Why is the GPS Reference Meridian 100m to the East of the Prime Meridian?

I've answered this question in passing while answering another of your question.

The Greenwich Observatory was defined as a prime meridian, based on the observations by the astronomer Sir George Airy in 1851. London was selected as the official prime meridian for international maps by the International Meridian Conference in 1884.

When you use a GPS, by default it uses the WGS84 datum. This is different from the old coordinate system. WGS84 is a global datum based on calculations from readings across the earth, and its prime meridian is different. The difference is about 100 meters at Greenwich.

More details are available in these links:

• https://productforums.google.com/forum/#!msg/gec-nature-science-moderated/ANkXU1I5pzA/7fsj3kLqGjQJ
• http://www.thegreenwichmeridian.org/tgm/articles.php?article=7

The short answer is: there was a historical shift between the first global datum and the Greenwich meridian; and it continues to move (slowly) because of continental drift. You can find more detailed information on this site

In the late 1950s (under the auspices of the US Navy), the Applied Physics Laboratory (APL) of the Johns Hopkins University began the development of what was to become the world's first operational satellite navigation system. Known as Transit, it worked by making use of the Doppler effect, the same effect that makes a siren carried by a moving vehicle change in pitch as it passes. The surveyed longitude of the Laboratory's site in Maryland, as measured in the North American Datum (NAD27), became its assumed longitude in the first World Datum, the APL datum. It was this pragmatic adoption of the longitude coordinate on one ellipsoid as the assumed value on another that has caused the apparent shift not only in the position of the Meridian, but also of all other locations.

The size of the shift remained unknown until the summer of 1969, when an opportunity arose to measure it. A satellite receiver was set up on a platform above the roof over the Airy Transit Circle at Greenwich. The results showed that fixes resulting from the use of the satellite navigation system should have their longitude values shifted by 5.64" if the Greenwich (Geodetic) Meridian was to have its longitude as zero in this system. Although an academic paper on this subject was published in 1971, it appears to have been largely forgotten about until the mid noughties. The offset (since refined) also applies to the WGS84 datum used by current GPS systems. WGS84 was adopted as the global standard for air navigation on 1 January 1998 and soon afterwards by hydrographers for use on electronic and nautical charts.

This article in the Journal of Geodesy explains that it is caused by the local deflection of the vertical in London, due to regional variation in the thickness and density of the Earth's crust.

What Airy's Transit Circle in the observatory in Greenwich defines is not directly a place on the surface of the Earth, but a direction in space, namely that of the local zenith, or plumb line.

The article above argues that this direction is actually, with reasonably good accuracy, still the direction of the modern IERS zero meridian used to define WGS84 and thus GPS coordinates. The various changes of definition over the last 150 years have kept good continuity with it.

However, even though WGS84 uses this direction as a reference, the x-z plane in WGS84 geocentric coordinate is parallel translated 102 meters such that it passes through the Earth's center of mass.

So the real difference is not merely about using a different origin for your coordinate system, but using a different principle for what the coordinates mean. In Airy's time there was no way of measuring the location of the Earth's center with much precision -- what one did was measure the direction of the local zenith and declare that direction (relative to the pole and to the orientation of the transit circle in Greenwich) to be one's coordinates. On the other hand GPS measures your position directly, and the center of the Earth relative to the satellite orbits is well known. In order to express this position as old-style coordinates, the GPS unit will compute a "virtual zenith line" as the normal to the reference ellipsoid that passes through you. The difference between this normal and the IERS zero meridian (which, again, agrees with the orientation of the Airy transit circle) becomes your coordinates.

So when you walk out into the park in Greenwich to find the place where your GPS receiver shows 0 degrees longitude, what you've actually found is the point (modulo latitude) where the normal to the WGS84 reference ellipsoid is parallel to a plumb line erected at the observatory itself.

Neither continental drift nor random accumulated errors from definition changes have had effects comparable in size to this.