According to National Geographic, predictions of its orbital trajectory indicate that if it survives its close approach to the Sun, the comet will be brightest in the sky in November 28, 2013 as it moves away from the Sun. It will be visible during December after sunset and in the morning sky before sunrise. New Scientist reports that scientists at the Remanzacco Observatory say that by December 9 it should be about as bright as Polaris, the North Star, and should remain visible to the naked eye until mid-January 2014. According to Astronomy Now, the comet could become brighter than the full moon around its closest approach to the Sun.
Astronomers say that the orbit of C/2012 S1 is similar to that of the Great Comet of 1680, one of the brightest in history. Space.com reports that the Great Comet of 1680 was very bright in the sky and was visible even in daylight, throwing off a bright tail that spanned the western twilight sky. Some astronomers say that given the close orbital relationship between C/2012 S1 and the Great Comet of 1680, the objects may be the same.
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