Applied Mathematics and Mechanics >
Asteroid impact trajectory based on Jupiter-perturbed Sun-Earth planar bicircular restricted four-body problem invariant manifolds
Received date: 2025-12-27
Revised date: 2026-03-26
Online published: 2026-06-18
Supported by
Project supported by the National Natural Science Foundation of China (Nos.?12322202 and 12172013)
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This paper proposes a novel low-energy impact trajectory design framework for near-Earth asteroids (NEAs), exploiting the dynamical properties of invariant manifolds within a Jupiter-perturbed Sun-Earth planar bicircular restricted four-body problem (RFBP). First, we investigate the influence of Jupiter’s perturbation on the instantaneous Jacobi constant C, which governs the evolutionary behavior of the zero-velocity curves. An energy mechanism is then established to link the instantaneous C with the feasible region for asteroid entry into the Earth-Moon sphere of influence (EMSOI). Using this mechanism, a screening procedure is developed to identify potential Earth-impacting asteroids by analyzing their accessible impact regions. Subsequently, low-energy impact trajectories are designed by joining unstable manifolds and the Lambert transfer, which is further optimized via the particle swarm optimization (PSO) algorithm. Finally, the numerical simulations conducted for asteroids 2010 XC15 and 2023 JD6 demonstrate that the proposed method significantly reduces propellant consumption. Overall, this study provides a practical and low-energy strategy for asteroid defense and deep-space mission design.
Meiling LI , Yingjing QIAN , Wenxue CHEN , Yan SHEN , Yue LIU . Asteroid impact trajectory based on Jupiter-perturbed Sun-Earth planar bicircular restricted four-body problem invariant manifolds[J]. Applied Mathematics and Mechanics, 2026 , 47(6) : 1279 -1300 . DOI: 10.1007/s10483-026-3390-8
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