In ArcGIS can a feature set use multiple coordinate systems?

Question

I'm new to learning GIS and ArcMap, but have some confusion about coordinate systems. I thought I understood that there are two main types of coordinate systems, Projected Coordinate Systems which are in feet or meters, or Geographic Coordinate Systems in lat/long units.

Working on a project in ArcMap I see that in the Layer Properties, it shows the coordinates systems as a projected system, NAD_83 and also a geographic system, GCS North America 1983 (The block below is a cut and paste from "Layer Properties").

I thought that the coordinate systems were supposed to be mutually exclusive? Does it make sense that a feature set would be in a projected and geographic system at the same time?? Or does it mean that NAD83 based on GCS North American 1983? Would it be possible to use NAD83 and a differentGCS?

My understanding is that NAD_1983_StatePlane_California_V_FIPS_0405_Feet measures everything in Meters from 34'N and 118'W, so how can it work with GCS that references the Greenwich prime meridian in lat/long?

Projected Coordinate System:  NAD_1983_StatePlane_California_V_FIPS_0405_Feet
Projection:   Lambert_Conformal_Conic
False_Easting:    6561666.66666667
False_Northing:   1640416.66666667
Central_Meridian: -118.00000000
Standard_Parallel_1:  34.03333333
Standard_Parallel_2:  35.46666667
Latitude_Of_Origin:   33.50000000
Linear Unit:  Foot_US

Geographic Coordinate System: GCS_North_American_1983
Datum:    D_North_American_1983
Prime Meridian:   Greenwich
Angular Unit:     Degree

Answer 1

Within the ArcGIS platform, each feature class (or all the feature classes within a feature dataset) may only have one SpatialReference. The coordinate system is one aspect of a SpatialReference (the others include a vertical coordsys, and the XY/Z/M origins, precisions, and tolerances which define basis for coordinate comparison).

Coordinate systems can either be geographic (GCS) or projected (PCS). A GCS defines the datum, prime meridian, and angular units. These properties are also required for a PCS, so they are defined in the PCS as a GCS, making a GCS a property of a PCS. They could have been modelled differently, but the software engineering precept of encapsulation is a powerful influence, and that is how the Projection Engine (and the EPSG model, on which the PE is based) treats them.

So, rather than multiple coordinate systems, the layer properties report a single projected coordinate system, which is defined with respect to a GCS (which is listed with an extra newline).

Answer 2

@Vince mentioned that all PCS are with respect to GCS or you may say that (PCS) does not work without (GCS)

Geographic coordinate system (GCS) is used to define the shape of the earth, that is mean the 3D of Earth.

Projected coordinate system (PCS) is used to show the 3D earth into a 2D flat sheet using projection methods.

ArcMap does project data, but if a single element ( it refers to the mismatch of an angular unit of measure (lat-long), a prime meridian, or a datum) in the Geographic Coordinate System (GCS) is different (which refers to the correct projections/what pragmatically is expected not just for the sake of looking correct) then ArcMap will ask for a Geographic Transformation even if one is not needed.

It does not apply any Geographic (datum) transformations automatically. When the warning appears about the Geographic Coordinate System differing from other data in the map, a Geographic (datum) transformation must be selected by the user.

References: GeoNet: The Esri Community