Hello,

I am using ArcMap 10.4.1.

I am looking for confirmation of my understanding of the below scenario. I am trying to understand what happens when two different coordinate systems do not align. The concept appears simple but want to confirm that I am not missing something. I have attached an image of the Lambert Conic Conformal projection model showing the Grid Origin and the Geodetic Origin, as an example. It is my understanding that the grid origin (red X) would correspond to the cad/Esri program 0,0,0 (origin of northing-easting values). While the geodetic origin corresponds to the projected ellipsoid origin, centered on the map (red square). It appears that coordinate systems with different ellipsoids and units would shift the map false northing/easting to a different location, causing data to misalign. By toggling the coordinate system alone is not enough to change the map data, but by performing a transformation-projection on the data allows the software to read the northing-easting coordinate values relative to the false northing/easting of the ellipsoid that is active in coordinate definition.

Does the above concept sound correct or could there be more to this concept that I am not aware?

I always like to think of it in these terms.

Take a big long rope that can't change length under any circumstances.

Your bud stands at some spot along the longitudinal origin (arbitrarily Greenwich... btw).

You unfurl the rope and go some place and record your longitude and latitude using the ellipsoidal model that you were using at the time. You know the length of the rope because you measured it in planar units... the metre of course . Now.. along comes the latest news that states that your prior knowledge of the equatorial and/or polar radii was all wrong and new values have been adopted. Grief! The only thing that can happen if you bud hasn't moved and your rope is the same length... is that your coordinates have to change.

Same principle applies when measuring anything relative to an arbitrary origin or know fixed distance and a relative coordinate system that depends on other properties (like radii)