Third-Body Perturbation in Orbits Around Natural Satellites

Abstract

An analytical and a numerical study of the perturbation imparted to a spacecraft by a third body is developed. There are several important applications of the present research, such as calculation of the effect of lunar and solar perturbations on high-altitude Earth satellites. The goal is to study the evolution of orbits around some important natural satellites of the solar system, such as the moon, the Galilean satellites of Jupiter, Titan, Titania, Triton, and Charon. There is special interest in learning under which conditions a near-circular orbit remains near circular. The existence of circular, equatorial, and frozen orbits are also considered for a lunar satellite, but the results are valid for any system of primaries by making a time transformation that depends on the masses of the bodies involved. Several plots will show the time histories of the Keplerian elements of the orbits involved. Then, a study is performed to estimate the lifetime of orbits around those natural satellites.

Stable low-altitude polar orbits around Europa

“…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.…”

“…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, 2005b Lara & Russel, 2006, 2007Domingos et al, 2008;Carvalho et al, 2010 Carvalho et al, , 2012a Carvalho 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.…”

Orbital Elements Evolution Due to a Perturbing Body in an Inclined Elliptical Orbit

“…The initial conditions found in Prado (2003) and Domingos, et al (2008) ; a lunar satellite with � � = 0.01 (������), � � = 0.01, � � = 15°, 60° and � � = Ω � = 0° were used to show the behavior of the evolutions of the spacecraft orbital elements with time. The perturbing body was in elliptical (� � = 0.1) inclined ( 10°� �� � �0°).…”

“…In this paper, the study done by Broucke (2003), Prado (2003) and Domingos et al (2008) is expanded, including the eccentricity and inclination of the perturbing body. A three-dimensional model is used to study the effects of a third-body gravitational potential on the spacecraft that orbits near a celestial body including the eccentricity and the inclination of the third-body in the formulation.…”

“…Solórzano & Prado (2007) developed a semi-analytical study of the perturbation caused on a spacecraft by a third body with a single averaged model to eliminate the terms due to the short-lived periodic motion of the spacecraft. Prado (2003) studied the evolution of retrograde orbits around the Earth. The existence of circular, equatorial and frozen orbits was also considered.…”