Periodic motion around the triangular libration point in the restricted problem of four bodies

Carpenter, L.; Kolenkiewicz, R.

doi:10.1086/110214

Cited by 7 publications

(5 citation statements)

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“…Schechter (1968) also concluded that the triangular points are no longer stable. Similarly, Kolenkiewicz and Carpenter (1967), using the Huang's model (Huang, 1960) for the Sun-Earth-Moon system, found two stable, periodic orbits, larger than what Schechter (1968) predicted (145, 000 km), and one small, unstable orbit very close to L 4 , in agreement with Schechter (1968)'s conclusion. Later, Gómez et al (2001b), using a continuation method to pass from the Earth-Moon CRTBP to the Sun-EarthMoon BCFBP, found three periodic orbits with initial phase angle θ S = 0, whose period is equal to the period of revolution of the Sun in the Earth-Moon synodical system, i.e., 6.791 units of dimensionless time (about 29 days).…”

Section: Solutions Around Triangular Libration Points In the Bcfbpsupporting

confidence: 58%

“…The equations of motion of the BCFBP in the synodic system can be written in an autonomous fashion; however, L 4 and L 5 are no longer equilibrium points, only retaining their geometrical meaning. Using different approaches, Kolenkiewicz and Carpenter (1967), Kolenkiewicz and Carpenter (1968), and Gómez et al (2001b) have obtained three periodic orbits in the synodical coordinate frame, that have the same period as the Sun. Two of them are linearly stable, lying far away from the triangular libration points of the CRTBP, while the other one, small and slightly unstable.…”

Section: Introductionmentioning

confidence: 99%

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Natural formations at the Earth–Moon triangular point in perturbed restricted problems

Salazar

Winter

Macau

et al. 2015

Advances in Space Research

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Previous studies for small formation flying dynamics about triangular libration points have determined the existence of regions of zero and minimum relative radial acceleration with respect to the nominal trajectory, that prevent from the expansion or contraction of the constellation. However, these studies only considered the gravitational force of the Earth and the Moon using the Circular Restricted Three Body Problem (CRTBP) scenario. Although the CRTBP model is a good approximation for the dynamics of spacecraft in the Earth-Moon system, the nominal trajectories around equilateral libration points are strongly affected when the primary orbit eccentricity and solar gravitational force are considered. In this manner, the goal of this work is the analysis of the best regions to place a formation that is flying close a bounded solution around L 4 , taking into account the Moon's eccentricity and Sun's gravity. This model is not only more realistic for practical engineering applications but permits to determine more accurately the fuel consumption to maintain the geometry of the formation.

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Section: Solutions Around Triangular Libration Points In the Bcfbpsupporting

confidence: 58%

Section: Introductionmentioning

confidence: 99%

Natural formations at the Earth–Moon triangular point in perturbed restricted problems

Salazar

Winter

Macau

et al. 2015

Advances in Space Research

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“…The equations of motion of the BCFBP in the synodic system can be written in an autonomous fashion; however, L 4 and L 5 are no longer equilibrium points, only retaining their geometrical meaning. Using dierent approaches, Kolenkiewicz and Carpenter (1967), Kolenkiewicz and Carpenter (1968), and Gómez et al (2001b) obtained three periodic orbits in the synodical coordinate frame, that have the same period as the Sun. Two of them are linearly stable, lying far away from the triangular libration points of the CRTBP, while the other one is small and slightly unstable.…”

Section: Introductionmentioning

confidence: 99%

Zero drift regions and control strategies to keep satellite in formation around triangular libration point in the restricted Sun–Earth–Moon scenario

Salazar

Winter

Macau

et al. 2015

Advances in Space Research

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Assume that a group of two or more satellites are ying close a given nominal trajectory around Earth-Moon triangular point, in such a way that, there is some freedom in the selection of the geometry of the constellation. We are interested in avoiding large variations of the mutual distances between spacecraft and controlling the conguration of the formation. Previous studies about triangular libration points have determined the existence of regions of zero relative radial acceleration with respect to the nominal trajectory that prevent from the expansion or contraction of the formation. In this work, we carry out two dierent control strategies for a formation near a given nominal trajectory around L4: a bang-o-bang control and a minimum weighted total ∆V consumption. This study involves a linear approximation of the equations of motion relative to the bounded solutions around the triangular libration point, and it considers dierent geometrical possibilities in the zero drift regions. To investigate the inuence of the gravitational force of the Sun, the Bicircular Four Body Problem is studied. According to the results obtained, some suggestions on the design of the geometric conguration in the formation are given.

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“…They used the methodology of Musen and Carpenter [26] and assumed a trigonometric series for the perturbations and numerically determined the coefficients such that a periodic solution can be found [26,27].…”

Section: Introductionmentioning

confidence: 99%

On the quasi-equilibria of the BiElliptic four-body problem with non-coplanar motion of primaries

Assadian

Pourtakdoust

2010

Acta Astronautica

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Periodic motion around the triangular libration point in the restricted problem of four bodies

Cited by 7 publications

References 0 publications

Natural formations at the Earth–Moon triangular point in perturbed restricted problems

Natural formations at the Earth–Moon triangular point in perturbed restricted problems

Zero drift regions and control strategies to keep satellite in formation around triangular libration point in the restricted Sun–Earth–Moon scenario

On the quasi-equilibria of the BiElliptic four-body problem with non-coplanar motion of primaries

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