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I'm confused about the following basic points:

  • Do lat/long points have a projection or are they projection agnostic?
  • Do these points live in a sphere or a plane?

I understand that projections are used to transform a spheroid into a plane while attempting to minimize artifacts along desired attributes (e.g. distance).

  • Is a lat/long measurement agnostic to projections in the sense that it captures some sort of "absolute position" on Earth?

  • If it is in fact agnostic (if the point lives in the spheroid), is this the reason why we use havesine to calculate distances?

  • How do CRS come into play when dealing with lat/long coordinates?

I seek feedback on misconceptions and pointers to material to learn about this stuff.

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Latitude-Longitude coordinates are not projected, they live on an ellipsoid. Occasionally, you'll find lat-lon values referenced to a sphere instead. This ellipsoid is, however, defined by a coordinate reference system (CRS) which includes information like the size and shape of the ellipsoid. According to a given CRS, the lat-lon is absolute (i.e. one location has one coordinate value).

A CRS includes a geodetic datum which includes the ellipsoid definition, optioally a prime meridian (often defaults to Greenwich, UK - sets the origin of longitude values), angular unit (usually degrees), and axes.

The lat-lon coordinates of a location are almost always different if the CRS is different. The differences can be large--a few hundred meters--or small--centimeters.

Since the coordinates are on a ellipsoid, you can't apply Cartesian, 2D, measurements. Measuring the distance from the north pole to the south pole, we don't want a line through the center or the earth (shortest) but rather on the earth surface. To do so, the geodesic formula like Vincenty's method are used. A simpler formula called the haversine can be used if your accuracy requirements are lower.

Many software packages if displaying data as a 2D plane, will show lat-lon coordinates in a pseudo-Plate Carree projection. The angular units are treated as if they're linear so you see the world as a rectangle.

  • Is it accurate to say that one datum can be assigned to multiple projections (coordinate system to plane), but a given projection has one and only one datum? – xv70 Sep 12 '18 at 17:37
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    nyes.... depending how you define "a given projection". The mathematical computation transforming a lat-long to a planar coordinate is the same regardless of the datum, but we don't refer to the projections by their equations but rather by a name/code, such as EPSG, which also specifies the datum. – JGH Sep 12 '18 at 17:53

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