# For a non-geocentric ellipsoid, how does the Lat/Long/Ell Ht & semi-major axis & flattening implicitly define the centre of the ellipsoid?

For example if we compare the AGD84 (Australian Geodetic Datum) with GDA94 (Geocentric Datum Australia), the centre of the AGD Datum is 200 metres different to GDA, because it is a best fit to the geoid.

But how is this difference realised (implicitly) given only the Lat/Long/ Ellipsoidal Height of a Point (Johnstone), the semi-major axis (a) and the flattening (f)? I realise that (a) is different by 23 metres, but it is the angle between the 2 datums that makes the most difference, this is what I am trying to get a handle on.

Asking another way, how could I calc the ECEF coords for the centre of the AGD, to see how different it is to GDA?

Asking yet another way, how to determine the shift & angles between the axes of of AGD & GDA?

I already have the GDA manual - http://www.icsm.gov.au/gda/gdatm/gdav2.3.pdf and am working through writing C++ code for this. I also understand how AGD is not very consistent, so a conversion between the 2 datums requires the use of a model, it is just that I am trying to truly understand the mathematical difference between the two.

Sorry for the particularly nerdy question, & thanks in advance for any answers.