Solar sail dynamics in the three-body problem: homoclinic paths of points and orbits

In this paper we consider the orbital previous termdynamicsnext term of a previous termsolar sailnext term in the Earth-Sun circular restricted three-body problem. The equations of motion of the previous termsailnext term are given by a set of non-linear autonomous ordinary differential equations, which are non-conservative due to the non-central nature of the force on the previous termsail.next term We consider first the equilibria and linearisation of the system, then examine the non-linear system paying particular attention to its periodic solutions and invariant manifolds. Interestingly, we find there are equilibria admitting homoclinic paths where the stable and unstable invariant manifolds are identical. What is more, we find that periodic orbits about these equilibria also admit homoclinic paths; in fact the entire unstable invariant manifold winds off the periodic orbit, only to wind back onto it in the future. This unexpected result shows that periodic orbits may inherit the homoclinic nature of the point about which they are described

Three-dimensional formation flying using bifurcating potential fields

This paper describes the design of a three-dimensional formation flying guidance and control algorithm for a swarm of autonomous Unmanned Aerial Vehicles (UAVs), using the new approach of bifurcating artificial potential fields. We consider a decentralized control methodology that can create verifiable swarming patterns, which guarantee obstacle and vehicle collision avoidance. Based on a steering and repulsive potential field the algorithm supports flight that can transition between different formation patterns by way of a simple parameter change. The algorithm is applied to linear longitudinal and lateral models of a UAV. An experimental system to demonstrate formation flying is also developed to verify the validity of the proposed control system

Trajectory and spacecraft design for a pole-sitter mission

This paper provides a detailed mission analysis and systems design of a pole-sitter mission. It considers a spacecraft that is continuously above either the North or South Pole and, as such, can provide real-time, continuous and hemispherical coverage of the polar regions. Two different propulsion strategies are proposed, which result in a near-term pole-sitter mission using solar electric propulsion and a far-term pole-sitter mission where the electric thruster is hybridized with a solar sail. For both propulsion strategies, minimum propellant pole-sitter orbits are designed. Optimal transfers from Earth to the pole-sitter are designed assuming Soyuz and Ariane 5 launch options, and a controller is shown to be able to maintain the trajectory under unexpected conditions such as injection errors. A detailed mass budget analysis allows for a trade-off between mission lifetime and payload mass capacity, and candidate payloads for a range of applications are investigated. It results that a payload of about 100 kg can operate for approximately 4 years with the solar-electric spacecraft, while the hybrid propulsion technology enables extending the missions up to 7 years. Transfers between north and south pole-sitter orbits are also considered to observe either pole when illuminated by the Sun

