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Day and Night - Mercator Projection

Thinking about the Earth as a sphere in space, illuminated by the Sun... The boundary between day and night - all places experiencing dawn/dusk - looks like a circle around the sphere (try to imagine it). If this same night/day boundary was drawn on a 'standard' 2D map of the Earth (the Mercator projection, as commonly viewed online or in an atlas), what would the shape of that boundary be? Try to make a prediction. Then use the app below to check... (Instructions are below.)
On the right A sphere representing the Earth. Day/night regions are shown, with the boundary between these in purple. The North pole is directly up; the South pole directly down. Drag the pink/purple points and watch how the corresponding points on the map move. The buttons/sliders on the left
  • 'Fraction of year': 0/0.5/1 are the December/June solstices; 0.25/0.75 are the March/September equinoxes.
  • 'Fraction of day': 0/1 are midnight GMT; 0.5 is midday GMT.
  • Show/hide the regions of day/night on the map using the button.
  • With a specific fraction of year and fraction of day set, click the 'draw boundary of night/day' button to draw the boundary. You can stop this, change the fractions, and draw a different boundary, to compare.