A particle-linkage model for non-axisymmetric elongated asteroids

Abstract

This paper investigates a simplified model for describing the gravitational fields of non-axisymmetric elongated asteroids. The connection between the simplified model and the target asteroid is built by the positions of the equilibrium points. To improve the performance of position matching the equilibrium points of these non-axisymmetric asteroids, a non-axisymmetric triple-particle-linkage model is proposed based on two existing axisymmetric particle-linkage models. The unknown parameters of the simplified model are determined by minimization of the matching error using the nonlinear optimization method. The proposed simplified model is applied for three realistic elongated asteroids 243 Ida, 433Eros and 1996 HW1. The simulation results validate that the current particle-linkage model has better matching accuracy than the two existing particle-linkage model. The comparison between the simplified model and the polyhedral model on the topological cases of the equilibrium points and the distribution of the gravitational potential further validate the rationality and accuracy of the simplified model.

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

“…In this study, considering the simplified model, the total mass and angular velocity of the asteroids are equivalent to the actual values of those same asteroids. Therefore, the 2D The unknown parameters are determined using the locations of the external equilibrium points obtained from the Mascon approach, similar to the approach used by Zeng et al (2015Zeng et al ( , 2016a; Yang et al (2018). The main idea is to find the parameters that generate equilibrium points as close as possible to the ones obtained by using the Mascon model.…”

“…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).…”

“…Qualitative analyses can be used to investigate the effects of some parameters, such as relating the characteristics of the motion around elongated asteroids and the dynamical properties of the body (Yang et al 2015), or to analyse the distribution of stable periodic orbits close to the equatorial plane (Lan et al 2017), etc. Furthermore, qualitative analysis has the potential to conduct preliminary real mission design (Yang et al 2018), leaving detailed studies for a later stage, based on more accurate models that require more computer time, but will study a small number of trajectories.…”

Dynamics Around an Asteroid Modeled as a Mass Tripole

“…The optimized parameters of the bodies under analysis in this article are shown in Table 3, where Φ is determined by setting Φ = arctan (2σ) in which σ is given by l 2 /l 1 and was determined in Lan et al (2017) and Yang et al (2018).…”

“…Inspired by the double-particle-linkage model, Lan et al (2017) proposed that small arched bodies can be modeled by a triple-particle-linkage model determined by five parameters: M , ω, l 1 , τ and β. Analyzing asteroids 433 Eros, 243 Ida, and the Martian moon M1 Phobos, they validated the so called tripole model, by verifying that the gravitational field distribution of unstable annular regions is similar to the one found with the polyhedral model. Later, Yang et al (2018) proposed the non-axisymmetric triple particle-linkage model as a further step to improve the modeling towards a more realistic scenario. The authors analyzed the non-axisymmetric tripole model using three different elongated asteroids (243 Ida, 433 Eros, and (8567) 1996 HW1) and verified that the asymmetrical tripole model was more accurate than its predecessors, the dipole and the symmetrical tripole model.…”