advocate high standards in computer software development (ACM, 2021).

The literature review shows that due to their large size, power consumption, and fragility, digital computers were used sparingly by NASA in the early Mercury and Gemini programs. However, as digital computers became more powerful and more reliable, by 1968, they were used in the guidance systems in the Apollo program (Ceruzzi, 2009; Hansen, 2018). When Neil Armstrong and Buzz Aldrin descended on the surface of the Moon, the lack of atmosphere meant that landing on the surface will be challenging and will require high precision beyond human capabilities (Ceruzzi, 2009). Therefore, the descending trajectory was fully automated by the computer program written by Margaret Hamilton (Ceruzzi, 2009; NASA, 2020). The advancements in computer graphics provided more opportunities in the next decades, among them the ability to create graphical visualisation and simulations of spacecraft and events that could happen during the mission (Weinberg, 1978). This in return provided a safe environment for testing individual divisions of the trajectory and assessing associated dangers, i.e., collisions with other objects or damage to onboard instruments caused by the electromagnetic environment around larger planets such as Jupiter. This in return reduced the costs and provided grounds for the establishment of functional requirements, procedures, and evaluation of spacecraft design before its construction (Weinberg, 1978). In the human spaceflight program between 1981 and 2011, engineers at NASA fully embraced digital computers in the design of the reusable Space Shuttle. Because it was extremely challenging to manually control ascend and descend of the vehicle, computer software provided an effective solution to the problem of keeping the Space Shuttle under control and on the trajectory towards the target during its hypersonic atmospheric reentry at around 17,500 mph (Ceruzzi, 2009). On the other hand, according to Shirazi et al. (2018), once the vehicle enters the space, it needs to use its thrusters to perform manoeuvres to correct its orbit direction. Therefore, mission planners use Evolutionary Algorithms to provide a solution to trajectory optimisation problems, i.e., through the computer simulation of the spacecraft dynamics.

The literature review shows that today, mission planners rely on the implicit and explicit knowledge gathered from the studies and previous experiences. However, Berquand et al. (2019) argue that searching through knowledge is time-consuming and some information is limited or not widely available. Having quick access to knowledge can be beneficial when planning the spacecraft trajectory, therefore Berquand et al. (2019) suggests that Artificial Intelligence (AI) could be used in the creation of an AI-based Design Engineering Assistant (DEA) that would, for instance, process and analyse data from previous missions and studies using a combination of, i.e., Natural Language Processing and Machine Learning to search the Internet and query databases for valuable information. Future space exploration missions could also take advantage of the advancements in the optical sensors and Machine Learning algorithms developed for the Visual-Based Navigation systems in deep space missions, where conventional navigation systems are unavailable (Airbus, 2021). Consequently, this could give the spacecraft more autonomy and decide whether or not to adjust its trajectory without human intervention. Nevertheless, the ultimate goal would be to send robotic spacecraft capable of autonomous exploration of outer space, that does not require the human controller to send commands (Shekhtman, 2019). However, the application of AI in autonomous space exploration should be considered as a topic for further research.

Measuring Success and Impact on the Society

The literature review shows that the most significant achievement of Computer Science in space exploration was the moon landing in 1969, which Ceruzzi (2009) describes as one of the first times when human life fully depended on the successful operation of a digital computer. Today, there are over 27 active probes with onboard computers designed to study the Sun, Mercury, Venus, Earth, the Moon, Mars, Jupiter, and various smaller moons and asteroids (The Planetary Society, 2021). Reliability and cost reduction of computer-generated trajectories and their simulation, enabled space agencies to look at different types of missions, for instance, NASA’s OSIRIS-REx sample return missions from asteroids Bennu (Englander et al., 2019). Additionally, the European Space Agency’s Rosetta mission to rendezvous with a comet 67P/Churyumov- Gerasimenko and deployment of a lander to its surface. The fly-by of the dwarf planet Pluto by the New Horizon probe in 2015 provided first, high-resolution photographs of the distant world, whereas Voyager and Pioneer probes are on a trajectory towards the interstellar space. One of the most successful unmanned missions was NASA's Cassini spacecraft that studied Saturn and its moons, including its rings and the landing of the Huygens probe on the surface of Titan (The Planetary Society, 2021).

