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\subsection{Co-rotation signal}  In this subsection, we investigate pairs of satellite pairs located diametrically opposite their host for signals of co-rotation. To facilitate this, we will introduce the parameter $\alpha$, defined as the angle between the line extending from one satellite through the host and the position vector of the second satellite. This definition is sketched in Figure \ref{fig:alpha}.  We first focus on the co-rotation signal at small $\alpha$, where for the duration of this paper we will refer to a satellite pair as ``co-rotating" if they have opposite-signed velocity offsets relative to the hosts and their associated $\alpha$ is greater than $90^{\circ}$, or they have same-signed velocity offsets relative to the hosts and their associated $\alpha$ is less than $90^{\circ}$ ; otherwise, they are deemed counter-rotating. Figure \ref{fig:zoom} shows the fraction of satellite pairs that are co-rotating as a function of $\alpha$ for $\alpha \lt 45^{\circ}$. At $alpha $\alpha  \gt 45^{\circ}$, the signal is consistent with the sample being divided equally between co-rotating and counter-rotating, i.e. a co-rotation fraction of 0.5, as is what would be expected in the absense of any co-rotating structure. At small $\alpha$, the co-rotation signal increases to $\gt 1 \sigma$ above 0.5, potentially indicating a relative overabundance of co-rotating pairs versus counter-rotating ones. Viewed in this way, the data would seem to indicate the presense of coherently rotating scrutures that can only be detected at small $\alpha$. However, viewed a different way the picture becomes less clear. Figure \ref{fig:full} shows the co-rotating fraction of satellite pairs over the full domain of $\alpha$. It no longer seems to be the case that the data is described as being consistent with a flat line at 0.5 over most of the domain and an increase at small alpha. Rather, it seems to be the case that the spike at $\alpha \sim 10^{\circ}$ is consistent with random noise present in the data, and that the data is consistent with a flat line. The remainder of this paper will examine the argument that the spike at small alpha is significant, and indicative of ubiquitous coherent co-rotation in satellite populations (of the kind seen in M31) by comparing the data to statistical models of satellite kinematics.