# What do different realizations of the same datum have in common?

Firstly, am I correct in assuming that the process of determining the shape and the size of the spheroid is independent from the process of determining the origin and the orientation?

For example, for NAD27, it seems that the following equation -- called the Clarke 1866 ellipsoid (reference 1) -- was fitted to the surveyed points: where the parameters to be determined were x_0, y_0, and z_0 instead of a general equation of an oblate spheroid: Suppose we have the complete equation (with parameters already determined), and the origin and the orientation relative to some arbitrary standard coordinate system, of each different realization of all the datums. Further suppose we do not know the name of each. For example, NAD83(CORS94) may be called "1" and WGS84 (G730) perhaps "2". So they are all jumbled up. Is it possible to sort them into different groups so that each group consists of the different realizations of the same datum?

References:

1. ARSITECH "Constants for Reference Ellipsoids used for Datum Transformations" http://www.arsitech.com/mapping/geodetic_datum/
• In case no-one here can answer, i've posted the question over at surveyorconnect.com – Martin F Dec 14 '13 at 1:25
• I do not understand the distinction you are making between those two equations: they are essentially the same, differing only in how the semiminor axis is parameterized. – whuber Dec 14 '13 at 21:19
• @whuber I am assuming that if I fit equation (2) to the surveyed points used for NAD27, SemiMajorAxis will not come out as 6,378,206.4 . Equation 1 is for 3 parameter fitting while equation 2 is for 5 parameter fitting. – user24397 Dec 14 '13 at 22:45