Asteroid impact trajectory based on Jupiter-perturbed Sun-Earth planar bicircular restricted four-body problem invariant manifolds

doi:10.1007/s10483-026-3390-8

Abstract

Abstract:

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.

Key words: asteroid defense, feasible region, invariant manifold, zero-velocity curve, restricted four-body problem (RFBP)

2010 MSC Number:

O313.7

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. Applied Mathematics and Mechanics (English Edition), 2026, 47(6): 1279-1300.

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URL: https://www.amm.shu.edu.cn/EN/10.1007/s10483-026-3390-8

https://www.amm.shu.edu.cn/EN/Y2026/V47/I6/1279

Figures/Tables 28

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Table 1

Orbital and physical parameters of ten asteroids"

NEA	a	e	I/(°)	$M OID$	C	α/(°)	β/(°)
2000 SG344	0.977 387 0	0.066 898 0	0.113 08	0.000 788	2.996 6	164.589 5	-97.016 7
2006 GB	0.958 543 5	0.179 454 1	10.064 98	0.008 840	2.939 9	325.048 5	-101.617 6
2007 CT26	0.855 243 0	0.386 780 5	2.891 42	0.002 220	2.873 3	145.987 8	-98.901 8
2010 XC15	0.732 385 6	0.419 930 8	8.240 18	0.002 290	2.903 1	131.972 9	-91.031 2
2016 WJ1	1.339 919 4	0.503 108 0	2.888 89	0.000 240	2.744 8	209.041 5	-94.047 2
2019 XB	0.727 853 7	0.402 836 6	6.130 47	0.006 010	2.927 2	59.918 5	-93.742 9
2022 OF1	1.014 809 5	0.640 576 3	1.059 10	0.002 510	2.532 6	11.851 8	-97.940 2
2022 QX4	0.680 812 6	0.504 583 5	0.138 13	0.000 040	2.894 0	63.502 3	-93.047 2
2023 JD6	1.162 715 4	0.432 456 3	11.675 52	0.005 070	2.765 0	87.555 2	-90.131 6
2023 YR	0.921 788 8	0.405 143 8	5.718 68	0.005 770	2.832 0	14.401 6	-94.925 7
Note: I denotes the orbital inclination

Table 1

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Table 2

Target asteroids identified through the screening processes"

Parameter	2010 XC15	2023 JD6
Type	Aten	Apollo
H	21.48	21.34
a	0.732 385 6	1.162 715 4
e	0.419 930 8	0.432 456 3
I/(°)	8.240 18	11.675 52
Ω/(°)	94.400 96	123.699 08
ω/(°)	158.113 82	263.079 9
M/(°)	65.586 15	45.215 97
m₃/kg	$3.556 × 109$	$4.313 × 109$
D/km	0.150 3	0.160 3
Note: Ω, ω, and M denote the longitude of the ascending node, argument of perihelion, and mean anomaly, respectively

Table 2

Fig. 22

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Table 3

Optimization results of impact trajectories based on invariant manifolds"

Parameter	2010 XC15	2023 JD6
Departure	2028-06-27	2028-06-27
$Δ v 1 / (km ⋅ s − 1)$	2.36	2.36
$Δ v 2 / (km ⋅ s − 1)$	0.649 9	0.402 8
Flight time in the stable manifold/d	188.024	188.024
Flight time in the unstable manifold/d	961	601
Transfer time/d	274.556 3	309.905 0
Impact date	2032-05-21	2031-07-01
Impactor mass/t	6.69	10
Impact velocity/ $(km ⋅ s − 1)$	10.101 0	14.867 5

Table 3

Fig. 24

Fig. 25

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