Atlas1,635 of 3,942

II.C.97

m₃ = 0.5

From Li & Liao (2017)

II.C.97 m₃ = 0.5 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.5 that return to their starting positions and velocities every 64.027 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is unstable (largest Floquet multiplier 88.57), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000251 of each other at a top speed of 73, line up 136 times a period, and the computed loop closes to 9.1×10⁻²⁵.

Measured over one period

Period: 64.02687172
Masses: 1 : 1 : 0.5
Energy: -1.38468
Angular momentum: 0
Closest approach: 2.5×10⁻⁴
Top speed: 72.95
Path length: 171.54
Alignments per period: 136
Topology: aabAbaBABaBAbabAbabABaBAAbbAbaaBBabAAbbAAbaBBaaBAbbAABaBAbabAbabABaBAAbbAbaaBBabAAbbAAbaBB (free-group class)
Stability: unstable (|λ|max 88.57)
Loop closure: 9.1×10⁻²⁵

Neighbours on the map

All II.C orbits, the families of periodic three-body orbits, or the atlas map.