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Figure-8 satellite HS.413

From Hristov, Hristova & Tanikawa (2026)

Figure-8 satellite HS.413 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 315.79 time units, published by Hristov, Hristova & Tanikawa (2026). Stable orbits found by an exhaustive search of the figure-eight’s neighbourhood: each traces the eight with extra loops and twists, and every one is linearly stable to 40 digits. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.42 of each other at a top speed of 1.61, line up 348 times a period, and the computed loop closes to 5.6×10⁻²⁸.

Measured over one period

Period: 315.7903623
Masses: 1 : 1 : 1
Energy: -1.42251
Angular momentum: 0
Closest approach: 0.4204
Top speed: 1.606
Path length: 866.04
Alignments per period: 348
Topology: (abAB)⁵⁸ (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 5.6×10⁻²⁸

Neighbours on the map

All Figure-8 satellites, the families of periodic three-body orbits, or the atlas map.