# Do latitude/longitude coordinates ever refer to "real" earth, not idealized sphere or ellipsoid?

I'm new to the world of geographic information systems. While trying to learn the basics of spatial reference systems, I wonder whether there is any situation in which we can have latitude and longitude coordinates that refer to the "real" earth with its bumps and irregularities, and not an idealized sphere or ellipsoid. I think that such a situation doesn't exist, as all the mathematical methods used to arrive at latitude/longitude values (e.g. in astronomic navigation) need some geometric idealization to be tractable. As far as I understand, the same goes for GPS.

Is it correct that we never have latitude/longitude coordinates referring to the "real" earth, or am I mistaken?

• Remember (in addition to Rob Skelly's primer) that local, ground coordinates are often given based on measured or observed ground "truth". These coordinates are almost-never given in Lat/Lon but instead are X/Y intentionally.... still the issue of "what is truth" exists with these measurements. Aug 8, 2017 at 19:59

With these sorts of questions, the issue isn't so much with the earth or the reference system, but with the definition of "real." Angular coordinates only make sense in an axiomatic framework, with reference to an origin and an axis. There are no straight lines or points in nature, of course. These are things that are only defined in the mind.

In the case of WGS84, angular coordinates are taken with respect to a reference frame that is anchored as closely as possible to the centre of the Earth, as measured by the orbits of satellites. The orientation of the frame is set by alignment with distant quasars. Basically, it's a hypothetical box with with a hypothetical centre, with the earth inside of it. Projected coordinate systems such as recent editions of NAD83 are realisations of this model, with adjustments to account for tectonic drift, etc. (In contrast to this geocentric coordinate system, you've probably learned about NAD27, in which the reference ellipsoid is anchored to the Earth not by its centre, but at a spot on the surface of the Earth in Kansas.)

Elevations in this framework are measured from the surface of an ellipsoid, then usually adjusted using a geoid model to represent the equipotential surface -- roughly, the elevation of the ocean surface, if it covered the whole planet. Elevations measured relative to the geoid are called orthometric heights.

Of course, it is impossible to measure, with infinite precision, the "real" position of anything on a dynamic rock in space the way you would expect to do in a pure math context. Everything is modelled, which implies compromise. Though the compromises get smaller all the time, the rate of improvement is slowing -- naturally, the closer you get to an unattainable "truth", the slower your progress becomes. All measurements and positions on Earth merely have to be good enough, just as NAD27 was good enough for the time and the region it was intended to represent.

• Thanks a lot for this insightful answer! I wasn't aware of many of these details, e.g. exactly how WGS84 is anchored to the center of the earth. And you're definitely right, "real" is a tricky term here. Aug 4, 2017 at 18:37
• Your welcome. I added a couple of links, but this is not my area of specialisation, so it's possible someone will come along with more comprehensive insights. I think it's a fundamental quandary in geography: "where is 'here'?" Aug 8, 2017 at 0:51
• Note that there is also an earth tide that moves the surface, periodically moving 'real' around on scales of tens of centimeters vertically and by centimeters horizontally. Jan 2, 2018 at 22:11