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The line on the ground at the Greenwich Observatory is itself on a tectonic plate that is moving, so is the prime meridian still 0 degrees, 0 minutes, 0 seconds?

If not - what are the implications (if any)? For example, if my GPS says I am 100 km west of Greenwich Observatory, am I 100 km west of 0 0 0 or 100 km west of the line on the ground? Who (and what) decides this kind of thing?

Curious punter, not a scientist....

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Remember it is just an imaginary line on the Earth's surface used for georeferencing purposes, so movement of the reference line has no implications so long as we can still reference to it (hence the International Reference Meridian).

In fact, the position of the Greenwich meridian has changed throughout history, mainly due to the Airy Transit Observatory (the original location of the Greenwich meridian) being built next door to the previous one (to maintain the service to shipping). Such changes had no significant practical effect. Historically, the average error in the determination of longitude was much larger than the change in position. The adoption of WGS84 ("World Geodetic System 84") as the positioning system has moved the geodetic prime meridian 102.478 metres east of its last astronomic position (measured at Greenwich). The position of the current geodetic prime meridian is not identified at all by any kind of sign or marking (as the older astronomic position was) in Greenwich, but can be located using a GPS receiver. Due to the movement of Earth's tectonic plates, the line of 0° longitude along the surface of the Earth has slowly moved toward the west from this shifted position by a few centimetres; that is, towards the Airy Transit Observatory (or the Airy Transit Observatory has moved toward the east, depending on your point of view) since 1984 (or the 1960s). With the introduction of satellite technology, it became possible to create a more accurate and detailed global map. With these advances there also arose the necessity to define a reference meridian that, whilst being derived from the Airy Transit Circle, would also take into account the effects of plate movement and variations in the way that the Earth was spinning - the International Reference Meridian.

See:

Malys, S., Seago, J.H., Pavlis, N.K. et al. (2015) "Why the Greenwich meridian moved" Journal of Geodesy. 89 (12) pp 1263–1272

Dolan, G (2013). "WGS84 and the Greenwich Meridian". The Greenwich Meridian.

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This is quite a good question. There is no simple solution for it.

Prime Meridian

Nowadays prime meridian is still in Greenwich but it was slightly moved from the original 0° 0' 0'' position (shifted by 5.34 arcseconds). It is denoted as IERS Reference Meridian (IRM). The prime Meridian should be on a plane, which splits the Earth's mass into exact halves. Due to higher resolved data on the Earth's shape and mass distribution, one realized that this was not the case for the 'original' prime Meridian. See Malys et al. (2015) [doi: 10.1007/s00190-015-0844-y] for details.

Movement of Tectonic Plates

As you say: the continental plates move. Thus, a global perfect map from 1985 would differ from a global perfect map from 2017. If we keep our lon-lat-coordinate system constant, some real world locations move with respect to their geographical coordinates.

At this point a 'reference datum' comes into play: one fixes the coordinate system on a specific date and for a specific tectonic plate. Examples are the North American Datum 1983 (NAD83) and the European Terrestrial Reference Frame 1989 (ETRF89). Thus, using NAD83, a specific building in New York did not 'move' between 1985 and 2017. With respect to ETRF89 it would have moved.

Further problems: shape of the Earth

We need to assume a defined shape of the Earth to map coordinates to geographic places. The simplest assumption is: the Earth is a perfect sphere. However, this is not the case. GPS coordinates are based on the World Geodetic System of 1984 (WGS84). It uses a ellipsoid is shape for the Earth and the IRM as reference meridian. The English Wikipedia article is quite detailed.

If we assume another shape for the Earth but the same zero-meridian, most geographic locations will be projected on slightly different coordinates than they currently have. In order to maintain consistency of lon-lat-coordinates, standards like WGS84 and data like NAD83 were defined on an international level.

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The answer to your question: '...if my GPS says I am 100 km west of Greenwich Observatory, am I 100 km west of 0 0 0 or 100 km west of the line on the ground?' is You are 100km west of the reference meridian (0 deg 0 min 0 arc sec). The line on the ground is slowly moving with its tectonic plate by about 3cm/year to the northeast (that 3cm/yr is with respect to the best terrestrial reference frame, the ITRF, now ITRF2014).. Any line on the ground would have to be redrawn/reinstalled periodically if it were intended to remain an accurate depiction of the reference meridian's location on the ground.

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