Studies of complementary DNAs corresponding to skeletal muscle proteins

The initial objective of the work described in this thesis was to isolate complementary DMAs (cDNAs) corresponding to mRNAs encoding proteins expressed solely in skeletal muscle. To this end a mouse skeletal muscle cDNA library was differentially screened with radioactively-labelled single-stranded cDNA probes derived from skeletal and cardiac muscle. Of 15,000 individual colonies subjected to the mass screening procedure of colony hybridisation, 247 were selected on the basis that they gave a hybridisation signal only with the skeletal muscle probe. Southern blot analysis of plasmid DNA isolated from each of these revealed eight which continued to produce a differential hybridisation signal with the two single-stranded cDNA probes. However subsequent hybridisation of these eight radioactively-labelled cDNA clones with poly(A)+ RNA isolated from skeletal muscle, cardiac muscle, liver and brain, revealed only a single clone which appeared to represent an mRNA specific to skeletal muscle. The nucleotide sequence of the cDNA insert of this clone, which was approximately 500 base pairs (bp) in length, was determined. It was found to contain an open reading-frame, the predicted product of which corresponded to part of the sequence of the beta-isoform of rabbit tropomyosin. This isoform has only been found in skeletal muscle, although other isoforms are found in cardiac muscle, smooth muscle, and non-muscle tissues. No previous mouse beta-tropomyosin cDNA clones have been described. The skeletal muscle cDNA library was rescreened in an attempt to obtain a full-length beta-tropomyosin cDNA clone. Three clones were selected and sequenced. One of these was found to be identical to the original clone selected from the initial screening. The second, however, contained the entire beta-tropomyosin amino-acid coding region together with 72 nucleotides of the 5' non-coding region and 151 nucleotides of the 3' non-coding region. The remaining clone lacked sequence from the 3' half of the mRNA, but extended the 5' noncoding region to 95 nucleotides. From comparison with the size of the mRNA (1.3kb), revealed by Northern blotting, it is estimated that the sequence of the mouse beta-tropomyosin determined represents approximately 90% of the mRNA. The expression of tropomyosin mRNAs was examined during the differentiation of a cultured mouse cell line from the individual myoblast stage to the multinucleate cell stage. Northern blot analysis of the mRNA isolated from the cells at different stages of their development revealed that upon fusion of the cells, the expression of several different tropomyosin mRNAs is induced. In particular two species, with lengths of 1.2kb and 2.6kb, which are not found in the RNA isolated from 11-day old mouse skeletal muscle, are expressed during the differentiation of skeletal muscle cells. The two remaining species expressed upon fusion of the cells, a 1.3kb species and a 2.4kb species, correspond to the species identified in the RNA from 11-day old mice. The identities of all four tropomyosin species are unknown, except for the 1.3kb beta-tropomyosin mRNA. However comparison with published work suggests that the 1.2kb and 2.4kb species may correspond respectively to the alternatively spliced products from the primary transcripts which also give rise to the beta-tropomyosin and the a2 tropomyosin species. No previous work has reported the possible coexpression of alternatively spliced isoforms of tropomyosin. Analysis of the nucleotide sequence corresponding to mouse beta-tropomyosin mRNA revealed some unusual features. There was a deficit of the dinucleotide CpG in the codon position [2,3], but not in the [3,1] position, throughout the amino-acid coding region of beta-tropomyosin. One possible explanation of this is that there is strand-specific hemi-methylation of the corresponding germ line DNA. Previously published comparisons of a partial human beta-tropomyosin cDNA sequence with a human non-muscle tropomyosin (TM36) cDNA sequence had indicated the likelihood that beta-tropomyosin and TM36-tropomyosin are encoded by the same gene, with each of the isoforms arising from the alternative splicing of two pairs of mutually exclusive exons. Comparison of these sequences with the mouse beta-tropomyosin cDNA allowed the conclusion that none of the 5' exons not represented in the human beta-tropomyosin cDNA clone are involved in alternative splicing. Nucleotide comparisons with other beta-tropomyosin cDNA sequences reported during the completion of this work indicated that the 3' and 5' non-coding regions of the beta-tropomyosin mRNA had been subject to some selective evolutionary pressure for conservation, although not to the extent found for certain other mRNAs encoding muscle proteins (e.g. actin mRNAs)

Invariant manifolds and orbit control in the solar sail three-body problem

In this paper we consider issues regarding the control and orbit transfer of solar sails in the circular restricted Earth-Sun system. Fixed points for solar sails in this system have the linear dynamical properties of saddles crossed with centers; thus the fixed points are dynamically unstable and control is required. A natural mechanism of control presents itself: variations in the sail's orientation. We describe an optimal controller to control the sail onto fixed points and periodic orbits about fixed points. We find this controller to be very robust, and define sets of initial data using spherical coordinates to get a sense of the domain of controllability; we also perform a series of tests for control onto periodic orbits. We then present some mission strategies involving transfer form the Earth to fixed points and onto periodic orbits, and controlled heteroclinic transfers between fixed points on opposite sides of the Earth. Finally we present some novel methods to finding periodic orbits in circumstances where traditional methods break down, based on considerations of the Center Manifold theorem

Solar sail formation flying for deep-space remote sensing

In this paper we consider how 'near' term solar sails can be used in formation above the ecliptic plane to provide platforms for accurate and continuous remote sensing of the polar regions of the Earth. The dynamics of the solar sail elliptical restricted three-body problem (ERTBP) are exploited for formation flying by identifying a family of periodic orbits above the ecliptic plane. Moreover, we find a family of 1 year periodic orbits where each orbit corresponds to a unique solar sail orientation using a numerical continuation method. It is found through a number of example numerical simulations that this family of orbits can be used for solar sail formation flying. Furthermore, it is illustrated numerically that Solar Sails can provide stable formation keeping platforms that are robust to injection errors. In addition practical trajectories that pass close to the Earth and wind onto these periodic orbits above the ecliptic are identified

Generation of optimal trajectories for Earth hybrid pole sitters

A pole-sitter orbit is a closed path that is constantly above one of the Earth's poles, by means of continuous low thrust. This work proposes to hybridize solar sail propulsion and solar electric propulsion (SEP) on the same spacecraft, to enable such a pole-sitter orbit. Locally-optimal control laws are found with a semi-analytical inverse method, starting from a trajectory that satisfies the pole-sitter condition in the Sun-Earth circular restricted three-body problem. These solutions are subsequently used as first guess to find optimal orbits, using a direct method based on pseudospectral transcription. The orbital dynamics of both the pure SEP case and the hybrid case are investigated and compared. It is found that the hybrid spacecraft allows savings on propellant mass fraction. Finally, it is shown that for sufficiently long missions, a hybrid pole-sitter, based on mid-term technology, enables a consistent reduction in the launch mass for a given payload, with respect to a pure SEP spacecraft

