Solar sail orbits at the Earth–Moon libration points

Simo, Jules; McInnes, Colin R.

doi:10.1016/j.cnsns.2009.03.032

Cited by 58 publications

(31 citation statements)

References 13 publications

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“…The approximations in (11) and (12) replace the first and second time derivatives in (8), and the result is an equation at each epoch of the form…”

Section: Augmented Finite-difference Methodsmentioning

confidence: 99%

“…This dynamical system is complex due to the gravitational effects of the two primaries and, in the case of solar sails, the fact that the Sun, which influences the direction and magnitude of the resulting sail thrust vector, continually moves relative to a fixed Earth-Moon system. A previous approach, based on an understanding of the dynamical structure and using that knowledge to design an orbit, has been successful in developing some solar sail orbits in the vicinity of the lunar Lagrange points [5][6][7][8][9]. However, motion below one of the lunar poles requires an alternative strategy.…”

Section: Introductionmentioning

confidence: 99%

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Generating Solar Sail Trajectories in the Earth-Moon System Using Augmented Finite-Difference Methods

Wawrzyniak¹,

Howell²

2011

International Journal of Aerospace Engineering

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Using a solar sail, a spacecraft orbit can be offset from a central body such that the orbital plane is displaced from the gravitational center. Such a trajectory might be desirable for a single-spacecraft relay to support communications with an outpost at the lunar south pole. Although trajectory design within the context of the Earth-Moon restricted problem is advantageous for this problem, it is difficult to envision the design space for offset orbits. Numerical techniques to solve boundary value problems can be employed to understand this challenging dynamical regime. Numerical finite-difference schemes are simple to understand and implement. Two augmented finite-difference methods (FDMs) are developed and compared to a Hermite-Simpson collocation scheme. With 101 evenly spaced nodes, solutions from the FDM are locally accurate to within 1740 km. Other methods, such as collocation, offer more accurate solutions, but these gains are mitigated when solutions resulting from simple models are migrated to higherfidelity models. The primary purpose of using a simple, lower-fidelity, augmented finite-difference method is to quickly and easily generate accurate trajectories.

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“…The approximations in (11) and (12) replace the first and second time derivatives in (8), and the result is an equation at each epoch of the form…”

Section: Augmented Finite-difference Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generating Solar Sail Trajectories in the Earth-Moon System Using Augmented Finite-Difference Methods

Wawrzyniak¹,

Howell²

2011

International Journal of Aerospace Engineering

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“…Previous work on solar sail periodic orbits in the EarthMoon system either linearised the equations of motion (McInnes 1993;Simo and McInnes 2009) or searched for bespoke orbits, e.g., below the lunar South Pole by solving the accompanying optimal control problem (Ozimek et al 2009;Ozimek et al 2010;Wawrzyniak and Howell 2011). The results in the linearised system have been transferred to the full non-linear dynamical system (Wawrzyniak and Howell 2011a), but the results presented are limited to one specific steering law and only show one family of orbits at the Earth-Moon L 2 point.…”

Section: Introductionmentioning

confidence: 99%

Extension of Earth-Moon libration point orbits with solar sail propulsion

Heiligers

Macdonald

Parker

2016

Astrophys Space Sci

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This paper presents families of libration point orbits in the Earth-Moon system that originate from complementing the classical circular restricted three-body problem with a solar sail. Through the use of a differential correction scheme in combination with a continuation on the solar sail induced acceleration, families of Lyapunov, halo, vertical Lyapunov, Earth-centred, and distant retrograde orbits are created. As the solar sail circular restricted three-body problem is non-autonomous, a constraint defined within the differential correction scheme ensures that all orbits are periodic with the Sun's motion around the Earth-Moon system. The continuation method then starts from a classical libration point orbit with a suitable period and increases the solar sail acceleration magnitude to obtain families of orbits that are parametrised by this acceleration. Furthermore, different solar sail steering laws are considered (both in-plane and out-of-plane, and either fixed in the synodic frame or fixed with respect to the direction of Sunlight), adding to the wealth of families of solar sail enabled libration point orbits presented. Finally, the linear stability properties of the generated orbits are investigated to assess the need for active orbital control. It is shown that the solar sail induced acceleration can have a positive effect on the stability of some orbit families, especially those at the L 2 point, but that it most often (further) destabilises the orbit. Active control will therefore be needed to ensure long-term survivability of these orbits.

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“…Previous work on solar sail periodic orbits in the Earth-Moon system either linearised the equations of motion [11,12] or searched for bespoke orbits (e.g. below the lunar South Pole [13]) by solving the optimal control problem.…”

Section: Introductionmentioning

confidence: 99%

Solar sail Lyapunov and Halo orbits in the Earth–Moon three-body problem

Heiligers¹,

Hiddink

Noomen

et al. 2015

Acta Astronautica

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Solar sailing has been proposed for a range of novel space applications, including hovering above the ecliptic for high-latitude observations of the Earth and monitoring the Sun from a sub-L 1 position for space weather forecasting. These applications, and many others, are all defined in the Sun-Earth threebody problem, while little research has been conducted to investigate the potential of solar sailing in the Earth-Moon three-body problem. This paper therefore aims to find solar sail periodic orbits in the Earth-Moon three-body problem, in particular Lagrange-point orbits. By introducing a solar sail acceleration to the Earth-Moon three-body problem, the system becomes non-autonomous and constraints on the orbital period need to be imposed. In this paper, the problem is solved as a twopoint boundary value problem together with a continuation approach: starting from a natural Lagrange-point orbit, the solar sail acceleration is gradually increased and the result for the previous sail performance is used as an initial guess for a slightly better sail performance. Three in-plane steering laws are considered for the sail, two where the attitude of the sail is fixed in the synodic reference frame (perpendicular to the Earth-Moon line) and one where the sail always faces the Sun.The results of the paper include novel families of solar sail Lyapunov and Halo orbits around the Earth-Moon L 1 and L 2 Lagrange points, respectively. These orbits are double-revolution orbits that wind around or are off-set with respect to the natural Lagrange-point orbit. Finally, the effect of an out-of-plane solar sail acceleration component and that of the Sun-sail configuration is investigated, giving rise to additional families of solar sail periodic orbits in the Earth-Moon three-body problem.

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Solar sail orbits at the Earth–Moon libration points

Cited by 58 publications

References 13 publications

Generating Solar Sail Trajectories in the Earth-Moon System Using Augmented Finite-Difference Methods

Generating Solar Sail Trajectories in the Earth-Moon System Using Augmented Finite-Difference Methods

Extension of Earth-Moon libration point orbits with solar sail propulsion

Solar sail Lyapunov and Halo orbits in the Earth–Moon three-body problem

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