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

Abstract

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.

High-precision repeat-groundtrack orbit design and maintenance for Earth observation missions

“…The short-periodic variations, therefore, are averaged out. According to the idea of averaging from nonlinear mechanics (Kozai 1959;Liu 1974;Liu et al 2012), the gravitational perturbations on the orbital elements can be averaged in terms of mean anomaly M from 0 to 2, and thus secular and long-periodic terms, denoted by RC and RL, respectively, are separated from the gravitational perturbations, i.e.,…”

Stable low-altitude polar orbits around Europa

“…For a better view of this solution, it is plotted alone in Fig.10. According the results obtained by the simulations, the set of initial conditions with smaller amplitude of libration is given by a = 1850 km, e = 0.02, g = 270 Liu et al, 2012). The Fig.2, Fig.6 and Fig.11 show the diagrams e vs i.…”

“…It is important highlight that the mean anomaly (l J ) of the disturbing body was not eliminated as it was performed in previous papers (Scheeres et al, 2001;Prado, 2003;Liu et al, 2012). The orbit of Jupiter is considered circular and fixed in space, so the Jupiter's mean anomaly was not eliminated.…”

“…This disturbing potential were developed considering Jupiter and Europa on the same plane. Thus, the existence of a small inclination between the orbit of Jupiter around Europa was neglected (see Liu et al, 2012).…”

“…As an example, we can cite the Jupiter Europa Orbiter (JEO, NASA) and the Jupiter IcyMoon Explorer (JUICE, ESA). Several papers have contributed to a better understanding of the dynamics involved in this type of mission (see for example Scheeres et al, 2001;Prado, 2003;Paskowitz & Scheeres, 2005a, 2005bLara & Russel, 2006, 2007Domingos et al, 2008;Carvalho et al, 2010Carvalho et al, , 2012aCarvalho et al, , 2012bLiu et al, 2012). The study performed in this paper is related to the orbital motion of artificial satellites around Europa considering polygenic perturbations due to its non-spherical shape and the third-body perturbation due to Jupiter.…”