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Figure-8 satellite HS.129

From Hristov, Hristova & Tanikawa (2026)

Figure-8 satellite HS.129 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 186.96 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 0.466 of each other at a top speed of 1.53, line up 204 times a period, and the computed loop closes to 1.1×10⁻²⁸.

Measured over one period

Period: 186.9596439
Masses: 1 : 1 : 1
Energy: -1.41317
Angular momentum: 0
Closest approach: 0.4656
Top speed: 1.531
Path length: 512.23
Alignments per period: 204
Topology: (abAB)³⁴ (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 1.1×10⁻²⁸

Neighbours on the map

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