Convert Eps to geographic distance using DBSCAN

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I am using the dbscan cluster (package fpc) in R to find clusters on a set of latitudes/longitudes coordinates. I want to find an eps distance that corresponds to a meaningful geographic distance (e.g., a mile or kilometer)

My data looks like this:

Longitude Latitude1 -87.53163 41.686402 -87.59986 41.673413 -87.80099 41.954694 -87.82481 41.974095 -87.67671 41.688326 -87.67751 41.73192Through trial and error, I got a set of clusters that look plausible. In the attached map.

dbscan.clust1
 
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