8:7 resonant orbit for k = n for 7+1 bodies
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Spatial choreographies
Spatial n+1
Spatial choreographies in the $n+1$ body problem with a central mass.
Overview
These are spatial choreographies in the $n+1$ body problem: $n$ equal bodies move around an additional central mass. The projection in the $xy$-plane has winding number $l$ and is invariant under rotations by $2\pi/m$.
The bodies form groups of $h$ polygons, where $h=\gcd(n,k)$. In the examples below, the central mass is $\mu=200$ for the $7+1$ body cases and $\mu=300$ for the $8+1$ body cases.
Gallery
15:14 resonant orbit for k = n for 7+1 bodies
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13:12 resonant orbit for k = 4 for 8+1 bodies
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15:12 resonant orbit for k = 4 for 8+1 bodies
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9:8 resonant orbit for k = n for 8+1 bodies
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17:16 resonant orbit for k = n for 8+1 bodies
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