Long-term orbit prediction for the Venus Radar Mapper Mission using an averaging method

Kwok, Johnny H.

doi:10.2514/6.1984-1985

Cited by 5 publications

(2 citation statements)

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“…In the last years, several researches, based on both analytical and numerical approaches, studied the third-body perturbation. The majority of them concentrated on studying the effects of a perturbation caused by a third body using a double-averaged technique, like those ofŠidlichovskyý [14], Kwok [15,16], Broucke [17], and Prado [18]. The disturbing function is expanded in Legendre's polynomials, and the average is made over the periods of the perturbing and the perturbed body, using an approximated model expanded to some order.…”

Section: Introductionmentioning

confidence: 99%

A Study of Single- and Double-Averaged Second-Order Models to Evaluate Third-Body Perturbation Considering Elliptic Orbits for the Perturbing Body

Domingos

Prado

Moraes

2013

Mathematical Problems in Engineering

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The equations for the variations of the Keplerian elements of the orbit of a spacecraft perturbed by a third body are developed using a single average over the motion of the spacecraft, considering an elliptic orbit for the disturbing body. A comparison is made between this approach and the more used double averaged technique, as well as with the full elliptic restricted three-body problem. The disturbing function is expanded in Legendre polynomials up to the second order in both cases. The equations of motion are obtained from the planetary equations, and several numerical simulations are made to show the evolution of the orbit of the spacecraft. Some characteristics known from the circular perturbing body are studied: circular, elliptic equatorial, and frozen orbits. Different initial eccentricities for the perturbed body are considered, since the effect of this variable is one of the goals of the present study. The results show the impact of this parameter as well as the differences between both models compared to the full elliptic restricted three-body problem. Regions below, near, and above the critical angle of the third-body perturbation are considered, as well as different altitudes for the orbit of the spacecraft.

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Section: Introductionmentioning

confidence: 99%

A Study of Single- and Double-Averaged Second-Order Models to Evaluate Third-Body Perturbation Considering Elliptic Orbits for the Perturbing Body

Domingos

Prado

Moraes

2013

Mathematical Problems in Engineering

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“…Plenty of papers contributed research, the details of which were well reviewed in (Broucke 2003;Prado 2003). In the past century, the method of averaging technique to deal with the third-body perturbation already aroused great attentions (Musen et al 1961;Cook 1962;Lorell 1965;Harrington 1969;Williams and Benson 1971;Lidov and Ziglin 1974;Ash 1976;Collins and Cefola 1979;Hough 1981;Šidlichovský 1983;Kwok 1985;Lane 1989;Kinoshita and Nakai 1991;Kwok 1991;Ferrer and Osacar 1994;Delhaise and Morbidelli 1997). Recently, the subject of averaged third-body perturbation is still a popular topic.…”

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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Mean Element Propagations Using Numerical Averaging

Ely

2014

J of Astronaut Sci

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Long-term orbit prediction for the Venus Radar Mapper Mission using an averaging method

Cited by 5 publications

References 1 publication

A Study of Single- and Double-Averaged Second-Order Models to Evaluate Third-Body Perturbation Considering Elliptic Orbits for the Perturbing Body

A Study of Single- and Double-Averaged Second-Order Models to Evaluate Third-Body Perturbation Considering Elliptic Orbits for the Perturbing Body

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

Mean Element Propagations Using Numerical Averaging

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