Periodic Orbits Above the Ecliptic in the Solar-Sail Restricted Three-Body Problem

Waters, Thomas J.; McInnes, Colin R.

doi:10.2514/1.26232

Cited by 86 publications

(73 citation statements)

References 13 publications

(4 reference statements)

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“…For larger amplitude periodic orbits, we compute high order approximations using the method of Linstedt-Poincaré. 5 This procedure is well known and is described in the literature, for example. 3,4 We let ε be a perturbation parameter and expand each coordinate as x → x e + εx 1 + ε 2 x 2 + .…”

Section: High-order Approximations To Periodic Orbitsmentioning

confidence: 99%

“…We find that periodic orbits exist at linear order, and we use these linear solutions to find higher order approximations to periodic solutions of the non-linear system using the method of Lindstedt-Poincaré. 5,6 These approximate orbits are then fine-tuned using a differential corrector to find initial conditions that yield periodic solutions to the full non-linear model. 5 Following this we generalize the problem to the solar sail ERTBP 7 in the Earth-Sun system.…”

Section: Introductionmentioning

confidence: 99%

“…5,6 These approximate orbits are then fine-tuned using a differential corrector to find initial conditions that yield periodic solutions to the full non-linear model. 5 Following this we generalize the problem to the solar sail ERTBP 7 in the Earth-Sun system. A numerical continuation, with the eccentricity e as the varying parameter, is used to find periodic orbits above the ecliptic, starting from a known orbit in the CRTBP (e = 0) and continuing to the required eccentricity e = 0.0167.…”

Section: Introductionmentioning

confidence: 99%

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New Periodic Orbits in the Solar Sail Three-Body Problem

Biggs

Waters

McInnes

2011

Nonlinear Science and Complexity

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In this paper we consider periodic orbits of a solar sail in the Earth-Sun restricted three-body problem. In particular, we consider orbits which are high above the ecliptic plane, in contrast to the classical Halo orbits about the collinear equilibria. We begin with the Circular Restricted Three-Body Problem (CRTBP) where periodic orbits about equilibria are naturally present at linear order. Using the method of Lindstedt-Poincaré, we construct nth order approximations to periodic solutions of the nonlinear equations of motion. In the second part of the paper we generalize to the Elliptic Restricted ThreeBody Problem (ERTBP). A numerical continuation, with the eccentricity, e, as the varying parameter, is used to find periodic orbits above the ecliptic, starting from a known orbit at e = 0 and continuing to the required eccentricity of e = 0.0167. The stability of these periodic orbits is investigated.

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Section: High-order Approximations To Periodic Orbitsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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New Periodic Orbits in the Solar Sail Three-Body Problem

Biggs

Waters

McInnes

2011

Nonlinear Science and Complexity

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“…Waters and McInnes studied the periodic orbits around artificial Lagrange points 15) and the invariant manifolds associated to the periodic orbits. 16) Baoyin and McInnes 17) used two methods to obtain solar sail halo orbits at the sub L1 point: one to direct the sail normal vector orientated along the Sun-sail line, and the other to orient the sail normal vector along the Sun-Earth line.…”

Section: Artificial Lagrange Points and Periodic Orbitsmentioning

confidence: 99%

Solar Sail Halo Orbit Control using Reflectivity Control Devices

Gong

2014

Trans. Japan Soc. Aero. S Sci.

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A new solar sail orbit control strategy is proposed for the solar sail halo orbit mission. The reflectivity control device, initially developed for attitude control, is utilized to control the solar sail orbit by switching the states between absorption and specular reflection. The solar radiation pressure force of a solar sail equipped with reflectivity control devices is modeled, and can be changed continuously by adjusting a continuous variable associated with the reflectivity control device. This model is used to study the artificial Lagrange point and periodic orbit around it in the restricted three-body problem. The dynamical equations of motion are linearized around the periodic orbit, and linear quadratic regulator and Floquet theory are utilized to design the control law for the linear time-periodic system. Utilization of attitude adjustment is a way to control the orbit of the solar sail without reflectivity control devices. In this paper, the reflectivity control device is used to stabilize the periodic orbit without attitude adjustment. The results based on attitude adjustment and reflectivity control devices are compared. The simulations indicate that the strategy using reflectivity control devices is more robust with respect to initial errors.

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“…These studies also include investigations for observing high-latitude regions. In particular, notable examples are those relying on artificial displaced equilibria and non-Keplerian orbits (NKOs) [11,12]. A further comparison of these concepts is provided in Reference [1].…”

Section: Introductionmentioning

confidence: 99%

Mission analysis and systems design of a near-term and far-term pole-sitter mission

et al. 2014

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Mission analysis and systems design of a near-term and far-term pole-sitter mission. Acta Astronautica, 94 (1). pp. [455][456][457][458][459][460][461][462][463][464][465][466][467][468][469] Copyright © 2013 IAA.A copy can be downloaded for personal non-commercial research or study, without prior permission or chargeThe content must not be changed in any way or reproduced in any format or medium without the formal permission of the copyright holder(s) This paper provides a detailed mission analysis and systems design of a near-term and far-term polesitter mission. The pole-sitter concept was previously introduced as a solution to the poor temporal resolution of polar observations from highly inclined, low Earth orbits and the poor high-latitude coverage from geostationary orbit. 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. Being on a non-Keplerian orbit, a continuous thrust is required to maintain the pole-sitter position. For this, two different propulsion strategies are proposed, which result in a near-term pole-sitter mission using solar electric propulsion (SEP) and a far-term pole-sitter mission where the SEP thruster is hybridized with a solar sail. For both propulsion strategies, minimum propellant pole-sitter orbits are designed. In order to maximize the spacecraft mass at the start of the operations phase of the mission, the transfer from Earth to the pole-sitter orbit is designed and optimized assuming either a Soyuz or an Ariane 5 launch. The maximized mass upon injection into the pole-sitter orbit is subsequently used in a detailed mass budget analysis that will allow for a trade-off between mission lifetime and payload mass capacity. Also, candidate payloads for a range of applications are investigated. Finally, transfers between north and south pole-sitter orbits are considered to overcome the limitations in observations due to the tilt of the Earth's rotational axis that causes the poles to be alternately situated in darkness. It will be shown that in some cases these transfers allow for propellant savings, enabling a further extension of the pole-sitter mission.

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Periodic Orbits Above the Ecliptic in the Solar-Sail Restricted Three-Body Problem

Cited by 86 publications

References 13 publications

New Periodic Orbits in the Solar Sail Three-Body Problem

New Periodic Orbits in the Solar Sail Three-Body Problem

Solar Sail Halo Orbit Control using Reflectivity Control Devices

Mission analysis and systems design of a near-term and far-term pole-sitter mission

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