An accurate center of gravity calculator for Google Earth is now available here. All the code is Brammeleman‘s, taken from his calculator page here, save for the one final altered latitude correction, which places the center of gravity closer to the poles — at the correct position.
Abbreviated instructions: In Google Earth, collect your placemarks in a folder and save that folder to your hard drive as a KML file (not KMZ). Upload this file into the calculator and open the returned file in Google Earth. Voila.
So what does this center of gravity calculator do, precisely?
Practically speaking, the spot you get back minimizes the total distance people at placemarks will need to travel in order to meet up together. And if you calculate the center of gravity for just two placemarks, the straight line you can draw through all three points will be the shortest distance as the jumbo jet flies between your two placemarks.
Mathematically speaking, the code first finds the center of gravity for given points of equal mass on the surface of a sphere in three dimensional space. (The center of gravity will thus be inside the sphere.) It then finds the point on the sphere closest to the center of gravity by projecting a straight line from the center of the sphere through the center of gravity to the surface of the sphere.
The algorithm assumes Earth is a sphere, even though it is actually a geoid, so errors of tens of meters will persist. Correcting for those is something I am two PhDs short of being able to do.
The original story is three posts down, here. As a result of the correction, my family’s actual center of gravity is now 43km further north, in Bree, near the Dutch border.