Artificial equilibrium points for a generalized sail in the elliptic restricted three-body problem

Aliasi, Generoso; Mengali, Giovanni; Quarta, Alessandro A.

doi:10.1007/s10569-012-9425-z

Cited by 19 publications

(28 citation statements)

References 37 publications

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“…Equation 37provides the spacecraft propulsive acceleration that is required to travel an assigned spiral trajectory with r ∝ θ α . The next section analyzes the problem of creating a generic spiral trajectory using a generalized sail-based spacecraft [30][31][32].…”

Section: Required Propulsive Accelerationmentioning

confidence: 99%

“…The results obtained so far are general because they may be applied to any propulsive system that is able to provide a purely radial thrust. An interesting class of propulsion systems that may be employed for generating spiral trajectories is offered by the generalized sails [30][31][32]. The concept of generalized sail is useful for describing, in a heliocentric mission scenario, the propulsive acceleration of a propellantless propulsion system when the thrust vector is oriented along the outward radial direction and its magnitude depends on a given power of the Sunspacecraft distance r. Precisely, the expression of a r •r for a generalized is…”

Section: Generalized Sail-based Spiral Trajectoriesmentioning

confidence: 99%

“…The general solution, which can be applied to any propulsion system that can provide a purely radial thrust, is specialized in a heliocentric framework to the class of the generalized sails [30][31][32]. This type of thrusters includes all the propellantless propulsion systems that provide an outward radial propulsive acceleration with a magnitude that scales as a certain power of the Sunspacecraft distance.…”

Section: Introductionmentioning

confidence: 99%

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Spiral trajectories induced by radial thrust with applications to generalized sails

et al. 2020

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In this study, new analytical solutions to the equations of motion of a propelled spacecraft are investigated using a shape-based approach. There is an assumption that the spacecraft travels a two-dimensional spiral trajectory in which the orbital radius is proportional to an assigned power of the spacecraft angular coordinate. The exact solution to the equations of motion is obtained as a function of time in the case of a purely radial thrust, and the propulsive acceleration magnitude necessary for the spacecraft to track the prescribed spiral trajectory is found in a closed form. The analytical results are then specialized to the case of a generalized sail, that is, a propulsion system capable of providing an outward radial propulsive acceleration, the magnitude of which depends on a given power of the Sun-spacecraft distance. In particular, the conditions for an outward radial thrust and the required sail performance are quantified and thoroughly discussed. It is worth noting that these propulsion systems provide a purely radial thrust when their orientation is Sun-facing. This is an important advantage from an engineering point of view because, depending on the particular propulsion system, a Sun-facing attitude can be stable or obtainable in a passive way. A case study is finally presented, where the generalized sail is assumed to start the spiral trajectory from the Earth’s heliocentric orbit. The main outcome is that the required sail performance is in principle achievable on the basis of many results available in the literature.

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Section: Required Propulsive Accelerationmentioning

confidence: 99%

Section: Generalized Sail-based Spiral Trajectoriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spiral trajectories induced by radial thrust with applications to generalized sails

et al. 2020

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“…The use of Solar sails to generate non-Keplerian geostationary orbits was considered by Baig and McInnes (2008) and Heiligers et al (2012). Many authors have also established the existence, stability, and controllability conditions of such orbits (McInnes 1977(McInnes , 1998Scheeres 1999;Xu and Xu 2008;Bombardelli and Pelez 2011;Ceriotti et al 2012;Aliasi et al 2012), and recently McKay et al performed a broad survey of NKOs and their utility (McKay et al 2011). Recently, Wang et al offered a new methodology for analysis of the formation flight of electric sails operating in NKOs, and subsequently presented a control framework for such sail formations (Wang et al 2017a, b).…”

Section: Forced Relative Motionmentioning

confidence: 99%

“… 2012 ; Aliasi et al. 2012 ), and recently McKay et al performed a broad survey of NKOs and their utility (McKay et al. 2011 ).…”

Section: Introductionmentioning

confidence: 99%

Orbit period modulation for relative motion using continuous low thrust in the two-body and restricted three-body problems

Arnot

McInnes

McKay

et al. 2018

Celest Mech Dyn Astr

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This paper presents rich new families of relative orbits for spacecraft formation flight generated through the application of continuous thrust with only minimal intervention into the dynamics of the problem. Such simplicity facilitates implementation for small, lowcost spacecraft with only position state feedback, and yet permits interesting and novel relative orbits in both two-and three-body systems with potential future applications in space-based interferometry, hyperspectral sensing, and on-orbit inspection. Position feedback is used to modify the natural frequencies of the linearised relative dynamics through direct manipulation of the system eigenvalues, producing new families of stable relative orbits. Specifically, in the Hill-Clohessy-Wiltshire frame, simple adaptations of the linearised dynamics are used to produce a circular relative orbit, frequency-modulated out-of-plane motion, and a novel doubly periodic cylindrical relative trajectory for the purposes of on-orbit inspection. Within the circular restricted three-body problem, a similar minimal approach with position feedback is used to generate new families of stable, frequency-modulated relative orbits in the vicinity of a Lagrange point, culminating in the derivation of the gain requirements for synchronisation of the in-plane and out-of-plane frequencies to yield a singly periodic tilted elliptical relative orbit with potential use as a Lunar far-side communications relay. The v requirements for the cylindrical relative orbit and singly periodic Lagrange point orbit are analysed, and it is shown that these requirements are modest and feasible for existing low-thrust propulsion technology.

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Special Orbits for Mercury Observation

2015

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Chapter 5, by Generoso Aliasi, Giovanni Mengali and Alessandro A. Quarta, deals with an advanced scientific mission concept in which the existence of suitable positions for the observation and the measurement of the Mercury’s magnetotail are investigated. The scientific mission is based on the use of artificial equilibrium points in the elliptic three-body system, constituted by the Sun, Mercury, and a spacecraft, which is modeled as a massless point. The spacecraft motion in the Sun–Mercury system is first discussed under the assumption that the propulsion\ud system provides a radial continuous thrust with respect to the Sun. In particular, the spacecraft is assumed to have a generalized sail as its primary propulsion system. A generalized sail models the performance of different types of advanced propulsion systems, including a (photonic) solar sail, an electric solar wind sail and an electric thruster, by simply modifying the value of a thrusting parameter. The location of the artificial equilibrium points is derived, and their stability is also investigated. It is shown that that collinear artificial equilibrium points are always\ud unstable, except for a range of L2-type points which are placed far away from Mercury. A similar result is obtained for triangular equilibrium points. A control strategy is introduced to maintain the spacecraft in the neighborhood of an artificial equilibrium point. In this context, a simple and effective way to actively control the spacecraft dynamics is by means of a Proportional-Integral-Derivative feedback control law. The latter control law is finally employed in the magnetotail mission scenario, whose fundamental idea is to continuously and slowly displacing the\ud artificial equilibrium point along the Sun–Mercury direction. Numerical simulations show the effectiveness of the proposed mission strategy

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Artificial equilibrium points for a generalized sail in the elliptic restricted three-body problem

Cited by 19 publications

References 37 publications

Spiral trajectories induced by radial thrust with applications to generalized sails

Spiral trajectories induced by radial thrust with applications to generalized sails

Orbit period modulation for relative motion using continuous low thrust in the two-body and restricted three-body problems

Special Orbits for Mercury Observation

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