I have a very big dataset in the form of longitude-latitude points in the US; with points from the entirety of contiguous US. I need to calculate the distances between points and check if they are less than 50 meters. For computational reason, I also need to use classic plane geometry; no distance in degree.
I am wondering what CRS I could/should use. I need one CRS for the entire dataset, that is the whole contiguous US. So far, I have used the North America Albers Equal Area Conic (EPSG: 102003), since it appears to be used by the Census. However, when I compare the distances as calculated from this CRS with the distances as calculated from the Haversine formula, the difference is remarkable. At least, for long distances -- I picked random points uniformly in the US, so the distances are in the order of 10^3 km.
Is there a better choice for a CRS?
Will it even make a difference for short distances in the order of 100 m?