Solar radiation pressure enabled femtosatellite based Earth remote sensing

Recent developments in electronics have pushed miniaturised satellites to the femto-scale, with masses between 10 and 100 g. Although femtosatellites have been proven as a feasible concept, most designs are limited in mission capacity and lifetime due to the lack of environmental protection and onboard propellant. In this paper, a novel concept for femtosatellites for Earth remote sensing is proposed. In particular, a swarm of femtosatellites are used as elements of a sparse array in orbit to receive radar echoes. They also feature active orbit control enabled by solar radiation pressure to extend their lifetime. A simple active orbit control algorithm has been demonstrated. A mission concept based on a Sun-synchronous circular orbit is proposed to maximise the benefit for both Earth remote sensing and active orbit control. A synthetic aperture radar mission has been used to characterise their performance

Asymptotic analysis of displaced lunar orbits

The design of spacecraft trajectories is a crucial task in space mission design. Solar sail technology appears as a promising form of advanced spacecraft propulsion which can enable exciting new space science mission concepts such as solar system exploration and deep space observation. Although solar sailing has been considered as a practical means of spacecraft propulsion only relatively recently, the fundamental ideas are by no means new (see McInnes1 for a detailed description). A solar sail is propelled by reflecting solar photons and therefore can transform the momentum of the photons into a propulsive force. Solar sails can also be utilised for highly non-Keplerian orbits, such as orbits displaced high above the ecliptic plane (see Waters and McInnes2). Solar sails are especially suited for such non-Keplerian orbits, since they can apply a propulsive force continuously. In such trajectories, a sail can be used as a communication satellite for high latitudes. For example, the orbital plane of the sail can be displaced above the orbital plane of the Earth, so that the sail can stay fixed above the Earth at some distance, if the orbital periods are equal (see Forward3). Orbits around the collinear points of the Earth-Moon system are also of great interest because their unique positions are advantageous for several important applications in space mission design (see e.g. Szebehely4, Roy,5 Vonbun,6 Thurman et al.,7 Gomez et al.8, 9). Several authors have tried to determine more accurate approximations (quasi-Halo orbits) of such equilibrium orbits10. These orbits were first studied by Farquhar11, Farquhar and Kamel10, Breakwell and Brown12, Richardson13, Howell14, 15.If an orbit maintains visibility from Earth, a spacecraft on it (near the L2 point) can be used to provide communications between the equatorial regions of the Earth and the lunar poles. The establishment of a bridge for radio communications is crucial for forthcoming space missions, which plan to use the lunar poles.McInnes16 investigated a new family of displaced solar sail orbits near the Earth-Moon libration points.Displaced orbits have more recently been developed by Ozimek et al.17 using collocation methods. In Baoyin and McInnes18, 19, 20 and McInnes16, 21, the authors describe new orbits which are associated with artificial Lagrange points in the Earth-Sun system. These artificial equilibria have potential applications for future space physics and Earth observation missions. In McInnes and Simmons22, the authors investigate large new families of solar sail orbits, such as Sun-centered halo-type trajectories, with the sail executing a circular orbit of a chosen period above the ecliptic plane. We have recently investigated displaced periodic orbits at linear order in the Earth-Moon restricted three-body system, where the third massless body is a solar sail (see Simo and McInnes23). These highly non-Keplerian orbits are achieved using an extremely small sail acceleration. It was found that for a given displacement distance above/below the Earth-Moon plane it is easier by a factor of order 3.19 to do so at L4=L5 compared to L1=L2 - ie. for a fixed sail acceleration the displacement distance at L4=L5 is greater than that at L1=L2. In addition, displaced L4=L5 orbits are passively stable, making them more forgiving to sail pointing errors than highly unstable orbits at L1=L2.The drawback of the new family of orbits is the increased telecommunications path-length, particularly the Moon-L4 distance compared to the Moon-L2 distance

Designing displaced lunar orbits using low-thrust propulsion

The design of spacecraft trajectories is a crucial task in space mission design. Solar sail technology appears as a promising form of advanced spacecraft propulsion which can enable exciting new space science mission concepts such as solar system exploration and deep space observation. Although solar sailing has been considered as a practical means of spacecraft propulsion only relatively recently, the fundamental ideas are by no means new (see McInnes1 for a detailed description). A solar sail is propelled by re ecting solar photons and therefore can transform the momentum of the photons into a propulsive force. This article focuses on designing displaced lunar orbits using low-thrust propulsion