Invariant relative orbits for satellite constellations: A second order theory

El-Salam, F. A. Abd; El-Tohamy, I.A.; Ahmed, M. K.; Rahoma, U. Ali; Rassem, M.

doi:10.1016/j.amc.2006.01.004

Cited by 9 publications

(6 citation statements)

References 7 publications

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“…Now we need to eliminate the short as well as the long periodic terms of the satellite motion in addition to the short periodic terms of the distance perturbing body. Using the perturbation technique based on Lie series and Lie transform, Kamel [9], the transformed Hamiltonian, for different orders 0, 1, 2 can be written as, Abd El-Salam et al [7] and Domingos et al [8]. Using the Hamiltonian canonical equations of the motion, to write   , argument of mean latitude ( ) is the sum of the mean anomaly and the argument of perigee (i.e.…”

Section: R J R J Nmentioning

confidence: 99%

“…Biggs and Becerra [6] proposed a me-thod to determinate the J 2 invariant orbit with the leader's orbit of zero inclination based on the targeting method in chaos dynamics. Abd El-Salam et al [7] used the Hamiltonian framework to construct an analytical method to design invariant relative constellation orbits due to the zonal harmonics 2 J ; 3 J ; 4 J up to the second order, assuming 2 J being of order 1. Our propose was to extend Schaub and Alfriend [1] and Abd El-Salam et al [7] model by adding the effect of the third body which have important at high altitude.…”

Section: Introductionmentioning

confidence: 99%

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Invariant Relative Orbits Taking into Account Third-Body Perturbation

Rahoma¹,

Métris²

2012

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For a satellite in an orbit of more than 1600 km in altitude, the effects of Sun and Moon on the orbit can’t be negligible. Working with mean orbital elements, the secular drift of the longitude of the ascending node and the sum of the argu-ment of perigee and mean anomaly are set equal between two neighboring orbits to negate the separation over time due to the potential of the Earth and the third body effect. The expressions for the second order conditions that guaran-tee that the drift rates of two neighboring orbits are equal on the average are derived. To this end, the Hamiltonian was developed. The expressions for the non-vanishing time rate of change of canonical elements are obtained

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Section: R J R J Nmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Invariant Relative Orbits Taking into Account Third-Body Perturbation

Rahoma¹,

Métris²

2012

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“…These models introduced conditions on the initial relative position and velocity so that the relative orbits result to be periodic, which are closed orbits. Recently, Schaub and Alfriend [4], Abd El-Salam et al [5] passing through Li and Li [6] until Abd El-Salam and El-Saftawy [7] in which they discussed the invariant relative orbits due to the influence of the perturbative effects of the asphericity of the Earth, the relativistic corrections and the direct solar radiation pressure. Rahoma [8] also, discussed the J 2 invariant relative orbits with the effect of lunisolar attraction.…”

mentioning

confidence: 99%

“…El-Salam et al [5] model by introducing an atlas for the curves of invariant relative orbits' conditions. This atlas will be presented using Mathematica program to calculate and plot graphics of the initial conditions of invariant relative orbits.…”

mentioning

confidence: 99%

Analytical Solution for Formation Flying Problem near Equatorial-Circular Reference Orbit

Altalhi¹,

Saftawy²

2019

IJAA

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The relative motion between multiple satellites is a developed technique with many applications. Formation-flying missions use the relative motion dynamics in their design. In this work, the motion in invariant relative orbits is considered under the effects of second-order zonal harmonics in an equatorial orbit. The Hamiltonian framework is used to formulate the problem. All the possible conditions of the invariant relative motion are obtained with different inclinations of the follower satellite orbits. These second-order conditions warrantee the drift rates keeping two, or more, neighboring orbits from drifting apart. The conditions have been modeled. All the possibilities of choosing mean elements of the leader satellite orbit and differences in momenta between leader and follower satellites' orbits are presented.

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“…Subsequently, (Yan and Alfriend, 2006;Breger and How, 2006;Xu and Xu, 2007;Sabatini et al, 2009) investigated J 2 invariant relative orbits from the perspective of relative orbital elements and relative Cartesian coordinates, thereby achieving different types of invariant conditions through numerical searches. El-Salam et al (2006) used the Hamiltonian framework to construct an analytical method to design invariant relative constellation orbits due to the zonal harmonics; up to the second order, assuming J 2 being of order 1. Rahoma and Metris (2012) constructed an analytical method using Hamiltonian framework to design invariant relative emphasized on secular oblateness perturbations due to the zonal harmonics J 2 , J 3 , J 4 and the third body effect, assuming J 2 being of order 1.…”

Section: Introductionmentioning

confidence: 99%