# Planes toy models

Left panel: Number of co-rotating satellite pairs (green line) and counter-rotating satellite pairs (orange line) with $$\alpha {<}35^{\circ}$$ as a function of $$\alpha$$. Right panel: Fraction of satellite pairs that are co-rotating as a function of $$\alpha$$. For hosts with two satellites, there is a significant excess of co-rotating pairs over counter-rotating pairs at small $$\alpha$$ (i.e. in satellites that are nearly diametrically opposed to each other). The suggests the possibile presence of coherently rotating planar satellite structures.

\label{fig:zoom}

Definition of the opening angle between satellite pairs, $$\alpha$$. Each unique satellite pair (here, S1 and S2) has a uniquely defined $$\alpha$$.

\ref{fig:alpha}

Left panel: Number of co-rotating satellite pairs (green line) and counter-rotating satellite pairs (orange line) as a function of $$\alpha$$ over the full $$180^{\circ}$$ domain. Right panel: Fraction of satellite pairs that are co-rotating as a function of $$\alpha$$. Viewed over this domain, the data seems more consistent with a flat line, which would indicate satellite velocities oriented independently along the line-of-sight and a lack of coherent rotation.

\label{fig:full}