In terms of social impact, using computers in calculating spacecraft trajectories enabled space agencies to send probes towards distant worlds to collect scientific data and take photographs for further study, educational purposes as an inspiration to youth (Aglietti, 2020). Additionally, frequent missions to other planets and asteroids increased the demand for the manufacturing, assembly, and transportation of hardware, including scientific instruments and demand for reliable launch vehicles, consequently expanding and creating new industries, specialised jobs (Butrica, 2001), and opportunities for innovative entrepreneurs (SpaceX, 2021). Computers provided a solution to precisely and continuously tracking satellites and space debris orbits. Several studies in the Space Policy suggest that Space Traffic Management systems could make the environment in the Earth’s orbit safer for existing and future missions (Aglietti, 2020). Moreover, this could also enable mission planners to launch and securely deploy new satellites in orbits that do not collide with other artificial satellites (Agrawal and Maini, 2014). According to Agrawal and Maini (2014), satellites have broad applications in communication services, navigation systems, weather forecasting, and Earth observation studies. The application of communication satellites enables global communication and television broadcasting across large geographical areas, whereas navigation satellites provide navigational aids to land-, air- and sea-based transportation. Ceruzzi (2009) points out that NASA’s development of computer networks for space missions later became an inspiration for the world-changing World Wide Web. The photographs of Earth, the “Blue Marble” taken by the Apollo astronauts in 1972, and “Pale Blue Dot” by the Cassini probe in 1990 affect the philosophical point of view of humanity’s place in the Universe that arguably helped humanity to focus more energy on preserving the home planet (Aglietti, 2020). However, no further evidence could be found to support this claim.

Legal, Ethical and Professional Issues

After the Apollo program, the government funding for NASA’s projects has been reduced during the Nixon presidency. Consequently, smaller projects could be cancelled in favour of the high- profile missions due to limited resources (Butrica, 2001). For this reason, NASA’s research centres would compete against each other for funding (Butrica, 2001) and focus on keeping the costs within the tight budgets and schedules. Leveson (2004) argues this could cause professional and ethical issues. For instance, neglect of the safety checks and quality assurance of computer software by the management. Although Computer Science helped the US space program to achieve success, the replacement of human computers increased the demand for qualified computer programmers. Leveson (2004) argues that human errors caused failures in space exploration. For instance, Leveson (2004) gives examples of complacency, underestimation, and lack of strict procedures for testing and validating computer hardware and software. In particular, the explosion of the Ariane 5 rocket during its maiden flight in 1996 set the focus on the improvement of reliability checks of critical systems. Additionally, NASA’s Mars Climate Orbiter software failure to convert data into metric units resulted in the loss of spacecraft in 1998. Although the mission is an example of faulty calculation of trajectory by the computer, human factors, such as poor project management, organisation and communication between mission design team (Leveson, 2004).

From an ethical perspective, advancements in Computer Science and Space Technologies provided opportunities for innovative entrepreneurs to commercialise outer space. Commercial satellite launch providers also actively develop the first-of-the-kind constellation of satellites to provide global access to the Internet by 2025 (SpaceX, 2021). The competition is likely to follow, and 12,000 new satellites could be deployed in the Low Earth Orbit (Grush, 2018). This could cause congestion and disruption to the current satellite infrastructure and increase the chance of collision between two satellites and create a vast amount of debris (Marks, 2009). Although measures to establish treaties and principles to regulate the use of outer space have been taken, i.e., Outer Space Treaty or the Convention for the International Liability for the Damaged Caused Space Objects (Aglietti, 2020), not all nations comply with the regulations (Marks, 2009). Also of importance is the issue of the long-term survival of humanity. According to Schwartz (2011), one of the most likely threats to Earth coming from outer space is an asteroid impact. Therefore, Schwartz (2011) argues that it is humanity’s moral responsibility to protect the environment and living organisms. However, at the same time ensuring that human activity in outer space does not contaminate other planets and moons (Losch, 2017). Marks (2009) argues that at the end of their lifetime, satellites should be safely removed from orbit to prevent the accumulation of space debris.

Conclution and Future Work

The main conclusion that can be drawn is that Computer Science played an important role in the success of early space exploration. NASA’s contribution in the development of special-purpose computer electronics and programming languages enabled mission planners to effectively, cheaply, and accurately calculate, simulate and test trajectories and mission design parameters that otherwise could take months to verify by hand, only to find out that the mission is not feasible. Future spacecraft missions to Mars and other destinations in the Solar System, as well as the application of satellite services on Earth, are partly possible due to the Computer Science discipline. It is, however, worth mentioning that these contributions could not be possible without the contributions of logicians and mathematicians who theorised and experimented with the early computation machines in the past. In future work, a detailed investigation of computer algorithms could prove important in developing a better understanding of how computer algorithms can be applied in spacecraft guidance control systems. Moreover, further research into methodologies used in developing programs to calculate trajectories. Besides, the application of AI in trajectory optimisation, guidance systems, and autonomous spacecraft might be an interesting area for future research. AI promises new opportunities in spacecraft trajectory optimisation and development of computer guidance systems that could provide more opportunities in robotic and human space exploration.


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