The square is ideal mainly for querying for results. Once you have the query results, the exact distance can be calculated to whatever precision is available from the original lat/lon data.
Geodetic calculations like this are quite cumbersome for us mere mortals, but once encoded, it is fairly trivial as far as server load goes, I see no issue as long as the returned results are a manageable size.
Since you envision world wide coverage, you will of course need to consider latitude in determining the longitudinal spread for the initial query. Not a big deal, just a bit more work.
You will need to find the formulas used to convert from km distance to the arc distance in degrees lat/lon. An example: For simplicity, let’s say 10 km is found to be equal to 0,1 degrees in both lat and lon (it’s not of course) at 52,3 deg N and 5,3 deg E (a bit East of Amsterdam actually). You would then query for records where the lat falls between 52,1 and 52,4 and lon falls between 5,1 and 5,4, which would be the bounds of a 20 km square. See why it’s very useful to have the lat separate from lon values?
You can then plug in the actual lat/lon of the center point and that of any found record into yet another formula and get the actual straight line (great circle arc actually) distance. Accurate to the mm if your lat/lon data is that accurate 🙂
The most accurate calculation is probably via Vincenty’s Formulae. Unless you’re a mathematics major, that link is going to look very scary! For your needs, less accurate methods should suffice. Take a look at Geographical Distance. You may want to skip past the planar solutions, they involve a lot of distortion. Spherical surface formulae should suit you fine.
You would first need to invert the problem because as illustrated it solves for distance, you have that, you want to solve for lat/lon. Of course, coding all of this is prone to error. Fortunately, there are online calculators with which you can check your work against. Just be sure the calculator you use uses the same underlying formulae.
If you can’t be bothered with all this sine and cosine stuff, another approach would be to use an online calculator to determine the degree longitude per kilometer for a range of latitudes and compile a look up table that the code can use to get a conversion constant for any particular latitude range. You will only need a few values for degree latitude per kilometer, perhaps just one value will work for you. Get a value at 0 deg latitude and 70 deg latitude to see how much variation we’re talking about.
For background information about geometric modeling of the earth, try reading Figure of the Earth. Much less mathematics than the previous links 🙂
