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Why is the size of the AGD-GDA vector calculated from the geodetic coordinates, different from that calculated from the grid coordinates?

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Why is the size of the AGD-GDA vector calculated from the geodetic coordinates, different from that calculated from the grid coordinates?

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When a position is transformed from AGD to GDA94 the magnitude of the apparent difference in position can be calculated from the difference in the original and transformed latitude and longitude. This is done by converting the difference in latitude and longitude to metres and using trigonometry to calculate the distance. If the AGD latitude & longitude is converted to AMG and the transformed position is converted from GDA94 to MGA94; the AMG and MGA coordinates are differenced and used to calculate a vector, it may be significantly different to the vector calculated from the latitude & longitude. This is because the two grid systems use different ellipsoids and this directly affects the meridian distance used in the calculation of the grid coordinates. This difference is most significant near the zone boundary and increases as the location moves away from the equator, being about 15 metres at 40 latitude. The grid differences shown in the spreadsheet of Chapter 7 in the GDA Technical

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