Atlas3,708 of 3,942

Moth satellite M13

m₃ = 1.001

From Three-body Moth-I¹³ computer-assisted proof (2026)

Moth satellite M13 m₃ = 1.001 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 1.001 that return to their starting positions and velocities every 193.91 time units, published by Three-body Moth-I¹³ computer-assisted proof (2026). A satellite of moth I whose existence at masses 1, 1, 1.001 is established by a computer-assisted proof. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.061 of each other at a top speed of 4.06, line up 208 times a period, and the computed loop closes to 4.8×10⁻²⁷.

Measured over one period

Period: 193.9144360
Masses: 1 : 1 : 1.001
Energy: -1.38185
Angular momentum: 0
Closest approach: 0.06104
Top speed: 4.061
Path length: 488.46
Alignments per period: 208
Topology: (abaBAbabAB)¹³ (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 4.8×10⁻²⁷

All Certified satellite orbits, the families of periodic three-body orbits, or the atlas map.