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Most GOTO mounts can be externally programmed as well. So as long as you know the location, direction of movement and rate of movement you can program your mount to track it.
A lot of GOTOs can find satellites, asteroids, comets etc which do not conform to normal celestial mechanics.
The issues between Alt/Az and Eq (GEM or Wedged forks) mounts relate mostly around long exposure photography and what is termed field rotation.
Both though can do a great job of finding stuff in the sky for visual use.
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