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It's accepted wisdom that geographic coordinate systems require a datum in order to assign lat/long to a point on Earth's surface.

However, every point in 3d space already has 3d polar coordinates which would appear to define a lat/long from a suitable origin (i.e. the center of the Earth) and reference axes (defined by e.g. Earth's axis of rotation, and one more arbitrary point such as the Greenwich Observatory).

From the fact that a datum is deemed necessary, it would seem that lat/long cannot simply be the angular part of polar coordinates; in other words the instructions for determining lat/long are not simply "measure the angles from an agreed origin".

Instead a datum defines an ellipsoid surface, which may be above or below the actual Earth's surface at the point we are trying to measure.

How does the datum's surface affect the assignment of lat/long to the point on Earth's surface?

For example do we look for the nearest point on the datum (as measured in 3d space) and take the lat/long of that one?

If so, why?

And if not, why is the datum needed?

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My understanding is that

to define a lat/long from a suitable origin (i.e. the center of the Earth) and reference axes

is not easily done as there is no obvious origin to mesure angle from.

As earth is not a perfect sphere or ellipsoid its center is not clearly defined and you don't really have a way to use common maths formula on it's surface.

To overcome that you have to create the best mathematical approximation of the earth shape and use that as datum.

As "the best mathematical approximation" will depend on your specific need and knowledge of the "real" earth shape, you will get different "best" approximation for different need and each one of those could be improved over time. In the end you get lots of datum...

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  • So you're saying the datum is needed to define an origin (something we agree is a valid centre of the earth) based on local observations of the surface? I guess historically, without positioning satellites, you couldn't easily determine the location of the poles or equator relative to yourself so finding the center was far from trivial. Commented Jun 16, 2022 at 17:33

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