Use your pinky finger to apprehend the sky dome. Imagine yourself at sea, out of sight of land, on a calm day. Keeping your arm extended, place your pinky-tip on the horizon due east, raise your arm directly overhead. The average sized pinky-tip will have spanned 90 of its lengths. The distance measured from the horizon to directly overhead, the zenith, is 90 degrees of sky dome, about one pinky-width per degree, one-fourth of the entire 360 degrees of sky around your spot on the globe.
The apparent width of the sun disk from earth covers 1/2 degree of sky dome. The disk center point moves 15 degrees per hour (360/24 = 15). Using these facts to estimate time to sunset is relatively straightforward. Estimating time to dawn from the sky is more difficult. This graphic, “Twilight-dawn subcategories,” is a way to grasping what happens. Your position on the earth globe affects the experience. For example, at northern latitudes above 60°34′ summer nights never become darker than civil twilight because the sun’s midpoint never drops lower than 6 degrees below the horizon. Civil twilight lasts all night long summer times in parts of Sweden and Finland.
The date-time stamp on the first photograph of this series is 6:46:23 am, Cocoa Beach sunrise for February 1st was 7:09:40, 00:23:17, 23.283 minutes in decimal notation, later. This duration divided by 60 minutes in an hour and multiplied by the sun’s apparent velocity across the sky (15 degrees per hour) and minus the .25 degree between sun’s center and disk edge, gives the sun’s center as 5.57 degrees below the horizon: this is a photograph of the sky a minute or so after the sun passed civil dawn into civil twilight. I am not more exact because this calculation does not account the deviation of the sun path from due east at this latitude, lengthening civil twilight duration by almost a minute.
The following photograph is time-stamped 7:05:06, 4.567 minutes until sunrise, sun center is just below the horizon, setting the dark clouds of the previous photograph fleetingly on fire.
Sunrise has passed in the following photographs, obscured by clouds and making for a great light show. Enjoy!!
“Dawn” Wikipedia page, the graphic “Twilight-dawn subcategories,” and the descriptions of subcategories came from this page.