Analytical Study of The Resonance Caused by Solar Radiation Pressure on a Spacecraft

El-Saftawy, M. I.

doi:10.1007/s10509-005-6563-8

Cited by 7 publications

(6 citation statements)

References 17 publications

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“…Substituting Eqs. (8) into Eq. 7and dropping the subscript '1' designating the satellite, we obtain the force function U grav.…”

Section: Development Of the Gravitational Disturbing Functionmentioning

confidence: 99%

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Analytical Solution for the Combined Solar Radiation Pressure and Luni- Solar Effects on the Orbits of High Altitude Satellites~!2010-02-02~!2010-02-16~!2010-06-11~!

Saad¹,

Khalil²,

Amin³

2010

TOAAJ

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A new analytical solution is obtained for the motion of high-altitude earth satellites. The basic idea is to study the joint effects of direct solar radiation pressure and the gravitation of the Earth, Moon and the Sun on the orbits of the satellites. The mathematical model includes the zonal harmonics of the geopotential effects up to 4 J. The order of magnitude of each perturbing term is assessed. The formulae for the all perturbations forces are obtained up to the fourth order (where the mean motion of the moon (~ 10-2) is considered a small quantity of first order). The short, intermediate and long-period terms are eliminated from the Hamiltonian using a perturbation technique based on the Lie-Deprit-Kamel transform through three canonical transformations. The solution is intended to be used for ephemeris predictions for orbiters whose orbital semimajor axes are in the range of 15000 to 70000 kms.

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“…Substituting Eqs. (8) into Eq. 7and dropping the subscript '1' designating the satellite, we obtain the force function U grav.…”

Section: Development Of the Gravitational Disturbing Functionmentioning

confidence: 99%

“…The study of the effect of direct solar radiation pressure on the orbits of the artificial satellites was discussed in a lot of literatures, starting from pioneering works of [1][2][3][4] and other of [5][6][7][8][9]. Also the theory of third body perturbations on an artificial satellite motion was developed by many authors in the past.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution for the Combined Solar Radiation Pressure and Luni- Solar Effects on the Orbits of High Altitude Satellites~!2010-02-02~!2010-02-16~!2010-06-11~!

Saad¹,

Khalil²,

Amin³

2010

TOAAJ

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“…O modelo TD-88 além de ser simples conduz resultados comparáveis com outros modelos mais sofisticados quando usado em teorias de satélite artificiais [21]. O modelo TD-88é bastante utilizado em teorias analíticas [3,7,22].…”

Section: Perturbações Devidas Ao Arrasto Atmosféricounclassified

“…Entre eles podemos citar: a) Em Brouwer e Hori [1]é apresentada uma solução analítica para o movimento de um satélite artificial no campo gravitacional terrestre considerando-se o efeito do arrasto atmosférico. A solução dada nesse trabalho apresenta termos espúrios de Poisson (função periódica do tempo multiplicada por uma função linear do tempo) que foram eliminados posteriormente por [2]; b) Segan [3] faz uma abordagem analítica levando em conta a influência do arrasto atmosférico sobre os elementos orbitais do satélite; c) Em [4,5]é desenvolvida uma teoria para estudar os efeitos da pressão de radiação solar direta e o achatamento da Terra considerando um potencial com correções relativísticas para um satélite artificial da Terra; d) Em [6] os termos de ressonâncias produzidos pelos efeitos da pressão de radiação solar direta no movimento de um satélite artificial no campo gravitacional da Terra são analisados; e) Em [7]é desenvolvida uma teoria considerando o arrasto atmosférico até segunda ordem baseado no modelo atmosférico TD-88.…”

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Efeitos de Forças Gravitacionais e Não-Gravitacionais sobre o Movimento Orbital de Satélites Artificiais

Carvalho

Moraes

2007

Sitientibus-Fisica

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Uma teoria para estudar o movimento orbital de satélites artificiais sobre efeitos do arrasto atmosférico e da pressão de radiação solar direta - considerando a sombra da Terra e alguns termos do geopotencial - é desenvolvida analiticamente. A sombra da Terra é modelada utilizando a função sombra (psi), como introduzida por Ferraz Mello: psi igual zero quando o satélite está na região de sombra e igual a um quando é iluminado pelo Sol. As componentes do arrasto são dadas por Vilhena de Moraes baseado no modelo atmosférico TD-88. O método de Hori para sistemas não-canônicos é aplicado para resolver as equações demovimento. Um software para manipulação algébrica é fundamental para fazer os cálculos necessários. Efeitos seculares e periódicos que influenciam no movimento orbital de satélites artificiais são analisados. Édada ênfase aos termos de acoplamento que surgem na soluçãodo sistema de equações diferenciais. Utilizando dados orbitais do satélite CBERS-1 é feito um estudo para analisar ordens de grandeza da variação do semi-eixo maior devidas às perturbações consideradas.

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“…The perturbing potential was doubly averaged first over one spacecraft orbit and second over one orbit of the third body (Scheeres 2001). The lunisolar effect that is double-averaged based on Lie transform was analyzed to deal with the resonance on a satellite's motion of the oblate Earth (Radwan 2002). With the disturbing function expanded in Legendre polynomials at the second-order term, the double-averaged method was applied to analyze the long-term effect of a third body, and two important first integrals (energy and angular momentum) were used to discuss and classify properties of the perturbed orbits (Broucke 2003).…”

Section: Introductionmentioning

confidence: 99%

Long-term perturbations due to a disturbing body in elliptic inclined orbit

Liu

Baoyin

2012

Astrophys Space Sci

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In the current study, a double-averaged analytical model including the action of the perturbing body's inclination is developed to study third-body perturbations. The disturbing function is expanded in the form of Legendre polynomials truncated up to the second-order term, and then is averaged over the periods of the spacecraft and the perturbing body. The efficiency of the double-averaged algorithm is verified with the full elliptic restricted three-body model. Comparisons with the previous study for a lunar satellite perturbed by Earth are presented to measure the effect of the perturbing body's inclination, and illustrate that the lunar obliquity with the value 6.68º is important for the mean motion of a lunar satellite. The application to the Mars-Sun system is shown to prove the validity of the double-averaged model. It can be seen that the algorithm is effective to predict the long-term 1 PhD candidate, School of Aerospace, Tsinghua University 2 Associate Professor, School of Aerospace, Tsinghua University 3 Professor, School of Aerospace, Tsinghua University behavior of a high-altitude Martian spacecraft perturbed by Sun. The double-averaged model presented in this paper is also applicable to other celestial systems.

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Analytical Study of The Resonance Caused by Solar Radiation Pressure on a Spacecraft

Cited by 7 publications

References 17 publications

Analytical Solution for the Combined Solar Radiation Pressure and Luni- Solar Effects on the Orbits of High Altitude Satellites~!2010-02-02~!2010-02-16~!2010-06-11~!

Analytical Solution for the Combined Solar Radiation Pressure and Luni- Solar Effects on the Orbits of High Altitude Satellites~!2010-02-02~!2010-02-16~!2010-06-11~!

Efeitos de Forças Gravitacionais e Não-Gravitacionais sobre o Movimento Orbital de Satélites Artificiais

Long-term perturbations due to a disturbing body in elliptic inclined orbit

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