Analysis of ballistic capture in Sun–planet models

Abstract

Analysis of ballistic capture orbits in Sun–planet systems is conducted in this paper. This mechanism utilizes purely gravitational forces, and may occur in non-Keplerian regimes. Ballistic capture orbits are generated by proper manipulation of sets of initial conditions that satisfy a simple definition of stability. Six Sun–planet systems are considered, including the inner planets, Jupiter, and Saturn. The role of planets orbital eccentricity, their true anomaly, and mass ratios is investigated. Moreover, the influence of the post-capture orbit in terms of inclination and orientation is also assessed. Analyses are performed from qualitative and quantitative perspective. The quality of capture orbits is measured by means of the stability index, whereas the capture ratio gives information on their statistical occurrence. Some underlying principles on the selection of the dynamical model, the initial true anomaly, and inclination are obtained. These provide a reference for practical cases

A flow-informed strategy for ballistic capture orbit generation

“…In the literature, the ballistic capture phenomenon has mainly been studied with respect to reference frames related to the orbit of the target body; in the Radial-Tangent-Normal frame at epoch t 0 (RTN@t 0 , for brevity), centred at the target body, the z-axis (z r ) is perpendicular to the plane of the Sun orbit, the x-axis (x r ) is aligned with the Sun-planet line, pointing from the Sun to the planet and the y-axis (y r ) completes the dextral orthonormal triad. The transformation from the RTN@t 0 to the EME2000 can be found in Luo and Topputo (2015).…”

“…Considering a system of n bodies, n − 1 of which called primaries, it is interesting to study the motion of a particle of negligible mass with respect to them. Following Luo and Topputo (2015), in order to underline the hierarchy of influence of the bodies on the motion of the particle, the motion is governed by:…”

“…This has been done using a number of stability criteria: García and Gómez (2007) and Topputo and Belbruno (2009) introduced algorithmic categorizations for the planar case, extended by Romagnoli and Circi (2009) and Makó et al (2010) to the 3D case; Belbruno (2004) presented analytical approximations of the same criterion. In this work, the orbit classification is performed using the method introduced in Luo et al ( 2014) and expanded in Luo and Topputo (2015), in which a number of indicators, associated to the semi-plane defined by the initial conditions, are used to investigate the evolution of the trajectory. The set of initial conditions can be divided into four subsets: the n-Weakly Stable Set (W n ), n-Unstable Set (X n ), the n-Crash Set (K n ) and the n-Acrobatic Set (D n ).…”

Investigation of Stable Regions of Spacecraft Motion in Binary Asteroid Systems by Terminal Condition Maps

“…It avoids large velocity changes near the asteroids to reduce the risk of execution errors or thruster failures. Ballistic capture can also save capture velocity increments by utilizing the multi-body gravities [35][36][37][38], though the effect may negligible and insignificant in binary asteroid systems. In general, the spacecraft will gradually reduce its velocity relative to the asteroid during the approaching phase.…”

Energy-Saving Capture at Mars via Backward-Stable Orbits

“…The application of ballistic capture to Mars transfer has also been studied in detail [22][23][24][25]. Due to the relatively large excess velocity in Earth-Mars transfer, it was found that Hiten-like captures do not exist in the Sun-Mars system [26].…”