MongoDB Bound Queries: How do I convert mile to radian?

Question

I have a collection of stores with a geospacial index on the location propery.

What I am trying to do is given the user's latitude, latitude and a search radius (mi), I want to return the list of stores that are within those parameters.

I saw the following example on the MongoDB documentation (http://www.mongodb.org/display/DOCS/Geospatial+Indexing), but it looks like the distance is in radians.

center = [50, 50]
radius = 10
db.places.find({"loc" : {"$within" : {"$center" : [center, radius]}}})

So, what is the formula to convert miles to radians?

Solution The awesome people at mongodb-user helped me find the answer. Basically, what I was really looking for was a way to limit the distance.

Per, the updated documentation, there is a 3rd parameter to the $near query: You can also use $near with a maximum distance

db.places.find( { loc : { $near : [50,50] , $maxDistance : 5 } } ).limit(20)

The value for $maxDistance is in radians; so, I had to take my distance in miles and divide it by 69.

Thank you!

I was able to find my answer by posting my question on the mongdb-user Google Group (groups.google.com/group/mongodb-user/browse_thread/thread/…). — Abe
Note: dividing by 69 is a rough conversion from miles to degrees, not radians. Degrees are correct here because this is a plain ol' $near query (which means $maxDistance must be in the same units as the coordinates are), not a spherical query (which do require $maxDistance to be in radians). — John Flatness

walla walla · Accepted Answer · 2010-10-07T09:42:39

As docs say:

All distances use radians. This allows you to easily multiply by the radius of the earth (about 6371 km or 3959 miles) to get the distance in your choice of units. Conversely, divide by the radius of the earth when doing queries.

so you simple need to divide your radius by the earth radius. in your example it would be:

radius = 10/3959

MongoDB Bound Queries: How do I convert mile to radian?

2 Answers