[GIS] Converting from different projections to WGS84 Web Mercator Auxillary Sphere

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I have multiple datasets in my ArcGIS, each having different map projections. All of them are vectors. Some are using Sphere Mercator, others using WGS84. I cannot perform the reprojection function in ArcGIS as I do not have the formula for geographic transformation. I am stuck and cannot proceed to make a map due to this issue.

Best Answer

The problem is almost certainly with the "Sphere_Mercator" data. This projected coordinate reference system (CRS) is using a sphere-based geographic CRS. ArcGIS doesn't have any predefined geographic/datum transformations that convert to or from a sphere.

The data may have been built on the sphere, or it might have been built on WGS 1984 and then projected to the Sphere_Mercator CRS.

If you have reference data in WGS 1984 that you can compare the Sphere_Mercator data to, add both to ArcMap. Set the data frame to use the WGS 1984-based CRS. Does the Sphere_Mercator line up correctly? If so, unproject it to "Sphere" GeoCRS using the Project Tool, then use the Define Projection tool to change the CRS to WGS 1984. Then use the Project Tool to convert it to EPSG:3857.

If it doesn't line up, try adding a transformation in ArcMap. 

1. Open data frame properties Click the Transformations tab on the
Coordinate System tab. 
2. In the top box, select "GCS_Sphere". The "Into:" box should list WGS 1984. 
3. Click the New button. In the new dialog, set the transformation method to Geocentric_Translations. Leave the transformation parameters set to zeroes.  
4. OK all dialogs and see if the data lines up better. 
5. If it does, right click the layer and select Data, Export Data. Write out a new dataset using the data frame's coordinate reference system.

Disclosure: I work for Esri.

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