The equations to convert x,y,z to longitude and lattitude?

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Discussion Overview

The discussion revolves around the conversion of Cartesian coordinates (x, y, z) to geographic coordinates (longitude and latitude), with references to polar and spherical coordinates. Participants explore the accuracy required for such conversions and the models of the Earth that should be considered.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks to convert x, y, z coordinates to longitude and latitude, indicating the center of the Earth as the origin.
  • Another participant questions the accuracy needed for the conversion, suggesting considerations of whether to assume a spherical model or use a more accurate geoid model or digital terrain model (DTM).
  • A participant identifies the conversion as related to polar coordinates but notes difficulty in finding relevant equations for x, y, z.
  • Several participants suggest looking up spherical coordinates as a potential solution.
  • One participant asserts that the equations for converting x, y, z to latitude and longitude are incorrect, emphasizing that the Earth is not a sphere and that latitude is not a spherical measure, while also noting uncertainty about the closeness of the approximations provided.
  • Another participant mentions the standard practice of modeling the Earth as an ellipsoid and references the WGS84 model, indicating variability in the models used.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of spherical coordinates for the conversion, with some asserting that they are not correct due to the Earth's shape. There is no consensus on the best approach or model to use for the conversion.

Contextual Notes

The discussion highlights limitations regarding the assumptions made about the Earth's shape and the accuracy required for the conversion, as well as the dependency on the chosen model (spherical vs. ellipsoidal).

CosmicVoyager
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Greetings,

I am trying to figure out how to convert an x,y,z coordinate to longitude and latitude (or right ascension and declination). Center of Earth is origin, of course.

Thanks
 
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How accurately do you need it?
Are you just assuming a sphere or do you need an accurate geoid model, or real world DTM data?
 
i now know that what i am looking for is called polar coordinates.

x,y,z to polar coordinates

i have only been able to find x,y to polar
 
Look up spherical coordinates.
 
nicksauce said:
Look up spherical coordinates.

Thanks :smile:
 
nicksauce said:
Look up spherical coordinates.
Those are not the correct equations for converting x,y,z to latitude and longitude. The Earth is not a sphere; latitude is not a spherical measure.

They are close, however. Whether they are close enough or not, we can't tell. CosmicVoyager never answered mgb_phys' question.
 
D H said:
Those are not the correct equations for converting x,y,z to latitude and longitude. The Earth is not a sphere; latitude is not a spherical measure.

They are close, however. Whether they are close enough or not, we can't tell. CosmicVoyager never answered mgb_phys' question.

Good point.
 

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