Equilibrium points in the restricted synchronous three-body problem using a mass dipole model

Numerical Investigations of the Orbital Dynamics Around a Synchronous Binary System of Asteroids

“…The classical Restricted Three-Body Problem corresponds to the particular case d = 0 and k = 1 (McCuskey 1963;Szebehely 1967). Also, when d ̸ = 0 and k = 1, we have the Restricted Synchronous Three-Body Problem (Barbosa Torres dos Santos et al 2017).…”

“…Simplified models can be used to approximate the gravitational field of irregularly shaped bodies, requiring less computational effort and generating considerable results in a short period of time. Another advantage of using a simplified model is that we can easily investigate the effects of a given parameter on the dynamics of a spacecraft around asteroids, such as, the distribution of stable periodic orbits (Lan et al 2017), the stability of the equilibrium points (Zeng et al 2015; Barbosa Torres dos Santos et al 2017), as well as the permissible parking regions (Yang et al 2015;). In addition, simplified models can be used to support the orbit design (Wang et al 2017) and feedback control (Yang et al 2017).…”

“…Other works have investigated the dynamics around small irregular bodies using a simplified model given by an homogeneous cube (Liu et al 2011), a simple flat plate (Blesa. 2006), a rotating mass dipole Barbosa Torres dos Santos et al 2017;dos Santos et al 2017), the dipole segment model (Zeng et al 2018), a rotating mass tripole (Lan et al 2017;dos Santos et al 2020;Santos et al 2021), and many others.…”

“…Thus, in this contribution, a more simplified model is used, whose results capture the essential parts of the physics of the problem, although its accuracy depends on the parameters of the specific mission. Therefore, we carry out a numerical investigation using the simplified model called a Restricted Synchronous Three-Body Problem, as introduced by Barbosa Torres dos Santos (2017). The practical advantage of using this model is that we can, in a relatively simple way, analyze the influence of the dimension of the secondary body on the dynamics of a spacecraft in the neighborhood of M 2 .…”

A particle-linkage model for elongated asteroids with three-dimensional mass distribution

“…Besides that, a simplified model can often determine a simple an-alytical expression for calculating the gravitational field of irregular bodies (Yang et al 2018). Another advantage of using a simplified model is that we can easily analyse the consequences of a given parameter on the dynamics around asteroids, such as, for example, the stability of the equilibrium points (Zeng et al 2015;Barbosa Torres dos Santos et al 2017), the distribution of stable periodic orbits (Lan et al 2017), as well as the permissible hovering regions Yang et al (2015); Zeng et al (2016a). Moreover, simplified models can be used to assist orbit design (Wang et al 2017) and feedback control (Yang et al 2017).…”