In my days as editor of Mining Magazine I was pleased to publish, in the August 1993 issue,
an article by Norman T. Olsen; Vice President of Engineering, Mentor Software, Inc., Denver, 
Colorado, an article which he entitled "The elusive geoid". Although now no doubt out of date,
the article highlights some of the problems involved (although no mention of moving continents!)
and the text reads as follows:

" What is a geoid and how can cartographers and surveyors avoid its mathematical complexity?  
There is considerable confusion within the GIS community about the meaning of the terms ellipsoid, 
spheroid and geoid.  To understand the differences, one must first become a 'casual geodesist'.
 Geodesy refers to a branch of applied mathematics which studies the size and shape of the earth, 
particularly for the purpose of making measurements and other determinations where the roundness 
of the earth must be considered.  This is important to cartographers because map making involves 
the conversion of angular measurements such as latitudes and longitudes into linear measurements 
of Xs and Ys.  One needs to know the radius of the earth in order to perform such calculations.  
Thus, basic geodesy is an important part of cartography.
 The first recorded calculation of the circumference of the earth was made by the Greek scientist 
Eratosthenes in 300 B.C.  Geodesists have been measuring the size and shape of the earth ever since, 
but no two have come up with exactly the same results.  Why?
In the 17th century, Sir Isaac Newton reasoned that since the surface of the earth is universally considered 
to be the surface of the oceans (i.e. sea level), the centrifugal force generated by the rotating earth would 
cause the surface of the fluid oceans to protrude somewhat more at the equator than at the poles.  
Measurements by geodists proved his reasoning to be correct and measured this protrusion to be about 
one part in 300.  Thus, the shape of the earth is not a sphere but closer to a three dimensional ellipse, 
known as an ellipsoid or spheroid, terms which are synonymous.
 Despite Newton's discovery, geodesists since that time have still arrived at many different determinations 
of the size and shape of the earth. To a large degree, these discepancies can be attributed to the techniques 
and equipment used by earth-bound observers trying to measure the enormous earth.  However, there is yet 
another fly in this ointment.  The earth is not exactly a true ellispoid either.
 The level of the oceans at any given point on the earth is determined by the force of gravity which keeps the 
oceans from flying off into outer space.  Gravity is a function of mass and since the material of which the earth 
is made is not of uniform density, the level of the oceans deviates from the ellipsoid shape.  In places, this 
deviation is as much as 100 m.  A geodesist who assumes that the earth is an ellipsoid and makes his 
measurements in North America will arrive at a different determination of the size and shape of the earth than 
would a geodesist who makes his or her measurements in India.
 As a result, we have a number of highly accurate, very scientific measurements of the size and shape of the 
earth which are all significantly different.  Typically, these measurements are distinguished from each other by 
the name of the individual or organisation responsible for the measurements.  If an individual made more than 
one determination, the year in which the results were published is also used.  Thus Clarke 1866 refers to the 
ellipsoid determination made by the British geodesist Alexander Ross Clarke published in 1866.
 Due to the non-uniformity of the materials of which the earth is made, the true exact shape is more like a blob.  
Since this terminology is not very scientific or aesthetically pleasing, geodesists invented a new shape, the 
shape of the earth, and called it a Geoid.  Thus, the term geoid refers to the true size and shape of the earth, 
whatever that is.
 Unlike the sphere and the ellispoid, the shape of the Geoid defies representation by a simple mathematical model.  
One model, which is only reasonably accurate, requires a power series of the 18th order and comes with page after 
page of coefficients.  The U.S. Defense Mapping Agency has developed a mathematical model for the geoid which 
is a power series of the 180th order which requires 32,755 different coefficients -- but coefficients for terms above 
the 18th order remain classified information.
In order to avoid the mathematical complexity of the true geoid, cartographers and surveyors simply use the 
ellipsoid model which represents the best fit to the geoid for the region within which they are working. When working 
in the U.S., for example, one could use the Clarke 1866.  This ellipsoid was used as the basis for most mapping 
and surveying done in the U.S. prior to 1986.
 Internationally accepted ellipsoids exist for each continent, such as the Krasovsky ellipsoid for the former Soviet 
Union, the Australian ellipsoid for Australia, the Everest elliopsoid for India, and so on.  Can there not be a single 
ellipsoid, or one worldwide standard, that represents the entire globe?  Until the advent of today's advanced computer 
technology, this has been a lot easier said than done.  The first attempt was made in 1924.  It is referred to as the 
International ellipsoid and has been widely used since that time.
 Today, the WGS84 (World Geodetic System of 1984) and GRS1980 (Geodetic Reference System of 1980) ellipsoids 
are the ellipsoids preferred by cartographers worldwide and represent the best fit for the entire geoid. Many of the 
differences between what are referred to as NAD27 and NAD83 have to do with converting measurements based on 
the Clarke 1866 ellipsoid to new ones based on the GRS1980 ellipsoid.
 With the advent of satelites, cartographers can now choose to use an ellipsoid which represents the best fit to the 
entire geoid and thus be consistent with their colleagues in other parts of the world."

Tony Brewis