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\label{sec:data}  \subsection{Sample Selection}  We draw our obseravational data from Data Release 7 (DR7) of the Sloan Digital Sky Survay (SDSS), making use of derived data products from the NYU Value-Added Galactic Catalog (VAGC). The r $r$  band magnitudes from the NYU VAGC that we use have been k-corrected $K$-corrected  to z $z  = 0.1 0.1$  using the code Kcorrect, \textsc{Kcorrect},  and we restrict ourselves to regions of SDSS where the spectroscopic completeness parameter FGOTMAIN exceeds 0.7. We also reject all galaxies with velocity errors greater than 25 km/s. In selecting our sample, we adhere closely to the procudure of I14. We select a sample of hosts in the magnitude range $-23 \lt r \lt -20$ and within a redshift range of $0.002 \lt z \lt 0.05$. A host is considered isolated if there are no brighter objects within 500 kpc on the sky in projection and within 1500 km/s in velocity space. Only isolated hosts are retained, reducing the number of sources to 22780 isolated hosts. From there we identified satellites around each host. Galaxies meet the criteria for being counted as satellites if their magnitudes lie in the range $M_{r,host} + 1 < M_{r,sat} < -16$, their projected distance from the host lies between 20 kpc and 150 kpc, and their velocity offset from the host lies in the range $$\rm $\rm  25 \, km/s < |v_{sat} - v_{host}| < 300 \,km/s \times exp(-(d_{proj}/300 \, kpc)^{0.8})$$ kpc)^{0.8})$  This velocity bound is taken from I14, and is designed to reduce the contamination from interlopers in the satellite sample. Since our interest is in pairs of satellites, we retain only hosts with two or more satellites. Our sample contains 427 such hosts, with 965 associated satellites. \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}.