Dear Thad > As many of us know, we can geometrically compute the distance > between two locations (lat, long) and (lat2, long2) assuming > that the Earth is a perfect sphere (which of course it isn't). > > Has anyone seen a correction for this flattening at the poles, > or bowing around the equator?
As always, Meeus has the answer. The crucial difference is that between geographic latitude and geocentric latitude: The geographic latitude is the apparent altitude of the nearer celestial pole measured above the northern (or southern) horizon. Meeus calls this phi. The geocentric latitude is the angle that a radius from the centre of the Earth to the observer makes with the plane of the Equator. Meeus calls this phi'. The difference is given as: phi - phi' = 692.73 sin(2 phi) - 1.16 sin(4 phi) The constants are arc-seconds. The greatest difference is at a latitude of 45 degrees when the difference is about 11.5 arc-minutes. This translates into about 11.5 nautical miles. This is the about the error where you live! Geographic latitude is what is normally measured and used. This is what is marked on maps. There is an implicit assumption that the plane of the horizon is perpendicular to the local gravitational vector. This means you can use a normal sextant or other instrument that measures relative to the horizon or you can use an instrument that has some kind of spirit-level built in. Beware of massive mountains nearby! Frank King University of Cambridge England -
