This Demonstration shows the hours of daylight for a given latitude and the night and daylight halves of the globe for a given date and time.
The hours of daylight are calculated as the center of the sun's disk passes the horizon and its altitude is zero.
Snapshot 1: always 12 hours of daylight at the Equator
Snapshot 2: up to 24 hours of daylight above the Arctic Circle
Snapshot 3: some days, 0 hours of daylight below the Antarctic Circle
The world map is a resized version of the one developed by the NOAA. 
The sunset and sunrise definitions are taken from 
 "Marine Geology & Geophysics." National Geophysical Data Center. (Jun 21, 2011). www.ngdc.noaa.gov/mgg/image/2minrelief.html.
 Paul Schlyter, "How to compute rise/set times and altitude above horizon", Stockholm, Sweden
Wolfram Demonstrations Project
Published: January 23 2012