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

Domingos, R. C.; Prado, A. F. B. A.; Moraes, Rodolpho Vilhena de

doi:10.1155/2013/260830

Cited by 8 publications

(12 citation statements)

References 30 publications

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“…The double averaged model is a little bit faster in those reductions. This fact is also observed in Domingos et al [ 37 ], which studied this problem considering an elliptic orbit for the disturbing body but considering the expansions only up to the second order.…”

Section: The Critical Inclination Problemsupporting

confidence: 68%

A Comparison of Averaged and Full Models to Study the Third‐Body Perturbation

Solórzano

Prado

2013

The Scientific World Journal

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The effects of a third-body travelling in a circular orbit around a main body on a massless satellite that is orbiting the same main body are studied under two averaged models, single and double, where expansions of the disturbing function are made, and the full restricted circular three-body problem. The goal is to compare the behavior of these two averaged models against the full problem for long-term effects, in order to have some knowledge of their differences. The single averaged model eliminates the terms due to the short period of the spacecraft. The double average is taken over the mean motion of the satellite and the mean motion of the disturbing body, so removing both short period terms. As an example of the methods, an artificial satellite around the Earth perturbed by the Moon is used. A detailed study of the effects of different initial conditions in the orbit of the spacecraft is made.

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Section: The Critical Inclination Problemsupporting

confidence: 68%

A Comparison of Averaged and Full Models to Study the Third‐Body Perturbation

Solórzano

Prado

2013

The Scientific World Journal

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“…Different initial eccentricities (0.0, 0.05, 0.10, 0.15 and 0.20) are considered for the orbit of the moon, which means that, in a system fixed in the moon, those are the eccentricities of the disturbing body, the planet. Those choices are made based on Domingos et al (2013Domingos et al ( , 2014, which showed that averaged models have good accuracy up to those values. The system used as an example for the present studies has the same physical data (masses and distances) of the Earth-Moon system, but considers possible eccentricities for the orbit of the secondary body around the primary.…”

Section: Mathematical Modelsmentioning

confidence: 99%

Studying the lifetime of orbits around Moons in elliptic motion

Gomes

Domingos

2015

Comp. Appl. Math.

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The main goal of the present paper is to study the lifetime of orbits around moons that are in elliptic motion around their parent planet. The lifetime of the orbits is defined as the time the orbit stays in orbit around the moon without colliding with its surface. The mathematical model used to solve this problem is the second order expansion of the potential of the disturbing planet, assumed to be in an elliptical orbit. The results are presented in maps showing the lifetime of the orbit as a function of its initial inclination and eccentricity. The only perturbation acting on the orbit of the spacecraft is assumed to be the gravity of the planet, so the problem is solved by studying the orbital evolution of the spacecraft perturbed by a third body in an elliptical orbit. The region of inclination above the critical value of the third-body perturbation (around 63 • ) is studied, since below that value the orbits survive for a long time. The influence of the eccentricity of the primaries is also investigated, assuming a hypothetical system that has the same mass parameter and sizes of the Earth-Moon system, but the eccentricity can be in the range 0.0-0.2.

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“…By substituting Eq. (1) into the Lagrange's planetary equations, the variation of the orbital elements is given by Domingos et al (2013a):…”

Section: Dynamical Modelmentioning

confidence: 99%

“…To remove the short-period oscillations and any dependence on the position of the thirdbody r , the single-averaged disturbing potential is averaged again, now with respect to the third-body's period (Domingos et al 2013a):…”

Section: Dynamical Modelmentioning

confidence: 99%

A study of the errors of the averaged models in the restricted three-body problem in a short time scale

2014

Self Cite

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The objective of the present research is to study the accuracy of the double-and single-averaged models that are usually considered to predict the motion of spacecrafts or celestial bodies that have their motion perturbed by a third-body. Those two models are compared with each other and then validated against the complete elliptic restricted threebody problem. Those models are developed to give a faster but general behaviour of the motion of the perturbed body in a medium or longer time scale. The researches performed here verify the accuracy of those methods for shorter time scales by showing the differences in terms of the values of the inclination and eccentricity of the perturbed body predicted by those models. Those differences are calculated both at every instant of time and as an integral over the time. The use of the integral along the time for the errors is a new form to study those differences and show a more complete comparison of the accuracy of those approximations, completing the instantaneous picture given by the usual approach of looking at the instantaneous measurement. If the value of the integral is divided by the time integration, the mean error is obtained. The results show that the single-averaged model is better in the short time scale and the difference among those models is smaller when predicting the eccentricity than the inclination. The effects of the time scale is verified by varying the study to values from 2 days up to 50 revolutions of the Moon (1,366 days). Another important point found in the present paper is the range of the eccentricities of the perturbing body that accelerates the dynamics.

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

Cited by 8 publications

References 30 publications

A Comparison of Averaged and Full Models to Study the Third‐Body Perturbation

A Comparison of Averaged and Full Models to Study the Third‐Body Perturbation

Studying the lifetime of orbits around Moons in elliptic motion

A study of the errors of the averaged models in the restricted three-body problem in a short time scale

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