Malcolm Macdonald

Survey of highly non-Keplerian orbits with low-thrust propulsion

Celestial mechanics has traditionally been concerned with orbital motion under the action of a conservative gravitational potential. In particular, the inverse square gravitational force due to the potential of a uniform, spherical mass leads to a family of conic section orbits, as determined by Isaac Newton, who showed that Kepler‟s laws were derivable from his theory of gravitation. While orbital motion under the action of a conservative gravitational potential leads to an array of problems with often complex and interesting solutions, the addition of non-conservative forces offers new avenues of investigation. In particular, non-conservative forces lead to a rich diversity of problems associated with the existence, stability and control of families of highly non-Keplerian orbits generated by a gravitational potential and a non-conservative force. Highly non-Keplerian orbits can potentially have a broad range of practical applications across a number of different disciplines. This review aims to summarize the combined wealth of literature concerned with the dynamics, stability and control of highly non-Keplerian orbits for various low thrust propulsion devices, and to demonstrate some of these potential applications.

Parametric model and optimal control of solar sails with optical degradation

Solar-sail mission analysis and design is currently performed assuming constant optical and mechanical properties of the thin metalized polymer films that are projected for solar sails. More realistically, however, these properties are likely to be affected by the damaging effects of the space environment. The standard solar-sail force models can therefore not be used to investigate the consequences of these effects on mission performance. The aim of this paper is to propose a new parametric model for describing the sail films optical degradation with time. In particular, the sail films optical coefficients are assumed to depend on its environmental history, that is, the radiation dose. Using the proposed model, the optimal control laws for degrading solar sails are derived using an indirect method and the effects of different degradation behaviors are investigated for an example interplanetary mission.

GEOSAIL: Exploring the Geomagnetic Tail Using a Small Solar Sail

Conventional geomagnetic tail missions require a spacecraft to be injected into a long elliptical orbit to explore the spatial structure of the geomagnetic tail. However, because the elliptical orbit is inertially fixed and the geomagnetic tail is directed along the sun-Earth line, the apse line of the elliptical orbit is precisely aligned with the geomagnetic tail only once every year. To artificially precess the apse line of the elliptical orbit in a sun-synchronous manner, which would keep the spacecraft in the geomagnetic tail during the entire year, would require continuous low-thrust propulsion or periodic impulses from a high-thrust propulsion system. Both of these options require reaction mass that will ultimately limit the mission lifetime. It is demonstrated that sun-synchronous apse-line precession can be achieved using only a small, low-cost solar sail. Because solar sails do not require reaction mass, a geomagnetic tail mission can be configured that provides a continuous science return by permanently stationing a science payload within the geomagnetic tail.

Solar polar orbiter: a solar sail technology reference study

An assessment is presented of a Solar Polar Orbiter mission as a Technology Reference Study. The goal is to focus the development of strategically important technologies of potential relevance to future science missions. The technology is solar sailing, and so the use of solar sail propulsion is, thus, defined a priori. The primary mission architecture utilizes maximum Soyuz Fregat 2-1b launch energy, deploying the sail shortly after Fregat separation. The 153 × 153 m square sail then spirals into a circular 0.48-astronomical-unit orbit, where the orbit inclination is raised to 90 deg with respect to the solar equator in just over 5 years. Both the solar sail and spacecraft technology requirements have been addressed. The sail requires advanced boom and new thin-film technology. The spacecraft requirements were found to be minimal because the spacecraft environment is relatively benign in comparison with other currently envisaged missions, such as the Solar Orbiter mission and BepiColombo.

GeoSail: An Elegant Solar Sail Demonstration Mission

In this paper a solar sail magnetotail mission concept was examined. The 43-m square solar sail is used to providethe required propulsion for continuous sun-synchronous apse-line precession. The main driver in this mission was found to be the reduction of launch mass and mission cost while enabling a nominal duration of 2 years within the framework of a demonstration mission. It was found that the mission concept provided an excellent solar sail technology demonstration option. The baseline science objectives and engineering goals were addressed, and mission analysis for solar sail, electric, and chemical propulsion performed. Detailed subsystems were defined for each propulsion system and it was found that the optimum propulsion system is solar sailing. A detailed tradeoff as to the effect of spacecraft and sail technology levels, and requirements, on sail size is presented for the first time. The effect of, for example, data acquisition rate and RF output power on sail size is presented, in which it is found that neither have a significant effect. The key sail technology requirements have been identified through a parametric analysis.

