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Another basic geodetic question


trmcconn
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It's hard for a non-specialist to get understandable answers to basic questions in a very technical field like Geodesy. The NGS website, useful as it is, bristles with an alphabet soup of confusing acronyms and, when it comes to actual details, usually refers you somewhere else. (Some arcane article in the Journal of Geodesy, for example.) One should of course start with a basic undergraduate text, but basic (101 level) undergraduate texts have their own problems. Students at that level can't handle the unvarnished truth because they lack sufficient mathematical training, so such texts routinely lie to them or fall back on vague language in the interest of simplicity. It is hard for the reader to identify the BS without already being an expert. 

 

Here's my question: our current beloved datum (NAD83) consists of two main ingredients: (i) an ellipsoid (GRS80) that represents a crude approximation to the actual figure of the earth; and (ii) an origin and set of 3-dimensional cartesian axes.  The origin coincides with the center of symmetry of the ellipsoid (anything else would be crazy) and I presume the z axis coincides with the semi-minor axis. This doesn't determine where the x-axis pokes through the "equator" of the ellipsoid, but it doesn't matter because the ellipsoid is symmetric under rotations around the z-axis.

 

The real question is how is this whole geometric rig actually attached to the physical Earth?  My understanding is that the origin was supposed to coincide with the center of mass of the Earth, but it's a meter or so off, and that's one of the reasons there's a new datum coming in 2022. Presumably the z-axis should coincide with the mean axis of rotation of the Earth. (One has to say "mean" here because the actual physical axis wanders around due to nutation and other more random effects.) What about the x-axis? Where does it poke through the (mean) equator of the earth? Is there a monument there or something? (For the older NAD27 datum, the Clarke ellipsoid was pinned down by declaring a particular point - Mead's Ranch - to have a specific latitude and longitude, and a nearby survey mark, station Waldo, to have a specified azimuth.) 

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Yeah, it's complicated, and I have only limited knowledge.

 

NAD83 doesn't really have an x axis, or if it does it isn't important, because NAD83 is tied to the North American tectonic plate and not to the rest of the earth.

 

WGS is fitted to the whole earth, and is a snapshot (updated every so many years) of the fit determined by international scientific groups. Its x axis is 0 degree longitude, and that is about 100 meters from the old Greenwich astronomical observatory meridian. There are discussions out on the web about why it doesn't match, which I vaguely recall had to do with deflection of the vertical due to gravity variation versus location, and continuity of time scales.

 

The 2022 datum will be more like  IGS and WGS, and there are documents and seminar recordings on the NGS site explaining it.

 

I hope something in this ramble helps sort out the stuff you read, and that Dave D comes along to correct my mistakes.

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trmcconn

Excellent questions.  You are correct that in a 3D Earth Centered Earth Fixed (ECEF) coordinate system, the Z axis is along the rotation axis of the Earth.  Since that is constantly changing, geodetic institutions such as the National Geodetic Survey will commonly “fix” that location at some point in time.  In the case of the North American Datum of 1983 it was chosen to be January 1, 1984 (1984.0), as was then defined by the Bureau International de ‘Heure (BIH) now incorporated in the International Earth Rotation and Reference System Service (IERS)  www.iers.org.  It then follows that the X axis is defined as being along the equatorial plane in the orientation of the internationally accepted orientation of 0 longitude which is Greenwich, UK as Bill93 so correctly pointed out and the Y axis is orthogonal east to the X axis.  At the time of the development of NAD 83 and the original WGS 84 the only active satellite positioning service was the Navy Transit Doppler https://en.wikipedia.org/wiki/Transit_%28satellite%29.  At that time the best we could do was about 1 meter with Doppler consequently the knowledge of the 3D location of Earth geocenter was about 2 m.  Today with the mega enhancements of space-based positioning systems and international collaboration we now know the location of geocenter to about .02 m (some say better).  Our national datum NAD 83 is still defined to its original geocenter location.  Again, as Bill93 indicated that will change with the new datums now scheduled for release in 2025 or 2026.

There are several short (1-hr) YouTube videos I did on geodetic datums for the Geospatial Users Group a few years ago that you may find helpful in understanding how these systems have evolved -- https://www.youtube.com/channel/UCG69vYuN1Q61fWKiXffzo9A/videos.  I hope this is helpful

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