A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robin Stuart
Date: 2017 Sep 26, 05:38 -0700
You wrote: “the Observer should always be south of N17° in order to see Gacrux”. But Gacrux in the northernmost star in the cross and you really need to see Acrux to be claim you can see the cross asterism.
You also wrote: “between S57° and N17° an observer can sight the Southern Cross at night with naked eyes any time during the year.” I don’t agree. The band is narrower than that.
To understand the essence of the problem let’s simplify your question and just focus on seeing Acrux when the Sun is below the horizon. We’ll take it that night falls instantaneously when the centre of the Sun is geometrically on the horizon. The worst time to see Acrux will be when it and the Sun have the same Right Ascension. This occurs at around 30 September and Acrux then culminates at local noon. For an observer on the equator on that date the Sun and Acrux set at the same time. Go a bit to the north and Acrux sets before and rises after the Sun. It’s never above the horizon when the Sun is below. I would sad say that the (geometric) band of visibility for Acrux is 0° and 67°S.
So let’s check. Using MICA I calculated the rise and set times for the Sun and Acrux on 30 September, 2017 at the position 5°N 0°E which is inside the band you identified.
Sun 05:48 17:52
Acrux 06:26 17:14
On that day the Acrux is only above the horizon during the hours of daylight,