Mongodb - Returning the points nearest to a location, with distance
MongoDB has built in support for geoindexing.  You don't need to do the calculation yourself.  

Basically, you would create a field with the lat/long stored as an array or as sub documents, something like one of these:

{ loc : [ 50 , 30 ] } //SUGGESTED OPTION
{ loc : { x : 50 , y : 30 } }
{ loc : { lon : 40.739037, lat: 73.992964 } }


Then index the new loc field appropriately:

db.places.ensureIndex( { loc : "2d" } )


Finally you can then use one of the operators to query a point for the nearest 20 results:

db.places.find( { loc : { $near : [50,50] } } ).limit(20)


You could, of course, just use MongoDB to store the data, then pull the information out of the DB with a find() and do the calculation client-side but I imagine that is not what you want to do.

If the distance part of the equation is what you want:

http://www.mongodb.org/display/DOCS/Geospatial+Indexing#GeospatialIndexing-geoNearCommand

The $geoNear operator will return the distance also.  An example:

&gt; db.runCommand( { geoNear : "places" , near : [50,50], num : 10 } );
{
        "ns" : "test.places",
        "near" : "1100110000001111110000001111110000001111110000001111",
        "results" : [
                {
                        "dis" : 69.29646421910687,
                        "obj" : {
                                "_id" : ObjectId("4b8bd6b93b83c574d8760280"),
                                "y" : [
                                        1,
                                        1
                                ],
                                "category" : "Coffee"
                        }
                },
                {
                        "dis" : 69.29646421910687,
                        "obj" : {
                                "_id" : ObjectId("4b8bd6b03b83c574d876027f"),
                                "y" : [
                                        1,
                                        1
                                ]
                        }
                }
        ],
        "stats" : {
                "time" : 0,
                "btreelocs" : 1,
                "btreelocs" : 1,
                "nscanned" : 2,
                "nscanned" : 2,
                "objectsLoaded" : 2,
                "objectsLoaded" : 2,
                "avgDistance" : 69.29646421910687
        },
        "ok" : 1
}


The "dis" : 69.29646421910687 elements are what you are looking for, there is also a spherical distance option.

For all this, how to use the distances, and more, take a look here for more information on geo indexes and how to use them:

http://www.mongodb.org/display/DOCS/Geospatial+Indexing/