Center-to-Center distance [duplicate]

Question

Possible Duplicate:
What is the right solution (and map projection) to compute distances between points located all over the World?

I want to know how I could calculate the center-to-center distance between two (or even more) circles, based on their center's Geo-coordinates values?

I'm new in this area, gonna use this one for Goolge Maps API 3 via Javascript and PHP. Probably the algorithm should be enough, however more details are appreciated. :)

Update:

The circles are not necessary to mention as part of the problem, as it could apply to two points, instead of two circles' centers. Actually I'm trying to do some overlap detection stuff on a crisis mapping application.

The locations are relatively close to each other, however I prefer to go for a fail-safe solution which could apply on most of the cases (if not all).

Also it doesn't need an accurate result, as all the visualizations on this web application are somehow approximate by default, so there is no great rush for having a perfect-accurate solution for now, but same as above, I personally prefer to go for the best choice, if it's not gonna add so much difficulties on the solution.

Answer 1

There's a fantastic explanation of the various algorithms for calculating distances between points given latitude and longitude located here.

The gist of it is this:

For intuitive simplicity, you could start with the Equirectangular approximation, which is derived from the pythagorean theorem. However, this is a bad choice as it grows in imprecision as you move away from the equator (the Mercator projection deficiency).

If you're not at all concerned about wrapping your head around the problem, just use the spherical law of cosines:

var d = Math.acos(Math.sin(lat1)*Math.sin(lat2) + 
              Math.cos(lat1)*Math.cos(lat2) *
              Math.cos(lon2-lon1)) * R;

where R is an approximation of the radius of the earth in the desired units.