Periodic and quasi-periodic motions of a solar sail close to SL 1 in the Earth–Sun system

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The Augmented Hill Three-Body problem is an extension of the classical Hill problem that, among other applications, has been used to model the motion of a solar sail around an asteroid. This model is a 3 degrees of freedom (3DoF) Hamiltonian system that depends on four parameters. This paper describes the bounded motions (periodic orbits and invariant tori) in an extended neighbourhood of some of the equilibrium points of the model. An interesting feature is the existence of equilibrium points with a 1:1 resonance, whose neighbourhood we also describe. The main tools used are the computation of periodic orbits (including their stability and bifurcations), the reduction of the Hamiltonian to centre manifolds at equilibria, and the numerical approximation of invariant tori. It is remarkable how the combination of these techniques allows the description of the dynamics of a 3DoF Hamiltonian system.

Section: Families Of Periodic Orbitssupporting

confidence: 77%

“…As it happens in the RTBP [FJ10b], the non-linear dynamics close to the displaced equilibrium point is very similar to the one when there is no solar sail. It is easy to see that when we linearise Eq.…”

Section: Families Of Periodic Orbitsmentioning

confidence: 57%

Numerical study of the geometry of the phase space of the Augmented Hill Three-Body problem

Farrés

Jorba

Mondelo

2017

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“…Table 1 lists the equilibrium characteristics of a number of selected candidate Sun-planet and planet-satellite systems. The four innermost planets enjoy favorable conditions in terms of minimum hovering distance, which is suitable for spacecraft communication purposes, and required acceleration, which could be easily supplied with state-of-the art solar sails (Mclnnes 2003b;Farres and Jorba 2010). Another important advantage is given by the fact that the sail orientation can be maintained with a fixed direction relative to the direction of both primaries and can be efficientlly repositioned at different azimuthal locations as proposed by Mclnnes (2003a).…”

Section: Applicationsmentioning

confidence: 99%

On the stability of artificial equilibrium points in the circular restricted three-body problem

Bombardelli

Peláez

2010

The article analyses the stability properties of minimum-control artificial equilibrium points in the planar circular restricted three-body problem. It is seen that when the masses of the two primaries are of different orders of magnitude, minimum-control equilibrium is obtained when the spacecraft is almost coorbiting with the second primary as long as their mutual distance is not too small. In addition, stability is found when the distance from the second primary exceeds a minimum value which is a simple function of the mass ratio of the two primaries and their separation. Lyapunov stability under non-resonant conditions is demonstrated using Arnold's theorem. Among the most promising applications of the concept we find solar-sail-stabilized observatories coorbiting with the Earth, Mars, and Venus.

“…It was also shown (Waters,McInnes 2007) that orbits exist around these artificial equilibrium points, when the sail attitude is maintained fixed throughout the orbit. Interestingly, Farrés,Jorba (2010) highlighted that if the sail is tilted in the out-of-plane direction, one loop of a figure-eight becomes wider than the other. Therefore, we can envisage using these orbits for enhancing the visibility over one of the two hemispheres of the Earth.…”

Section: Tilted-sail Orbitsmentioning

confidence: 99%

“…Sail-displaced eight-shaped orbits were also studied by Farrés,Jorba (2010): in that paper the authors fixed the sail lightness number at 0.051689 (the one used for the Geostorm mission), a reasonable value for a near-term application, and families of orbits at L 1 were designed by varying the out-of-plane angle of the solar sail with respect to the ecliptic plane.…”

Section: Introductionmentioning

confidence: 99%

Natural and sail-displaced doubly-symmetric Lagrange point orbits for polar coverage

Ceriotti

McInnes

2012

This paper proposes the use of doubly-symmetric, eight-shaped orbits in the circular restricted three-body problem for continuous coverage of the high-latitude regions of the Earth. These orbits, for a range of amplitudes, spend a large fraction of their period above either pole of the Earth. It is shown that they complement Sun-synchronous polar and highly eccentric Molniya orbits, and present a possible alternative to low thrust pole-sitter orbits. Both natural and solar-sail displaced orbits are considered. Continuation methods are described and used to generate families of these orbits. Starting from ballistic orbits, other families are created either by increasing the sail lightness number, varying the period or changing the sail attitude. Some representative orbits are then chosen to demonstrate the visibility of high-latitude regions throughout the year. A stability analysis is also performed, revealing that the orbits are unstable: it is found that for particular orbits, a solar sail can reduce their instability. A preliminary design of a linear quadratic regulator is presented as a solution to stabilize the system by using the solar sail only. Finally, invariant manifolds are exploited to identify orbits that present the opportunity of a ballistic transfer directly from low Earth orbit.2