topic GCS Figure in ESRI Presentation in ArcGIS Pro Questions

GCS Figure in ESRI Presentation

Bernd_Loigge — Mon, 05 Sep 2022 15:01:14 GMT

Hi,

I just came across this presentation https://www.esri.com/content/dam/esrisites/en-us/about/events/media/UC-2019/technical-workshops/tw-6197-466.pdf

A colleague and I couldn't figure out why on slide 13 the center of the ellipsoidal surface is not on the same level like the equator but slightly below.

Is this just a wrong drawing or does it show something?

Re: GCS Figure in ESRI Presentation

BojanŠavrič — Mon, 05 Sep 2022 20:56:45 GMT

Thank you, @Bernd_Loigge, for your question! The image of the GCS on the slide 13 is correct and intentional. Let me explain it…

A geographic coordinate system is defined on an ellipsoidal surface. The center of the ellipsoid is still where the polar axis intersects the equatorial plane. Latitude of the point P is measured between the equatorial plane and the normal on the ellipsoidal surface at the point P. In general, normals on an ellipsoidal surface do not go through the center of an ellipsoid. They intersect the polar axis below or above the center depending on whenever the latitude is positive or negative. Exceptions are points on the Equator and at the pole. Their normals go through the center. The distance between the point P and where the normal intersects the polar axis (Q) is called the transverse radius of curvature.

If Earth’s model would be a sphere instead an ellipsoid, then all normals would go through the center of the sphere.

I hope this helps,
Bojan

Re: GCS Figure in ESRI Presentation

Bernd_Loigge — Tue, 06 Sep 2022 07:14:50 GMT

Thank you. Very well explained!