I have a system that is based on PostGIS that holds a set of coordinates. It serves a lot of user requests where users send their own current coordinates and receive a set of points that are located nearby, like 5-10 km. Each time the DB pulls all points and calculates the distance between points.

Is there is a way to use a simpler way of calculation, like counting all distances to the base point, and then using some matrix transformation? Or maybe I am missing some PostGIS functionality?

UPD: The point info is stored this way:

ST_GeomFromGeoJSON('{"type":"Point","coordinates":[28.119871,48.542976]}')::geometry

The resulting SQL is really big, but the distance is calculated like:

ST_Distance(ST_Transform("fuelStation"."location",9015), ST_Transform(ST_GeomFromGeoJSON([user entered coordinates]),9015))

Maybe I need to clarify the question - the current realization works +- fast, but I wonder is there a way to "cache" distances table from 1 point and then recalculate when the point changes?