Are the equatorial and alt-azimuth coordinate systems the same, except for the way they are aligned, geometrically? I mean, I know that RA is in hours while Az is in degrees, but if I were to somehow rig an Alt-Az mount so that its base was aligned with the celestial equator rather than the ground*, could it function much like an equatorial mount?
And if this is the case, why are equatorial mounts more expensive that alt-az mounts of comparable stability? Does it have to do with the need for a counterweight and all that?
*Purely hypothetical. Not something I'm planning on doing.