n closest points in a set of lat/long coordinates

Question

Here's my problem:

I have a website where people can search based on their location (which is converted to lat/long coordinates). I have many products stored in a database with their lat/long coordinates. I also have a function to calculate the distance between two points based on their coordinates.

Now I'm looking for a way to find one of these things:

• The n nearest products to the user's location.
• All the products within a radius of x kilometers from the user's location.

Both solutions would be fine for my application.

Currently I just iterate over all the database entries, find their distance, and sort them. This obviously gets way too slow with a lot of entries.

Are there any algorithms/data structures I can apply here to make it faster?

Thanks in advance!