I have a map document in ArcMap which I want to convert to using Space oblique mercator projection, but I am not sure if ArcMap supports it.
Any hints on how to achieve this?
According to this addendum (PDF) to the documentation, the PROJ.4 library supports a "LANDSAT" projection which is "for use with LANDSAT satellite data and is a limited form of the more general Space Oblique Mercator projection". It is quite specific to Landsat, as the expected parameters include the satellite number and the path number (since the orbits periodically repeat the same path).
So, if there is no way to reproject your data in ArcMap (I don't know), you might at least be able to achieve it with PROJ.4's
The catch is that even this may not be useful if you need a space oblique projection appropriate for some other non-Landsat satellite or path. A generic form of this projection would be useful.
(Incidentally, thanks for bringing this projection to my attention. I had never heard of it before, but having spent some time learning about satellite ground path mapping earlier this year, it's quite interesting.)