Analytical Control Laws for Planet-Centered Solar Sailing

With increased interest in solar sailing from both ESA and NASA for future science missions comes the requirement to assess potential planet-centered orbits and generate algorithms for effective orbit maneuvering and control. Previous planet-centered solar-sail trajectory work has been limited mostly to Earth-escape or lunar flyby trajectories as a result of the difficulties of fully optimizing multirevolution orbits. A new method of blending locally optimal control laws is introduced, where each control law is prioritized by consideration of how efficiently it will use the solar sail and how far each orbital element is from its target value. The blended, locally optimal sail thrust vector is thus defined to use the sail as efficiently as possible, allowing the rapid generation of near-optimal trajectories. The blending method introduced is demonstrated for a complex orbit transfer and for two stationkeeping applications. Furthermore, the algorithms developed are explicitly independent of time, and as such the control system is demonstrated suitable as a potential future onboard sail controller.

Impact of Optical Degradation on Solar Sail Mission Performance

The optical properties of the thin metalized polymer films that are projected for solar sails are likely to be affected by the damaging effects of the space environment, but their real degradation behavior is to a great extent unknown. The standard solar sail force models that are currently used for solar sail mission analysis and design do not take these effects into account. In this paper we use a parametric model for describing the sail film’s optical degradation with its environmental history to estimate the impact of different degradation behaviors on solar sail mission performance for some example interplanetary missions: the Mercury rendezvous missions, fast missions to Neptune and to the heliopause, and artificial Lagrange-point missions.

Technology Requirements of Exploration Beyond Neptune by Solar Sail Propulsion

This paper provides a set of requirements for the technology development of a solar sail propelled Interstellar Heliopause Probe mission. The mission is placed in the context of other outer solar systems missions, ranging from a Kuiper Belt mission through to an Oort cloud mission. Mission requirements are defined and a detailed parametric trajectory analysis and launch date scan performed. Through analysis of the complete mission trade space a set of critical technology development requirements are identified which include an advanced lightweight composite High-Gain Antenna, a high-efficiency Ka-band travelling-wave tube amplifier and a radioisotope thermoelectric generator with power density of approximately 12 W/kg. It is also shown that the Interstellar Heliopause Probe mission necessitates the use of a spinning sail, limiting the direct application of current hardware development activities. A Kuiper Belt mission is then considered as a pre-curser to the Interstellar Heliopause Probe, while it is also shown through study of an Oort cloud mission that the Interstellar Heliopause Probe mission is the likely end-goal of any future solar sail technology development program. As such, the technology requirements identified to enable the Interstellar Heliopause Probe must be enabled through all prior missions, with each mission acting as an enabling facilitator towards the next.

Heliocentric Solar Sail Orbit Transfers with Locally Optimal Control Laws

Solar sailing is increasingly being considered by space agencies for future science missions. With the absence of reaction mass from the primary propulsion system arises the potential for new high-energy mission concepts in the mid to far term, such as a Solar Polar Orbiter or an Interstellar Heliopause Probe [1,2]. One of the most time consuming tasks of mission analysis is trajectory generation and optimization. Optimal trajectory generation is a complex field and many schemes exist; however, these are typically characterized as being computationally intensive systems requiring a good degree of engineering judgment [3-6].

Realistic Earth escape strategies for solar sailing

With growing interest in solar sailing comes the requirement to provide a basis for future detailed planetary escape mission analysis by drawing together prior work, clarifying and explaining previously anomalies. Previously unexplained seasonal variations in sail escape times from Earth orbit are explained analytically and corroborated within a numerical trajectory model. Blended-sail control algorithms, explicitly independent of time, which provide near-optimal escape trajectories and maintain a safe minimum altitude and which are suitable as a potential autonomous onboard controller, are then presented. These algorithms are investigated from a range of initial conditions and are shown to maintain the optimality previously demonstrated by the use of a single-energy gain control law but without the risk of planetary collision. Finally, it is shown that the minimum sail characteristic acceleration required for escape from a polar orbit without traversing the Earth shadow cone increases exponentially as initial altitude is decreased.